Effects of cosmetic ingredients on growth and virulence factor expression in Staphylococcus aureus: a comparison between culture medium and in vitro skin model medium
The effect of cosmetic ingredients on growth and virulence factor expression in Staphylococcus aureus may vary between culture medium and skin. Researchers have used an in vitro skin model with human heel callus to assess bacterial survival and growth on the stratum corneum of the epidermis. Here, we reconstituted a skin model using keratin as a base (instead of callus) and compared it with brain heart infusion (BHI) medium. We investigated the effects of five cosmetic ingredients (macadamia nut oil, sodium myristoyl methyl taurate, methyl p-hydroxybenzoate, 2-phenoxyethanol, and zinc oxide) on growth and virulence factor expression in S. aureus. Interestingly, the survival pattern of S. aureus in our skin model was similar to that reported in models using callus. Upon the addition of cosmetic ingredients to BHI or skin model medium, the sensitivity of S. aureus to these cosmetic ingredients differed between the two media. Notably, after adding the two tested cosmetic ingredients, the expression level of staphylococcal enterotoxin A in S. aureus reduced significantly in skin model medium compared with that in the BHI medium. Additionally, the expression levels of other S. aureus virulence factors (RNAIII, icaA, and hlb) differed between the two media. These findings suggest that our skin model is a valuable tool for evaluating the effects of cosmetic ingredients on growth and virulence factor expression in S. aureus.
Citation: Yuya Uehara, Yuko Shimamura, Chika Takemura, Shiori Suzuki, Shuichi Masuda. Effects of cosmetic ingredients on growth and virulence factor expression in Staphylococcus aureus: a comparison between culture medium and in vitro skin model medium[J]. AIMS Microbiology, 2025, 11(1): 22-39. doi: 10.3934/microbiol.2025002
Related Papers:
[1]
Yuejiao Wang, Chenguang Cai .
Equilibrium strategies of customers and optimal inventory levels in a make-to-stock retrial queueing system. AIMS Mathematics, 2024, 9(5): 12211-12224.
doi: 10.3934/math.2024596
[2]
Zhen Wang, Liwei Liu, Yuanfu Shao, Yiqiang Q. Zhao .
Joining strategies under two kinds of games for a multiple vacations retrial queue with $ N $-policy and breakdowns. AIMS Mathematics, 2021, 6(8): 9075-9099.
doi: 10.3934/math.2021527
[3]
Bharathy Shanmugam, Mookkaiyah Chandran Saravanarajan .
Unreliable retrial queueing system with working vacation. AIMS Mathematics, 2023, 8(10): 24196-24224.
doi: 10.3934/math.20231234
[4]
Vladimir Vishnevsky, Valentina Klimenok, Olga Semenova, Minh Cong Dang .
Retrial tandem queueing system with correlated arrivals. AIMS Mathematics, 2025, 10(5): 10650-10674.
doi: 10.3934/math.2025485
[5]
S. Sundarapandiyan, S. Nandhini .
Sensitivity analysis of a non-Markovian feedback retrial queue, reneging, delayed repair with working vacation subject to server breakdown. AIMS Mathematics, 2024, 9(8): 21025-21052.
doi: 10.3934/math.20241022
[6]
Shaojun Lan, Yinghui Tang .
An unreliable discrete-time retrial queue with probabilistic preemptive priority, balking customers and replacements of repair times. AIMS Mathematics, 2020, 5(5): 4322-4344.
doi: 10.3934/math.2020276
[7]
Ciro D'Apice, Alexander Dudin, Sergei Dudin, Rosanna Manzo .
Study of a semi-open queueing network with hysteresis control of service regimes. AIMS Mathematics, 2025, 10(2): 3095-3123.
doi: 10.3934/math.2025144
[8]
Linhong Li, Wei Xu, Zhen Wang, Liwei Liu .
Improving efficiency of the queueing system with two types of customers by service decomposition. AIMS Mathematics, 2023, 8(11): 25382-25408.
doi: 10.3934/math.20231295
[9]
Avijit Duary, Md. Al-Amin Khan, Sayan Pani, Ali Akbar Shaikh, Ibrahim M. Hezam, Adel Fahad Alrasheedi, Jeonghwan Gwak .
Inventory model with nonlinear price-dependent demand for non-instantaneous decaying items via advance payment and installment facility. AIMS Mathematics, 2022, 7(11): 19794-19821.
doi: 10.3934/math.20221085
[10]
Ciro D'Apice, Alexander Dudin, Sergei Dudin, Rosanna Manzo .
Analysis of a multi-server retrial queue with a varying finite number of sources. AIMS Mathematics, 2024, 9(12): 33365-33385.
doi: 10.3934/math.20241592
Abstract
The effect of cosmetic ingredients on growth and virulence factor expression in Staphylococcus aureus may vary between culture medium and skin. Researchers have used an in vitro skin model with human heel callus to assess bacterial survival and growth on the stratum corneum of the epidermis. Here, we reconstituted a skin model using keratin as a base (instead of callus) and compared it with brain heart infusion (BHI) medium. We investigated the effects of five cosmetic ingredients (macadamia nut oil, sodium myristoyl methyl taurate, methyl p-hydroxybenzoate, 2-phenoxyethanol, and zinc oxide) on growth and virulence factor expression in S. aureus. Interestingly, the survival pattern of S. aureus in our skin model was similar to that reported in models using callus. Upon the addition of cosmetic ingredients to BHI or skin model medium, the sensitivity of S. aureus to these cosmetic ingredients differed between the two media. Notably, after adding the two tested cosmetic ingredients, the expression level of staphylococcal enterotoxin A in S. aureus reduced significantly in skin model medium compared with that in the BHI medium. Additionally, the expression levels of other S. aureus virulence factors (RNAIII, icaA, and hlb) differed between the two media. These findings suggest that our skin model is a valuable tool for evaluating the effects of cosmetic ingredients on growth and virulence factor expression in S. aureus.
1.
Introduction
In stochastic queueing-inventory(SQI) models, many authors assumed that the chosen item could not be delivered immediately at the initial period, because the customered item not only requires some random time to deliver it also cause the queue formation in front of the system. For example, in a mobile shop, the sales man do not sale the product directly without demonstrating the features of an item and this demonstration took some random time and cause the queue formation. Such situations allow us to develop the SQI system in the area of service facility. Initially, service facility was introduced by Melikov [31] and Sigman and Simchi-Levi [37]. Berman et al.[9] discussed the inventory management system(IMS) along with service channel assuming one item per service, deterministic customer and service rates, during the stock out period only queues can occur and determined the minimum total cost using optimal order quantity. Berman and Kim [10] determined the SQI problem with service facility in which arrival and service times follow Poisson and exponential distributions, including average inter-arrival time is larger than average service time. He et al. [18] analyzed the related model in the production inventory system(PIS) which is generated by a single machine for a batch of size one.
Berman and Sapna [11] analyzed inventory control problem(ICP) with service channel assuming one item per service, Poisson arrival, arbitrary service times, finite capacity and zero lead times. They determined the minimized total cost using the feasible order quantity under the specified cost structure. Schwarz et al. [36] examined the SQI system with the Poisson arrival, exponential service time and randomized ordering polices(ROP). Paul Manual et al.[30] considered the perishable SQI system with service facility(SF) and retrial customers under the assumption of Markovian arrival process(MAP), phase-type(PH) service distribution and life time, lead time are follows an exponential distribution.
Lopez-Herrero [29] concentrated on measuring the waiting time, reorder time and time of a pending demand for the finite retrial group. Artalejo et al. [7] considered the retrial QIS in which the any arriving customer who knows that the server is busy, immediately they join into the retrial group. They studied the waiting time of a retrial customers using Laplace-Stieltjes transform. Amirthakodi and Sivakumar [2] discussed the single server SQI system containing a finite queue. They assumed that the unsatisfied customer may join into the orbit in which the customer who can attempt the service directly if the server is free and studied the waiting time distribution for both queue and retrial queues. Yadavalli et al. [41] analyzed the multi server inventory system of a finite queues and discussed the expectation and variance of the waiting time on the impact of parameters. Recently, Jeganathan and Abdul Reiyas [24] investigated the IMS with parallel heterogeneous servers having vacations and they discussed the waiting time for both queues.
Threshold based service rates also play a sufficient role in the SQI to diminish the waiting time of customer in the queue. Harris [17] studied the queueing systems in which the they assumed that the service rates are stochastic and state-dependent. Lakshmanan et al. [27] discussed the SQI system under the threshold based priority service of N-policy. Gautam Choudhury et al. [13] and Tae-Sung Kim et al. [25] discussed the threshold based services in their queueing models. Elango [14] has discussed the perishable inventory system(PIS) with exponential service time and zero lead time. They assumed that the service parameter dependent on the number of customers in the waiting hall Kuo-Hsiung Wang and Keng-Yuan Tai [40] introduced the concept of additional servers, that is the number of service channel has been changed depending upon size of the queue. The related work has been generalized in [19]. Martin Reiser [35] analyzed the queue-dependent server in closed networks by applying mean value analysis and convolution method. In SQI system, Jeganathan et al. [22] studied three heterogeneous servers, including one with a flexible server. Subsequently, many authors proposed the multi-server and retrial models to reduce the congestion. A queue with retrial facility has been discussed in [15,16,23,26,39]. For more description on multi server retrial queues one may refer [5,8,12,32] whereas in SQI system with multi sever service facility has been considered by [3,41]. Similarly, the references [14,20,34,42] gave a brief idea about PIS.
There are some gaps in SQI literature, one can realize that, although a multi-server SQI system will reduce the waiting time of a customer for an unit item per service, in real life; there are many single server SQI system and we do not extend into multi-server models for example, in a juice shop, they provide the juice to the customer on first come first service (FCFS) basis because they had only single server and do not extend into multi-server model due to economic and space problems.
All the above mentioned models, the corresponding authors assumed that the system had a single/multi server and exponential service time which is homogeneous(uniform). In real life experience, SQI system need not have a homogeneous service rate for example, in a restaurant, one can observe that the time spent by the server varies from one customer to another customer and this may happens in supermarket, textiles shop etc. Nowadays, we are living in a congested emerging society, homogeneous service rate is not enough to satisfy the customer in concerning the queues because, by nature, we have three categories of customer: 1) Balking 2) Reneging and 3) Jockeying. In order to satisfy these types of customers, one should improve the service facility.
Stochastic queueing-inventory modeling has a widespread attention in the area of service facility along with infinite retrial group. With the emerging society, customers who do not have adequate time to wait in the queue. There are three categories of people on the basis of their behavior: 1) some of them get appointment previously to purchase the items, 2) half of the remaining people are ready to wait in the queue until they get a service and 3) another set of people will also prefer to wait in the queue, but they become impatient after some random time. As a business owner, one has to plan to attract the three categories of peoples by reducing the waiting time. One can experience this kind of situations in vegetable market, super market, mobile shop, textile show room, service center, jewel shop etc.
In this competitive economic world, customer satisfaction is a key factor to earn more profits; if they are not satisfied, then they will move to another firm. So the waiting time is one of the main determinants to satisfy the customer. Consider the real-life situation, during lunchtime, a customer wants to have lunch used to visit a restaurant. On seeing the queue, they will decide to wait in the queue. After some random time, they realize that the server is working without changing the service speed and the queue length is long, so they become impatient and immediately move to another one. This real-life situation motivates us to bring this mathematical model in order to carry out the waiting time issues and customer lost due to impatient.
In many situation, there is a necessity that the server should increase the service speed to reduce the waiting time of a customer, since a customer may become impatient due to the increase of waiting time and it causes the customer lost. It is generally perceived that the waiting time plays a significant role in the stochastic modeling of queueing-inventory system(SMQIS). A customer satisfaction not only depends on the fair items and cost but also on the waiting time. For example, consider a dam; if the level of water in the dam is high, the speed of releasing water becomes high due to heavy pressure and vice-versa.
The queue-dependent service rate will give the more advantages for both the inventory management and the customer. It mainly reduce the waiting time of a customer in the queue and the impatiences of a waiting customer. Also, the customer lost, balking, reneging are to be decreased. On the other hand, the management receives a more number of customer in the system, this leads a more sale and profit of the firm. We conclude that if the waiting time is less, then there will be increase in the arrival, for this purpose speed of the server should be increased according to the length of queue.
On seeking the solution to fill such a gap in the SQI system, very few papers are discussed in the single server SQI literature. In this context, Jeganathan [21] has filled the gap partially using the flexible server under the threshold based level L for the queue length. They defined only two non-homogeneous service rates before L and after L. However, we can observe in real life, consider a footwear shop, for every customer the service time must be changed depending upon the customers waiting in the queue.
We extend this paper to the multi-threshold level; that is, the service rate is changed depend upon the number of customers in the queue. On utilizing this discussion, we present a model: single server queueing-inventory system(QIS) with queue-dependent service rates. In addition, any customer finds that the queue size is M, they may enter into the orbit of infinite size under the Bernoulli trials, and they can compete only through the queue. Hence, we propose a new model as a single server perishable SQI system with queue-dependent service rates and an infinite orbit having (s,Q) ordering policy. In the rest of this paper, we present a description in section 2, methods of analysis in section 3, waiting time analysis in section 4, economic analysis in section 5 and conclusion in section 6.
This model explores a performance of single server service channel in the perishable QIS. This system consists a finite waiting hall(queue) whose capacity is denoted as M, inventory of S items for sales and a single server. The server is always busy whenever the current inventory level and number of customers in the queue are positive. Otherwise the server become free. A customer approaches the QIS to purchase their inventory. Suppose any arriving customer finds that the server is busy, they must wait in the queue. The customer approaches QIS for the first time, say primary customer with an intensity λp and the primary customer arrival processes follows Poisson process.
This system provides the one more facility to attract their customer in order to avoid the customer lost, called the Orbit(virtual waiting place of infinite capacity). Whenever the arriving customer sees that the queue is fully occupied, they enter into an orbit with the probability p or leave the system with its complement 1−p. The customer in an orbit, called orbital customer who finds that the queue size is less than M, they immediately enter into the queue with an intensity λr under the classical retrial policy. Otherwise they repeatedly tries until get success. This process is known as retrial process. For retrial customer(a customer approaches QIS for the second time), the time interval between any two successive arrivals considered as exponential.
This system provides a well deserved service to their customer through a well experienced server. The server will change the speed of service according to the current queue size in order to reduce the customer waiting time. This service process follows an exponential process with an intensity μw where 1≤w≤M. The customer receives their inventory only when the time of service completion. Since the service rate is dependent on the queue size, it considered as heterogeneous service rate(not homogeneous).
Further, this system also concentrates on two more things, called as (1) ordering policy and (2) perishable items. Here, the current inventory level of the system getting decreased by the two following process: (ⅰ) service process and (ⅱ) perishable process. Such processes allow us to make a reorder process. This takes place a reorder of Q(=S−s) items whenever the current inventory level falls into the fixed s. This policy is known as (s,Q) ordering policy. The reorder process follows an exponential with an intensity β.
Generally, not all the items are being perfect until they sold to the customer. The system also consists this natural defectiveness of an item which could be happened by manufacturing defect, warranty expires, damage on handling items, etc., with a classical perishable policy(any one of S items getting perished) with an intensity γ and this perishable process also follows an exponential process. Stability of the system are to be discussed by the Neuts MGA and the waiting time distribution of both customers are to be derived with Laplace-Stieltjes transform(LST).
Remark 2.1.1) For the numerical calculations μw can be defined as μw=μwα, where 0≤α≤1.
2) If α=0, then the model deduced to homogeneous service rate model.
3) If α∈(0,1], then the model deduced to non-homogeneous service rate model.
2.3. Matrix building
Let P1(t),P2(t) and W(t) are the random variables and represent orbit size, present stock level(PSL), and queue size respectively. From the assumptions developed on the birth and death process of a SQIS in the descriptive analysis (subsection 2.2) forms a stochastic process {P(t),t≥0}={(P1(t),P2(t),W(t)),t≥0} at time t and it is also said to be a continuous-time stochastic process(CTSP) with the state space D such that
D={(u,v,w):u=0,1,⋯;v=0,1,⋯,S;w=0,1,⋯,M}.
Theorem 2.3.1.In a quasi birth and death process(QBD), the infinitesimal generator matrix, P, with discrete state space D, and the CTSP {P(t),t≥0}, is defined by
Proof: Using the assumptions of proposed model (subsection (2.2)), first consider P01 matrix which contains sub-matrix P0 of dimension (M+1) along the diagonal whose entries are the transition rate of primary arrival enter into the orbit under the probability p as follows:
(u,v,M)pλp→(u+1,v,M),u=0,1,2,⋯,;v=0,1,2,⋯S,
(2.7)
from Eq (2.7), the Eqs (2.2) and (2.3) are obtained.
Then the matrices below main diagonal, Pu0, where u=1,2,⋯, has the sub-matrix Pu of dimension (M+1) whose entries are the transition rate of retrial arrival enter into the waiting hall with classical retrial policy as follows:
by the Eq (2.8), the Eqs (2.4) and (2.5) are obtained. Then the diagonal matrices Puu where u=0,1,2,⋯ of dimension (M+1)(S+1) whose elements are of the transition rates as follows:
(1) β denotes the rate of reorder transition which follows the (s,Q) ordering policy,
(5) The diagonal element of the Puu matrices are filled by the sum of all the entries in the corresponding rows of Puu,Pu0 and P01 with a negative sign in order to satisfy the sum of all entries in each row of a matrix P yield zero.
From (1)-(5), the Eq (2.6) is achieved. Hence all the sub-matrices obtained through the respective transitions give the infinitesimal generator matrix P as in Eq (2.1).
Remark 2.2.From the normalizing condition of the infinitesimal generator matrix P, that is, Φ=(Φ(0),Φ(1),…,) preserves
ΦP=0,
(2.13a)
Φe=1,
(2.13b)
and one can obtain the solution of Φ's either using Direct truncation method or MGA. The partition of Φ(u) is defined as
Φ(u)=(Φ(u,0),Φ(u,1),…,Φ(u,S)),u≥0,
Φ(u,v)=(Φ(u,v,0),Φ(u,v,1),…,Φ(u,v,M)),u≥0;0≤v≤S.
3.
Methods of analysis
3.1. Direct truncation method (DTM)
This method is used to evaluate the stationary probability vector Φ of the CTSP, {P(t),t≥0}, by truncating the orbit size as the finite instead of infinite size. Suppose K be the size of orbit in the truncation process, then the arrival a of customer to orbit upon the size K as considered as lost. However, choosing a sufficiently larger K, one can reduce the customer lost. To get the smaller loss probability for this truncation system, we follow the below Theorem (3.1.1).
Theorem 3.1.1.Suppose K be the cut-off point for this DTM. Then the modified generator matrix ˉP and the steady state probability vector Φ(K), generates the truncation point K∗, if
max0≤u≤K∗−1‖Φ(u+1)−Φ(u)‖∞<ϵ,
(3.1)
where ϵ is an infinitesimal quantity.
Proof: The modified generator matrix for this DTM ˉP is obtained from the Eq (2.1) as follows:
Now, the corresponding steady state probability vector Φ can be partitioned into
Φ=(Φ(0),Φ(1),⋯,Φ(K)).
(3.3)
These Φ's can be determined by exploiting the significant structure of the coefficient matrices. We have several method to solve this system referring Stewart [38] such as Gauss-Seidel iterative process and agammaegate / dis-agammaegate iterative algorithm. But there is no proper algorithm to choose K, one may proceed the iterative process by choosing K=1 and increase gradually until there is no significant change happen in the elements of Φ. At such stage, the corresponding K considered as a K∗, be the truncation point and it obviously satisfies the norm as in Eq (3.1).
3.2. Matrix geometric approximation (MGA)
3.2.1. Steady state behaviour
This is also a method to find the stationary probability vector Φ of the SQIS, {P(t),t≥0} by assuming that whenever there exist almost N customer in the orbit, they follow the classical retrial policy to enter into the waiting hall. Suppose the orbit size exceeds N, they follow the constant retrial policy to go to the waiting hall. This assumption is called MGA and N is said to be the truncation point of MGA process which is introduced by Neuts [33]. To find the steady state of the considered system {P(t),t≥0}, we assume PU0=PN0 and PUU=PNN for all U≥N in Eq (2.1). The quasi birth and death process of this system have a repeating structure after a stage N which is sufficiently large, in particular, if the number of customer in the orbit exceeds N, then the retrial rate of customer remains unchanged. Then the modified generator matrix for the MGA having the below structure:
On solving the set of Eqs (3.9a) and (3.9b), we get an Eq (3.5) and using Eqs (3.5) and (3.9c), the equation (3.6) is obtained. The Eq (3.8b) produces an Eq (3.7). Hence, ϕ(Q), is obtained by solving (3.6) and (3.7).
Note: The partition of ϕ(v) is defined as
ϕ(v)=(ϕ(v,0),ϕ(v,1),…,ϕ(v,M)),0≤v≤S.
Theorem 3.2.2.The stability condition of the system at truncation point N is given by
k1pλp<k2λr
(3.10)
where k1=S∑v=0ϕ(v,M) and k2=S∑v=0M∑w=1ϕ(v,w)N.
Proof: By Neuts [33] stability condition and the matrices P01 and PN0, we have
By the partition of ϕ(v) and exploiting P0 and PN,
S∑v=0ϕ(v,M)pλp<S∑v=0M∑w=1ϕ(v,w)Nλr.
Hence, the Eq (3.10) is obtained as desired.
Remark 3.1.(1) Using (3.10), we get, k1pλpk2λr<1.
(2) If k1k2=k(say), then λpλr<1kp.
Remark 3.2.The most interesting factor in the stability condition is that it is independent of μ and β.
Remark 3.3.Using Theorems (3.2.1) and (3.2.2), the rate matrix P in Eq (2.1) has Markov process {(P(t),t≥0} with the state space D is regular. Hence the limiting probability distribution
Proof: The sub-vector (Φ(0),Φ(1),…,Φ(N−1)) and the block partitioned matrix of P satisfies the following relation
Φ(u)Puu+Φ(u+1)Pu0=0,u=0,
(3.18a)
Φ(u−1)P01+Φ(u)Puu+Φ(u+1)P(u+1)0=0,1≤u≤N−1.
(3.18b)
Using equations (3.18a) and (3.18b) recursively, we obtain Φ(0)=Φ(1)P10(−P′0)−1withP′0 = P00,Φ(1)=Φ(2)P20(−P′1)−1withP′1 = (P11+P10(−P′0)−1P01), Φ(2)=Φ(3)P30(−P′2)−1withP′2 = (P22+P20(−P′1)−1P01) and so on up to N times.
Hence, we conclude that,
Φ(u)=Φ(u+1)P(u+1)0(−P′u)−1,0≤u≤N−1
(3.19)
where
P′u={Puu,u=0(Puu−Pu0(−P′u−1)−1P01),1≤u≤N.
To find the sub-vector (Φ(N),Φ(N+1),Φ(N+2)…), we apply block Gaussian elimination method. The sub-vector (Φ(N),Φ(N+1),Φ(N+2)…) can be determined by
(Φ(N),Φ(N+1),Φ(N+2)…)(P′NP01PN0PNNP01⋱⋱⋱⋱⋱)=0.
(3.20)
Assume,
σ=∞∑u=NΦ(u)e
(3.21)
andX(u)=σ−1Φ(N+u),u≥0.
(3.22)
From (3.20), we get
Φ(N)P′N+Φ(N+1)PN0=0.
(3.23)
Applying the Eq (3.22) in (3.23) and (3.14) along with ∞∑i=0X(i)e = 1, the Eqs (3.17a) and (3.17b) are obtained. The unique solution of X(0) is found by solving the Eqs (3.17a) and (3.17b), and substituting it in (3.22), we get
Φ(u)=σX(0)R(u−N),u≥N
(3.24)
Again by (3.19) and (3.22),
Φ(u)=σX(0)N∏j=uPj0{−{−δ0jI+ˉδ0jP′j−1}},0≤u≤N−1
(3.25)
Therefore, combining (3.24) and (3.25), the Eq (3.15) is obtained as desired. And σ is found by applying the vector Φ in the Eq (2.13b).
Corollary 3.2.1.The mean inventory level(MIL) of the SQIS in the steady state, using the vector Φ along with positive inventory is defined by
MIL=∞∑u=0S∑v=1M∑w=0vΦ(u,v,w).
(3.26)
Corollary 3.2.2.Suppose there are (s+1) items in the PSL, due to either a service can be completed or an item may be perished, then the PSL dropped into the level s, we start the reorder process. The mean reorder rate(MRR) of the SQIS in the steady state, using the vector Φ is defined by
Corollary 3.2.3.The PSL may be diminished by perishing items. The mean perishable rate(MPR) of the SQIS in the steady state, using the vector Φ is defined by
MPR=∞∑u=0S∑v=1M∑w=0vγΦ(u,v,w).
(3.28)
Corollary 3.2.4.In the waiting hall, there should be at least one customer has to wait for getting a service and the PSL need not be positive. The mean customer in the queue(MCQ) of the SQIS in the steady state, using the vector Φ is defined by
MCQ=∞∑u=0S∑v=0M∑w=1wΦ(u,v,w).
(3.29)
Corollary 3.2.5.In the orbit, there should be at least one customer has to wait for entering into the waiting hall. The mean customer in the orbit(MCO) of the SQIS in steady state, using the vector Φ is defined by
MCO=∞∑u=1S∑v=0M∑w=0uΦ(u,v,w).
(3.30)
Corollary 3.2.6.Suppose the waiting hall is full, the new arrival has the choice to take the decision to become lost. The expected primary customer lost in the queue(EPL) of the SQIS in the steady state, using the vector Φ is defined by
EPL=∞∑u=0S∑v=0(1−p)λpΦ(u,v,M).
(3.31)
Corollary 3.2.7.The possible chances of an orbital customer for trying to enter into the waiting hall, called overall rate of retrial(ORR). The ORR of SQIS in steady state, using the vector Φ is defined by
ORR=∞∑u=1S∑v=0M∑w=0uλrΦ(u,v,w).
(3.32)
Corollary 3.2.8.The possible successful chances of an orbital customer to enter into the waiting hall, called successful rate of retrial(SRR). The SRR of SQIS in the steady state, using the vector Φ is defined by
SRR=∞∑u=1S∑v=0M−1∑w=0uλrΦ(u,v,w).
(3.33)
Corollary 3.2.9.The possible chances of any customer to enter into the waiting hall, say expected customer enter into queue(ECEQ). The ECEQ of SQIS in the steady state, using the vector Φ is defined by
Corollary 3.2.10.The expectation of a customer enter into the orbit, say ECEO. The ECEO of SQIS in the steady state, using the vector Φ is defined by
ECEO=∞∑u=0S∑v=0pλpΦ(u,v,M).
(3.35)
Corollary 3.2.11.The fraction of successful rate of retrial(FSSR) is defined by the ratio of ORR and SRR and is given by
FSSR=SRRORR.
4.
Waiting time analysis
The time interval between an epoch of arrival of a customer enter into the waiting hall and the instant at which their time of service completion, called waiting time(WT). We discuss the WT of a customer in the queue as well as orbit individually using LST. By nature, we restrict the orbit size to finite for finding the waiting time of the orbital customer as follows:
D1={(u,v,w):u=0,1,⋯,L;v=0,1,⋯,S;w=0,1,⋯,M}.
We represent Wp and Wo are the continuous time random variables to denote the WT of a customer in queue and orbit.
4.1. WT of a customer in queue
To find a WT of a customer in the queue, the state space D1 is redefined and is given by, D2={(u,v,w):u=0,1,⋯,L;v=0,1,⋯,S;w=1,2,⋯,M}
Theorem 4.1.1.The probability of a customer does not wait into the queue is considered as
P{Wp=0}=1−L∑u=0S∑v=0M−1∑w=0Φ(u,v,w)
(4.1)
Proof: Since the sum of probability of zero and positive waiting time is 1, we have
P{Wp=0}+P{Wp>0}=1
(4.2)
Clearly, the probability of positive waiting time of customer in the queue can be determined as
P{Wp>0}=L∑u=0S∑v=0M−1∑w=0Φ(u,v,w)
(4.3)
The Eq (4.3) can be found using Theorem (3.2.4) and substitute in equation (4.2) we get the stated result as desired.
To enable WT distribution of Wp, we shall define some complementary variables. Suppose that the QIS is at state (u,v,w), w>0 at an arbitrary time t,
1). Wp(u,v,w) be the time until chosen customer become satisfied.
2). LST of Wp(u,v,w) is W∗p(u,v,w)(x) and we denote Wp by W∗p(x).
3). W∗p(x)=E[exWP] LST of unconditional waiting time(UWT).
4). W∗p(u,v,w)(x)=E[exWP(u,v,w)] LST of conditional waiting time(CWT).
Theorem 4.1.2.The LST {W∗p(u,v,w)(x),(u,v,w)∈Dc2 where Dc2=D2∪{c}} satisfy the following system
Zp(x)W∗p(x)=−μwe(u,v,w),0≤u≤L,1≤v≤S,1≤w≤M
(4.4)
Zp(x)=(A−xI), the matrix A is obtained from P by removing the following state (u,v,0),0≤u≤K,1≤v≤S and {c} be the absorbing state and the absorption occurs if the primary customer is satisfied.
Proof: To obtain the CWT, we apply first step analysis as follows:
With reference to equations (4.9) and (4.10), one can examine the unknowns E[Wn+1p(u,v,w)] in terms of moments having one order less. On setting n=0, we attain the desired moments of particular order in an algorithmic way.
Theorem 4.1.4.The LST of UWT of a customer in the queue is given by
Proof: Using PASTA(Poisson arrival see time averages) property, one can obtain the LST of Wp as follows:
W∗p(x)=Φ(u)W∗p(u,v,w)(x),0≤u≤L,0≤v≤S,1≤w≤M
(4.12)
using the expression (4.12), we get the stated result. By referring Euler and Post-Widder algorithms in Abatt and Whitt [1] for the numerical inversion of (4.11), Wp is obtained.
Corollary 4.1.1.1. The nth moments of UWT, using Theorem (4.1.4), is given by
Proof: To evaluate the moments of Wp, we differentiate Theorem (4.1.4), n times and evaluate at x=0, we get the desired result which gives the nth moments of UWT in terms of the CWT of same order.
Corollary 4.1.2.The expected waiting time of a customer in the queue is defined by
E[Wp]=L∑u=0S∑v=0M−1∑w=0Φ(u,v,w)E[Wp(u,v,w+1)]
(4.14)
proof: Using equation (4.1.1) in Corollary (12), and substitute n=1, we get the desired result as in (4.14).
4.2. WT of orbital customer
To find a WT of a customer in the orbit, the state space D1 is redefined and is given by, D3={(u,v,w):u=1,⋯,L;v=0,1,⋯,S;w=0,1,⋯,M}
Theorem 4.2.1.The probability of an orbital customer does not wait into the orbit is given by
P{Wo=0}=1−b1
(4.15)
where b1=L−1∑u=1S∑v=0Φ(u,v,M)
Proof: Since the sum of probability of zero and positive waiting time is 1, we have
P{Wo=0}+P{Wo>0}=1
(4.16)
Clearly, the probability of positive WT of orbital customer can be determined as
P{Wo>0}=L−1∑u=1S∑v=0Φ(u,v,M)
(4.17)
The Eq (4.17) can be found easily using Theorem (3.2.4) and substitute in Eq (4.16) we get the stated result as desired in (4.15).
To enable the distribution of Wo, we shall define some complementary variables. Suppose that the QIS is at state (u,v,w),u>0 at an arbitrary time t,
1). Wo(u,v,w) be the time until chosen customer become satisfied.
2). LST of Wo(u,v,w) is (u,v,w)(x) and we denote Wo by W∗o(x).
3). W∗o(x)=E[exWo] LST of UWT.
4). W∗o(u,v,w)(x)=E[exWo(u,v,w)] LST of CWT.
Theorem 4.2.2.The LST {W∗o(u,v,w)(x),(u,v,w)∈Dd3 where Dd3=D3∪{d}} satisfy the following system
Zo(x)W∗o(x)=−λre(1,v,w),0≤v≤S,0≤w≤M−1.
(4.18)
Zo(x)=(B−xI), the matrix B is derived from P by deleting the following state (0,v,w),0≤v≤S,0≤w≤M and {d} be the absorbing state and the absorption appears if the orbital customer enters into the waiting hall.
Proof: To analyze the CWT, we apply first step analysis as follows:
With reference to Eqs (4.23) and (4.24), one can determine the unknowns E[Wn+1p(u,v,w)] in terms of moments of one order less. On setting n=0, we obtain the desired moments of particular order in an algorithmic way.
Theorem 4.2.4.The LST of UWT of orbital customer is given by
W∗o(x)=1−b1+b1W∗o(u+1,v,w)(x)
(4.25)
Proof: Using PASTA property, one can obtain the LS transform of Wo as follows:
W∗o(x)=Φ(i)W∗o(u,v,w)(x),1≤u≤L,0≤v≤S,0≤w≤M
(4.26)
using the expressions (4.26), we get the stated result. By considering Euler and Post-Widder algorithms in Abatt and Whitt [1] for the numerical inversion of (4.25), we obtain Wo.
Corollary 4.2.1.1. The nth moments of UWT, using Theorem (4.2.4), is given by
Proof: To evaluate the moments of Wo, we differentiate Theorem (4.2.4), n times and evaluate at x=0, we get the desired result which gives the nth moments of UWT in terms of the CWT of the same order.
Corollary 4.2.2.The expected waiting time of a orbital customer is defined by
E[Wo]=L−1∑u=0S∑v=0M∑w=0Φ(u,v,w)E[Wo(u+1,v,w)]
(4.28)
proof: Using Eq (4.27) in Corollary (4.2.1) and substitute n=1, we get the desired result as in (4.28).
5.
Economical analysis
Here, we discuss the feasibility of a proposed model through the system characteristics and sufficient economical illustrations. The expected total cost(ETC) is given by
Cpl- primary customer cost per customer at time t.
Cwp- waiting cost of a customer in the queue at time t.
Cwo- waiting cost of a customer in the orbit at time t.
To analyze numerically, we first fix the parameter as follows: S=19,s=8,λp=0.4,λr=0.002,β=0.6,α=0.06,γ=0.005,p=0.3,M=7 and μ=8 and the cost values are Ch=0.01.Cs=0.02,Cp=0.01,Cwp=0.5 and Cwo=0.4. The truncated point for the matrix geometric method is N=80.
Note: Under the behaviour of α, we can have a classification of the proposed model as follows:
1) If α=0, then the model become a single server SQI system with homogeneous service rates.
2) If 0<α<1, then this is a single server SQI system non-homogeneous service rates.
3) If α=1, then it will be a single server SQI system with linear service rates.
Example 1:
In Table 1, we discuss the local convex point on the ETC varying S and s. We observe that the minimum ETC exist in each row and column. Here, the minimum ETC in each row and column are differentiated by underlined numbers and bold numbers respectively. The intersection of underlined and bold numbers, called optimum point and indicated by (S∗,s∗) where S∗=19 is the optimum PSL and s∗=8 is the optimum reorder level and they gave a optimum total cost ETC∗=4.711953.
Table 1.
Impact of S and s focusing convex on ETC.
∙ The value of N decreases as α increases along with the increasing service rate μ.
∙ Whenever λr increases N decreases relating to the increasing service rate.
∙ Generally, if μ increases, one can observe from the Table 1, the truncation point N decreases, this SQI system become stable quickly.
∙ We can observe that, p is high, then N become significantly larger, that is they are directly proportional and highly sensitive.
∙ If β increases, then N decreases. Suppose α and β are small, then N is highly differ under μ.
∙ In Tables 2 and 3, we assure that, λr is small, N will be very larger.
∙ The appearance of truncation point become small, if we increase the α,λr and μ but p should be decreased.
Example 3:Investigation of fraction of successful rate of retrial(FSRR)
∙ From Table 4, one can observe that, although there is an increase in each λp for each μ, FSRR decreases if each α, but the very notable point is FSRR increases if α increases. Hence, α become a decision factor to increase the FSRR.
Table 4.
Impact of parameters λp,λr,γ,α and μ on FSRR.
∙ Meanwhile, there is an increase in λr, FSRR will increase for each α and μ because when we increase μ, MCQ will decrease and it cause the increase of FSRR.
∙ It is interesting to observe that if γ increases, FSRR will increases for every α,λp,λr and μ. However. the behaviour of γ never affect the increase of FSRR because γ and μ diminished the PSL to s, then replenishment should be placed immediately.
∙ The parameters λp and μ behave contrary to each other on the FSRR with respect to α.
∙ If we increase both λp and λr, then the FSRR decreases considerably.
∙ On comparing λr and μ, we note that, both are behave likely to each other for each α on FSRR.
Example 4: The E[Wp] and E[Wo] had been discussed in Figure 1 and Figure 2 respectively.
Figure 1.
Expected WT of customer in the queue on α vs μ.
∙Figure 1 shows that WT of a customer in the queue decreases as μ increases. As we predicted that the case α=0(homogeneous service rate) has higher WT than the case α=0.5 and α=1. Then the aim of model can be achieved.
∙Figure 2 explains E[Wo] with the non-homogeneous service rates. We observe that E[Wo] decreases when we increase μ, that is figure 1 and 2 have shown that WT and service rates are inversely proportional to each other. In particular, α=0.5 gave the predicted result when we analyzing both α=0 and α=1.
∙Figure 3 depicts that the expected WT of a queue is increases when the perishable rate γ increases. Clearly, α=0 gave the higher WT than the other cases α=0.5 and α=1.
Figure 3.
Expected waiting time of customer in the queue on α vs γ.
∙ Whenever we increase λp, we can observe the increased MCQ as well as MCO. However it is interesting to note that both MCQ and MCO decreases as α increases.
∙ The remarkable thing is, on increasing p, it never affect the MCQ but the domination of p reflects in MCO towards increasing.
∙ In Table 6, when λr increases, MCQ increases where as MCO decreases and both has been decreased as α increases, this is because due to faster service, MCQ will decrease which cause the decreasing MCO.
∙ Here, when we increase p, both MCQ and MCO will increase.
∙ On comparing Table 5 and Table 6, we can realize the significant of p with λp is that the MCQ is unchanged and λr has the considerable increment in MCQ.
Example 6: Investigation of β and γ on ETC with μ and α} We investigate the influence of the parameters β,γ,μ and α on the ETC in Table 7.
∙ As μ increases, the corresponding ETC decreases, in particular, for every increasing α, there can be seen that the ETC decreases.
∙ As we predicted earlier, the increase of γ provide the increasing ETC considerably for each μ and α.
∙ Although the γ sustains the ETC in an increasing manner, β dominates the ETC in a decreasing manner.
∙ However, when we increase β,γ,μ and α at time t, we get a minimized ETC, that is the optimum ETC is achieved.
∙ In the case α=0, the ETC always larger when we comparing other α's and Table 7 assures that the choice of α plays the key role to provide the best optimum ETC.
∙ Here, the impact of γ and β on ETC are contrary to each other where as β and μ behave the same but γ and μ are reacting against to each other.
6.
Conclusions and future work
The performance of a single server system in a perishable SQIS is investigated with the queue-dependent service rate. The stability condition and stationary probability vector of the proposed model is derived by the Neuts MGA. The waiting time of both primary and an orbital customer are constructed by the LST. The illustrated numerical examples explored the impact of queue-dependent service rate. With the system performance measures, the discussion made in the numerical section proved that queue-dependent service rate(non-homogeneous service rate) is much better than the homogeneous service rate. In all the examples, the case α=0 and α∈(0,1] are distinguished properly. Since the paper thoroughly analyzes the homogeneous and non-homogeneous service rates, it will give the generalized result for both cases(homogeneous and non-homogeneous service rates). Due to the increase of the service speed, number of customer serviced in the system is increased. This leads not only a more sale and profit to the management also this will reduce the impatient mindset of a customer. If a customer getting service quickly with the satisfaction, they will prefer the same system for the next purchase. Subsequently, the number of arriving customer to the system will increase day-by-day. Most of the inventory management purely dependent on the customer only. In this competitive society, every management wants to survive with a wealthy growth. For this growth, the concept made in this paper, will be much helpful to all the inventory management.
In future, this model can be extended into a multi server SQIS system involving additional service for a feedback customer of an infinite queue size.
Acknowledgments
The corresponding author thanks to Phuket Rajabhat University, Phuket Thailand-83000 for supporting this research. The authors would like to express their gratitude to the anonymous referees for precious remarks and suggestions that resulted in notable improvement and the excellence of this paper.
Conflicts of interest
The authors declare that there is no conflict of interests regarding the publication of this paper.
Acknowledgments
We thank KOSÉ Corporation for providing cosmetic ingredients for this study. We also thank Ruka Suzuki, Seiko Ota, and Ikuko Aoki of KOSÉ Corporation for their assistance in selecting versatile cosmetic ingredients. This research was funded by grants from the KOSÉ Cosmetology Research Foundation and a grant for specially promoted research of the University of Shizuoka.
Conflict of interest
The authors declare no conflicts of interest.
Author contributions
Conceptualization, Y.S. and S.M.; methodology, Y.S.; validation, C.T.; formal analysis, Y.U., Y.S., C.T. and S.S.; data curation, Y.S. and S.M.; writing—original draft preparation, Y.U.; writing—review and editing, Y.S. and S.M.; visualization, Y.U. and Y.S.; project administration, S.M.; and funding acquisition, Y.S. All authors have read and agreed to the published version of the manuscript.
References
[1]
Kong HH, Oh J, Deming C, et al. (2012) Temporal shifts in the skin microbiome associated with disease flares and treatment in children with atopic dermatitis. Genome Res 22: 850-859. https://doi.org/10.1101/gr.131029.111
[2]
Kobayashi T, Glatz M, Horiuchi K, et al. (2015) Dysbiosis and Staphylococcus aureus colonization drives inflammation in atopic dermatitis. Immunity 42: 756-766. https://doi.org/10.1016/j.immuni.2015.03.014
[3]
Queck SY, Jameson-Lee M, Villaruz AE, et al. (2008) RNAIII-independent target gene control by the agr quorum-sensing system: insight into the evolution of virulence regulation in Staphylococcus aureus. Mol Cell 32: 150-158. https://doi.org/10.1016/j.molcel.2008.08.005
[4]
Regassa LB, Betley MJ (1992) Alkaline pH decreases expression of the accessory gene regulator (agr) in Staphylococcus aureus. J Bacteriol 174: 5095-5100. https://doi.org/10.1128/jb.174.15.5095-5100.1992
[5]
Tremaine MT, Brockman DK, Betley MJ (1993) Staphylococcal enterotoxin A gene (sea) expression is not affected by the accessory gene regulator (agr). Infect Immun 61: 356-359. https://doi.org/10.1128/iai.61.1.356-359.1993
Otto M, Echner H, Voelter W, et al. (2001) Pheromone cross-inhibition between Staphylococcus aureus and Staphylococcus epidermidis. Infect Immun 69: 1957-1960. https://doi.org/10.1128/IAI.69.3.1957-1960.2001
[8]
Wang Q, Cui S, Zhou L, et al. (2019) Effect of cosmetic chemical preservatives on resident flora isolated from healthy facial skin. J Cosmet Dermatol 18: 652-658. https://doi.org/10.1111/jocd.12822
[9]
Shimamura Y, Yui T, Horiike H, et al. (2022) Toxicity of combined exposure to acrylamide and Staphylococcus aureus. Toxicol Rep 9: 876-882. https://doi.org/10.1016/j.toxrep.2022.04.018
[10]
Zeeuwen PL, Boekhorst J, van den Bogaard EH, et al. (2012) Microbiome dynamics of human epidermis following skin barrier disruption. Genome Biol 13: R101. https://doi.org/10.1186/gb-2012-13-11-r101
[11]
van der Krieken DA, Ederveen TH, van Hijum SA, et al. (2016) An in vitro model for bacterial growth on human stratum corneum. Acta Derm Venereol 96: 873-879. https://doi.org/10.2340/00015555-2401
Rudi K, Moen B, Drømtorp SM, et al. (2005) Use of ethidium monoazide and PCR in combination for quantification of viable and dead cells in complex samples. Appl Environ Microbiol 71: 1018-1024. https://doi.org/10.1128/AEM.71.2.1018-1024.2005
[14]
Aquino-Bolaños EN, Mapel-Velazco L, Martín-del-Campo ST, et al. (2017) Fatty acids profile of oil from nine varieties of Macadamia nut. Int J Food Prop 20: 1262-1269. https://doi.org/10.1080/10942912.2016.1206125
[15]
Desegaulx M, Sirdaarta J, Rayan P, et al. (2015) An examination of the anti-bacterial, anti-fungal and anti-Giardial properties of macadamia nut. Acta Hortic 1106: 239-246. https://doi.org/10.17660/ActaHortic.2015.1106.36
[16]
Bistline RG, Rothman ES, Serota S, et al. (1971) Surface active agents from isopropenyl esters: Acylation of isethionic acid and N-methyltaurine. J Am Oil Chem Soc 48: 657-660. https://doi.org/10.1007/BF02638512
[17]
Soni MG, Carabin IG, Burdock GA (2005) Safety assessment of esters of p-hydroxybenzoic acid (parabens). Food Chem Toxicol 43: 985-1015. https://doi.org/10.1016/j.fct.2005.01.020
[18]
Puschmann J, Herbig ME, Müller-Goymann CC (2018) Correlation of antimicrobial effects of phenoxyethanol with its free concentration in the water phase of o/w-emulsion gels. Eur J Pharm Biopharm 131: 152-161. https://doi.org/10.1016/j.ejpb.2018.08.007
[19]
Cole C, Shyr T, Ou-Yang H (2016) Metal oxide sunscreens protect skin by absorption, not by reflection or scattering. Photodermatol Photoimmunol Photomed 32: 5-10. https://doi.org/10.1111/phpp.12214
[20]
Saliani M, Jalal R, Goharshadi EK (2015) Effects of pH and temperature on antibacterial activity of zinc oxide nanofluid against Escherichia coli O157: H7 and Staphylococcus aureus. Jundishapur J Microbiol 8: e17115. https://doi.org/10.5812/jjm.17115
[21]
Shuai X, Dai T, Chen M, et al. (2021) Comparative study of chemical compositions and antioxidant capacities of oils obtained from 15 macadamia (Macadamia integrifolia) cultivars in China. Foods 10: 1031. https://doi.org/10.3390/foods10051031
[22]
Shimamura Y, Kidokoro S, Murata M (2006) Survey and properties of Staphylococcus aureus isolated from Japanese-style desserts. Biosci Biotechnol Biochem 70: 1571-1577. https://doi.org/10.1271/bbb.50617
[23]
Babicki S, Arndt D, Marcu A, et al. (2016) Heatmapper: web-enabled heat mapping for all. Nucleic Acids Res 44: W147-W153. https://doi.org/10.1093/nar/gkw419
[24]
Burian M, Plange J, Schmitt L, et al. (2021) Adaptation of Staphylococcus aureus to the human skin environment identified using an ex vivo tissue model. Front Microbiol 12: 728989. https://doi.org/10.3389/fmicb.2021.728989
[25]
Cruz AR, van Strijp JAG, Bagnoli F, et al. (2021) Virulence gene expression of Staphylococcus aureus in human skin. Front Microbiol 12: 692023. https://doi.org/10.3389/fmicb.2021.692023
[26]
Naik S, Bouladoux N, Linehan JL, et al. (2015) Commensal-dendritic-cell interaction specifies a unique protective skin immune signature. Nature 520: 104-108. https://doi.org/10.1038/nature14052
[27]
Edelblute CM, Donate AL, Hargrave BY, et al. (2015) Human platelet gel supernatant inactivates opportunistic wound pathogens on skin. Platelets 26: 13-16. https://doi.org/10.3109/09537104.2013.863859
[28]
Nataraj N, Anjusree GS, Madhavan AA, et al. (2014) Synthesis and anti-staphylococcal activity of TiO2 nanoparticles and nanowires in ex vivo porcine skin model. J Biomed Nanotechnol 10: 864-870. https://doi.org/10.1166/jbn.2014.1756
[29]
Van Drongelen V, Haisma EM, Out-Luiting JJ, et al. (2014) Reduced filaggrin expression is accompanied by increased Staphylococcus aureus colonization of epidermal skin models. Clin Exp Allergy 44: 1515-1524. https://doi.org/10.1111/cea.12443
[30]
Popov L, Kovalski J, Grandi G, et al. (2014) Three-dimensional human skin models to understand Staphylococcus aureus skin colonization and infection. Front Immunol 5: 41. https://doi.org/10.3389/fimmu.2014.00041
[31]
Stewart EJ, Payne DE, Ma TM, et al. (2017) Effect of Antimicrobial and Physical Treatments on Growth of Multispecies Staphylococcal Biofilms. Appl Environ Microbiol 83: e03483-16. https://doi.org/10.1128/AEM.03483-16
Zhao X, Zhong J, Wei C, et al. (2017) Current perspectives on viable but non-culturable state in foodborne pathogens. Front Microbiol 8: 580. https://doi.org/10.3389/fmicb.2017.00580
[34]
Belkaid Y, Segre JA (2014) Dialogue between skin microbiota and immunity. Science 346: 954-959. https://doi.org/10.1126/science
[35]
Findley K, Grice EA (2014) The skin microbiome: a focus on pathogens and their association with skin disease. PLoS Pathog 10: e1004436. https://doi.org/10.1371/journal.ppat.1004436
[36]
Ursell LK, Clemente JC, Rideout JR, et al. (2012) The interpersonal and intrapersonal diversity of human-associated microbiota in key body sites. J Allergy Clin Immunol 129: 1204-1208. https://doi.org/10.1016/j.jaci.2012.03.010
[37]
Rosenthal M, Goldberg D, Aiello A, et al. (2011) Skin microbiota: microbial community structure and its potential association with health and disease. Infect Genet Evol 11: 839-848. https://doi.org/10.1016/j.meegid.2011.03.022
Babayevska N, Przysiecka Ł, Iatsunskyi I, et al. (2022) ZnO size and shape effect on antibacterial activity and cytotoxicity profile. Sci Rep 12: 1-13. https://doi.org/10.1038/s41598-022-12134-3
[40]
Watanabe T, Yamamoto Y, Miura M, et al. (2019) Systematic analysis of selective bactericidal activity of fatty acids against Staphylococcus aureus with minimum inhibitory concentration and minimum bactericidal concentration. J Oleo Sci 68: 291-296. https://doi.org/10.5650/jos.ess18220
[41]
Okukawa M, Yoshizaki Y, Yano S, et al. (2021) The selective antibacterial activity of the mixed systems containing myristic acid against Staphylococci. J Oleo Sci 70: 1239-1246. https://doi.org/10.5650/jos.ess21090
[42]
Aleaghil SA, Fattahy E, Baei B, et al. (2016) Antibacterial activity of Zinc oxide nanoparticles on Staphylococcus aureus. Int J Advanced Biotechnol Res 7: 1569-1575. https://www.researchgate.net/publication/306960317
[43]
Ganesh VK, Barbu EM, Deivanayagam CCS, et al. (2011) Structural and biochemical characterization of Staphylococcus aureus clumping factor B/ligand interactions. J Biol Chem 286: 25963-25972. https://doi.org/10.1074/jbc.M110.217414
[44]
Mazmanian SK, Liu G, Ton-That H, et al. (1999) Staphylococcus aureus sortase, an enzyme that anchors surface proteins to the cell wall. Science 285: 760-763. https://doi.org/10.1126/science.285.5428.760
[45]
Oura Y, Shimamura Y, Kan T, et al. (2024) Effect of polyphenols on inflammation induced by membrane vesicles from Staphylococcus aureus. Cells 13: 387. https://doi.org/10.3390/cells13050387
[46]
Shimamura Y, Oura Y, Tsuchiya M, et al. (2024) Slightly acidic electrolyzed water inhibits inflammation induced by membrane vesicles of Staphylococcus aureus. Front Microbiol 14: 1328055. https://doi.org/10.3389/fmicb.2023.1328055
[47]
El-Masry RM, Talat D, Hassoubah SA, et al. (2022) Evaluation of the antimicrobial activity of ZnO nanoparticles against enterotoxigenic Staphylococcus aureus. Life 12: 1662. https://doi.org/10.3390/life12101662
[48]
Wallin-Carlquist N, Cao R, Márta D, et al. (2010) Acetic acid increases the phage-encoded enterotoxin A expression in Staphylococcus aureus. BMC Microbiol 10: 147. https://doi.org/10.1186/1471-2180-10-147
Simões M, Simões LC, Vieira MJ (2010) A review of current and emergent biofilm control strategies. LWT-Food Sci Technol 43: 573-583. https://doi.org/10.1016/j.lwt.2009.12.008
[51]
Martínez A, Stashenko EE, Sáez RT, et al. (2023) Effect of essential oil from Lippia origanoides on the transcriptional expression of genes related to quorum sensing, biofilm formation, and virulence of Escherichia coli and Staphylococcus aureus. Antibiotics 12: 845. https://doi.org/10.3390/antibiotics12050845
[52]
Jasim NA, Al-Gasha'a FA, Al-Marjani MF, et al. (2020) ZnO nanoparticles inhibit growth and biofilm formation of vancomycin-resistant S. aureus (VRSA). Biocatal Agric Biotechnol 29: 101745. https://doi.org/10.1016/j.bcab.2020.101745
Abdelghafar A, Yousef N, Askoura M (2022) Zinc oxide nanoparticles reduce biofilm formation, synergize antibiotics action and attenuate Staphylococcus aureus virulence in host; an important message to clinicians. BMC Microbiol 22: 244. https://doi.org/10.1186/s12866-022-02658-z
[55]
Abdelraheem WM, Khairy RMM, Zaki AI, et al. (2021) Effect of ZnO nanoparticles on methicillin, vancomycin, linezolid resistance and biofilm formation in Staphylococcus aureus isolates. Ann Clin Microbiol Antimicrob 20: 54. https://doi.org/10.1186/s12941-021-00459-2
[56]
Alves MM, Bouchami O, Tavares A, et al. (2017) New insights into antibiofilm effect of a nanosized ZnO coating against the pathogenic methicillin resistant Staphylococcus aureus. ACS Appl Mater Interfaces 9: 28157-28167. https://doi.org/10.1021/acsami.7b02320
[57]
Mempel M, Schnopp C, Hojka M, et al. (2002) Invasion of human keratinocytes by Staphylococcus aureus and intracellular bacterial persistence represent haemolysin-independent virulence mechanisms that are followed by features of necrotic and apoptotic keratinocyte cell death. Br J Dermatol 146: 943-951. https://doi.org/10.1046/j.1365-2133.2002.04752.x
[58]
Katayama Y, Baba T, Sekine M, et al. (2013) Beta-hemolysin promotes skin colonization by Staphylococcus aureus. J Bacteriol 195: 1194-1203. https://doi.org/10.1128/JB.01786-12
[59]
Fujii S, Itoh H, Yoshida A, et al. (2005) Activation of sphingomyelinase from Bacillus cereus by Zn2+ hitherto accepted as a strong inhibitor. Arch Biochem Biophys 436: 227-236. https://doi.org/10.1016/j.abb.2005.02.019
[60]
Morinaga N, Iwamaru Y, Yahiro K, et al. (2005) Differential activities of plant polyphenols on the binding and internalization of cholera toxin in vero cells. J Biol Chem 280: 23303-23309. https://doi.org/10.1074/jbc.M502093200
[61]
Barraza I, Pajon C, Diaz-Tang G, et al. (2023) Disturbing the spatial organization of biofilm communities affects expression of agr-regulated virulence factors in Staphylococcus aureus. Appl Environ Microbiol 89: e0193222. https://doi.org10.1128/aem.01932-22
This article has been cited by:
1.
K. Jeganathan, S. Selvakumar, S. Saravanan, N. Anbazhagan, S. Amutha, Woong Cho, Gyanendra Prasad Joshi, Joohan Ryoo,
Performance of Stochastic Inventory System with a Fresh Item, Returned Item, Refurbished Item, and Multi-Class Customers,
2022,
10,
2227-7390,
1137,
10.3390/math10071137
T. Harikrishnan, K. Jeganathan, S. Selvakumar, N. Anbazhagan, Woong Cho, Gyanendra Prasad Joshi, Kwang Chul Son,
Analysis of Stochastic M/M/c/N Inventory System with Queue-Dependent Server Activation, Multi-Threshold Stages and Optional Retrial Facility,
2022,
10,
2227-7390,
2682,
10.3390/math10152682
4.
Amir Aghsami, Yaser Samimi, Abdollah Aghaie,
A combined continuous-time Markov chain and queueing-inventory model for a blood transfusion network considering ABO/Rh substitution priority and unreliable screening laboratory,
2023,
215,
09574174,
119360,
10.1016/j.eswa.2022.119360
5.
K. Jeganathan, S. Vidhya, R. Hemavathy, N. Anbazhagan, Gyanendra Prasad Joshi, Chanku Kang, Changho Seo,
Analysis of M/M/1/N Stochastic Queueing—Inventory System with Discretionary Priority Service and Retrial Facility,
2022,
14,
2071-1050,
6370,
10.3390/su14106370
6.
V. Kuppulakshmi, C. Sugapriya, D. Nagarajan,
Economic ordering quantity inventory model with verhulst’s demand under fuzzy uncertainty for geographical market,
2023,
44,
10641246,
801,
10.3233/JIFS-220832
7.
Amir Aghsami, Yaser Samimi, Abdollah Aghaei,
A novel Markovian queueing-inventory model with imperfect production and inspection processes: A hospital case study,
2021,
162,
03608352,
107772,
10.1016/j.cie.2021.107772
8.
C. Sugapriya, M. Nithya, K. Jeganathan, N. Anbazhagan, Gyanendra Prasad Joshi, Eunmok Yang, Suseok Seo,
Analysis of Stock-Dependent Arrival Process in a Retrial Stochastic Inventory System with Server Vacation,
2022,
10,
2227-9717,
176,
10.3390/pr10010176
9.
M. Nithya, Gyanendra Prasad Joshi, C. Sugapriya, S. Selvakumar, N. Anbazhagan, Eunmok Yang, Ill Chul Doo,
Analysis of Stochastic State-Dependent Arrivals in a Queueing-Inventory System with Multiple Server Vacation and Retrial Facility,
2022,
10,
2227-7390,
3041,
10.3390/math10173041
10.
Mridula Jain, Indeewar Kumar,
Genetic algorithm in the single server inventory retrial queueing system with time and stock level dependent customer arrival rate,
2023,
15,
2511-2104,
4537,
10.1007/s41870-023-01440-2
11.
Chia-Huang Wu, Wen-Tso Huang, Jr-Fong Dang, Ming-Yang Yeh,
Optimal analysis of a multi-server queue with preprocessing time and replenishment inventory,
2024,
47,
0253-3839,
120,
10.1080/02533839.2023.2274089
12.
N. Nithya, N. Anbazhagan, S. Amutha, Gyanendra Prasad Joshi,
A perspective analysis of obligatory vacation and retention of impatient purchaser on queueing-inventory with retrial policy,
2024,
24,
1109-2858,
10.1007/s12351-024-00843-8
13.
Subramani Palani Niranjan, Suthanthira Raj Devi Latha, Sorin Vlase,
Cost Optimization in Sintering Process on the Basis of Bulk Queueing System with Diverse Services Modes and Vacation,
2024,
12,
2227-7390,
3535,
10.3390/math12223535
14.
Honggang Zhang, Zhiyuan Liu, Yu Dong, Hongyue Zhou, Pan Liu, Jun Chen,
A novel network equilibrium model integrating urban aerial mobility,
2024,
187,
09658564,
104160,
10.1016/j.tra.2024.104160
15.
S. Selvakumar, K. Jeganathan, Aster Seifu Senae, N. Anbazhagan, S. Amutha, Gyanendra Prasad Joshi, Woong Cho,
Performance of a dual service station in stochastic inventory system with multi server and optional feedback service,
2024,
15,
20904479,
102583,
10.1016/j.asej.2023.102583
16.
Cho Nilar Phyo, Pyke Tin, Thi Thi Zin,
A Markov Chain Model for Determining the Optimal Time to Move Pregnant Cows to Individual Calving Pens,
2023,
23,
1424-8220,
8141,
10.3390/s23198141
17.
Mukunda Choudhury, Sudipa Das, Gerhard-Wilhelm Weber, Gour Chandra Mahata,
Carbon-regulated inventory pricing and ordering policies with marketing initiatives under order volume discounting scheme,
2025,
0254-5330,
10.1007/s10479-025-06490-2
18.
V. Vinitha, S. Amutha, Gyanendra Prasad Joshi, M. Kameswari, N. Anbazhagan,
Integrated branching queueing-inventory system with diverted service,
2025,
0030-3887,
10.1007/s12597-025-00935-9
19.
R. Sivasamy,
On a queueing inventory system with lost sales, PH vacation and random order size (s, S) policy,
2025,
2193-5343,
10.1007/s40065-025-00529-9
Yuya Uehara, Yuko Shimamura, Chika Takemura, Shiori Suzuki, Shuichi Masuda. Effects of cosmetic ingredients on growth and virulence factor expression in Staphylococcus aureus: a comparison between culture medium and in vitro skin model medium[J]. AIMS Microbiology, 2025, 11(1): 22-39. doi: 10.3934/microbiol.2025002
Yuya Uehara, Yuko Shimamura, Chika Takemura, Shiori Suzuki, Shuichi Masuda. Effects of cosmetic ingredients on growth and virulence factor expression in Staphylococcus aureus: a comparison between culture medium and in vitro skin model medium[J]. AIMS Microbiology, 2025, 11(1): 22-39. doi: 10.3934/microbiol.2025002
Figure 1. Structure of the cosmetic ingredients used in this study (except ZnO). (A) Oleic acid, (B) palmitoleic acid ((A) and (B) are the main component of macadamia nut oil (MO)), (C) sodium myristoyl methyl taurate (SMMT), (D) methyl p-hydroxybenzoate (MP), and (E) 2-phenoxyethanol (PE)
Figure 2. Viable counts of Staphylococcus aureus and S. epidermidis incubated in the in vitro skin model medium with different compositions. Viable counts of (A) S. aureus and (B) S. epidermidis based on Model 1 (n = 2). Viable counts of (C) S. aureus and (D) S. epidermidis based on Model 2 (n = 2). Viable counts of (E) S. aureus and (F) S. epidermidis based on Model 3 (n = 3). The S. aureus and S. epidermidis bacterial solutions were added to the in vitro skin model medium at initial bacterial counts of 103, 105, and 107 CFU/well, and the bacterial counts were measured after incubation for 0, 1, and 4 days
Figure 3. The bacterial counts of Staphylococcus aureus and S. epidermidis after 1 and 4 days of culture in the in vitro skin model medium (Model 3). Measurements in (A) monoculture and (B) coculture. Bacterial counts were assessed using EMA treatment, followed by genomic DNA extraction and real-time PCR. The values represent the mean ± standard deviation (SD) of three independent experiments. Significance levels: *p < 0.05 compared with S. aureus after 4 days, †p < 0.05 compared with S. aureus after 1 day (two-way ANOVA with Sidak's multiple comparisons test)
Figure 4. Comparison of Staphylococcus aureus bacterial counts in the in vitro skin model medium and BHI medium upon the addition of cosmetic ingredients. S. aureus was inoculated into the in vitro skin model medium and BHI medium and incubated at 37°C for 24 h. MO: 10% macadamia nut oil; MP: 0.1% methyl p-hydroxybenzoate; PE: 0.1% 2-phenoxyethanol; ZnO: 0.5% zinc oxide; and SMMT: 1% sodium myristoyl methyl taurate. Sterile water was used as a control. * p < 0.05, †p < 0.05 compared with the control of BHI medium, and # p < 0.05 compared with the control of skin model medium (two-way ANOVA with Sidak's multiple comparisons test)
Figure 5. Comparison of the effects of five cosmetic ingredients on the expression of S. aureus virulence factor genes between in vitro skin model medium and BHI medium. (A) staphylococcal enterotoxin A (sea). (B) RNAIII. (C) β-hemolysin gene (hlb). (D) biofilm formation gene (icaA). (E) Heatmaps showing changes in gene expression levels in the BHI medium and in vitro skin model medium. Differential expression of mRNA is shown by the intensity of red (upregulation) versus green (downregulation). Staphylococcus aureus was inoculated into the in vitro skin model medium and BHI medium containing cosmetic ingredients and incubated at 37 °C for 6 h. MO: 10% macadamia nut oil; MP: 0.1% methyl p-hydroxybenzoate; PE: 0.1% 2-phenoxyethanol; ZnO: 0.5% zinc oxide; and SMMT: 1% sodium myristoyl methyl taurate. Sterile water was used as a control. * p < 0.05, †p < 0.05 compared with the control of BHI medium, and #p < 0.05 compared with the control of skin model medium (student t-test)