Research article

Assessment of indoor air quality in Tunisian childcare establishments

  • Received: 19 October 2024 Revised: 31 March 2025 Accepted: 03 April 2025 Published: 15 April 2025
  • Maintaining healthy indoor air quality (IAQ) in childcare settings is essential for infants and young children, as it directly impacts their early learning, development, and overall well-being. Given their vulnerability, continuous IAQ monitoring in these environments is crucial to ensuring a safe and supportive atmosphere. This study aimed to assess IAQ factors that may affect occupant health by measuring indoor concentrations of particulate matter (PM10), selected gases such as carbon dioxide (CO2) and formaldehyde (CH2O), and thermal conditions including temperature and relative humidity. Additionally, airborne microorganism levels were analyzed, and potential environmental factors influencing microbial abundance were investigated in three childcare centers in Megrine, Tunisia, across three seasonal periods. Results revealed frequent occurrences of hygrothermal discomfort and elevated levels of CO2, CH2O, and PM10, particularly in overcrowded classrooms with poor ventilation and heating. Pathogenic bacterial species, including Staphylococcus epidermidis, Staphylococcus haemolyticus, Bacillus cereus, and Bacillus licheniformis, were repeatedly detected. Significant correlations were found between bacterial abundance and environmental factors such as PM10, CO2 levels, temperature, and humidity. These findings provide valuable insights into IAQ dynamics in childcare environments, highlighting the need for improved ventilation and air quality management strategies to safeguard children's health and well-being.

    Citation: Meher Cheberli, Marwa Jabberi, Sami Ayari, Jamel Ben Nasr, Habib Chouchane, Ameur Cherif, Hadda-Imene Ouzari, Haitham Sghaier. Assessment of indoor air quality in Tunisian childcare establishments[J]. AIMS Environmental Science, 2025, 12(2): 352-372. doi: 10.3934/environsci.2025016

    Related Papers:

    [1] Minghuan Guo, Hao Wang, Zhifeng Wang, Xiliang Zhang, Feihu Sun, Nan Wang . Model for measuring concentration ratio distribution of a dish concentrator using moonlight as a precursor for solar tower flux mapping. AIMS Energy, 2021, 9(4): 727-754. doi: 10.3934/energy.2021034
    [2] Ibraheem Ahmad Qeays, Syed Mohd. Yahya, M. Saad Bin Arif, Azhar Jamil . Nanofluids application in hybrid Photovoltaic Thermal System for Performance Enhancement: A review. AIMS Energy, 2020, 8(3): 365-393. doi: 10.3934/energy.2020.3.365
    [3] Wei An, Yifan Zhang, Bo Pang, Jun Wu . Synergistic design of an integrated pv/distillation solar system based on nanofluid spectral splitting technique. AIMS Energy, 2021, 9(3): 534-557. doi: 10.3934/energy.2021026
    [4] Duong Van, Diaz Gerardo . Carbon dioxide as working fluid for medium and high-temperature concentrated solar thermal systems. AIMS Energy, 2014, 1(1): 99-115. doi: 10.3934/energy.2014.1.99
    [5] Alemayehu T. Eneyaw, Demiss A. Amibe . Annual performance of photovoltaic-thermal system under actual operating condition of Dire Dawa in Ethiopia. AIMS Energy, 2019, 7(5): 539-556. doi: 10.3934/energy.2019.5.539
    [6] Saad Eddin Lachhab, A. Bliya, E. Al Ibrahmi, L. Dlimi . Theoretical analysis and mathematical modeling of a solar cogeneration system in Morocco. AIMS Energy, 2019, 7(6): 743-759. doi: 10.3934/energy.2019.6.743
    [7] Kaovinath Appalasamy, R Mamat, Sudhakar Kumarasamy . Smart thermal management of photovoltaic systems: Innovative strategies. AIMS Energy, 2025, 13(2): 309-353. doi: 10.3934/energy.2025013
    [8] Yasong Sun, Jiazi Zhao, Xinyu Li, Sida Li, Jing Ma, Xin Jing . Prediction of coupled radiative and conductive heat transfer in concentric cylinders with nonlinear anisotropic scattering medium by spectral collocation method. AIMS Energy, 2021, 9(3): 581-602. doi: 10.3934/energy.2021028
    [9] Harry Ramenah, Philippe Casin, Moustapha Ba, Michel Benne, Camel Tanougast . Accurate determination of parameters relationship for photovoltaic power output by augmented dickey fuller test and engle granger method. AIMS Energy, 2018, 6(1): 19-48. doi: 10.3934/energy.2018.1.19
    [10] Joanna McFarlane, Jason Richard Bell, David K. Felde, Robert A. Joseph III, A. Lou Qualls, Samuel Paul Weaver . Performance and Thermal Stability of a Polyaromatic Hydrocarbon in a Simulated Concentrating Solar Power Loop. AIMS Energy, 2014, 2(1): 41-70. doi: 10.3934/energy.2014.1.41
  • Maintaining healthy indoor air quality (IAQ) in childcare settings is essential for infants and young children, as it directly impacts their early learning, development, and overall well-being. Given their vulnerability, continuous IAQ monitoring in these environments is crucial to ensuring a safe and supportive atmosphere. This study aimed to assess IAQ factors that may affect occupant health by measuring indoor concentrations of particulate matter (PM10), selected gases such as carbon dioxide (CO2) and formaldehyde (CH2O), and thermal conditions including temperature and relative humidity. Additionally, airborne microorganism levels were analyzed, and potential environmental factors influencing microbial abundance were investigated in three childcare centers in Megrine, Tunisia, across three seasonal periods. Results revealed frequent occurrences of hygrothermal discomfort and elevated levels of CO2, CH2O, and PM10, particularly in overcrowded classrooms with poor ventilation and heating. Pathogenic bacterial species, including Staphylococcus epidermidis, Staphylococcus haemolyticus, Bacillus cereus, and Bacillus licheniformis, were repeatedly detected. Significant correlations were found between bacterial abundance and environmental factors such as PM10, CO2 levels, temperature, and humidity. These findings provide valuable insights into IAQ dynamics in childcare environments, highlighting the need for improved ventilation and air quality management strategies to safeguard children's health and well-being.



    Evolutionary game theory studies populations where individuals can use different strategies, which are subsequently interpreted as different phenotypes [1,2,3]. Replicator dynamics are among the core dynamics used to describe the evolution of the frequencies of the strategies in EGT. It shows how populations allocate the different pure strategies that are related in a game over time.

    Cooperation is of great significance to the sustainable development of the population in evolutionary game theory [4,5]. How to promote cooperation is the core issue of evolutionary game theory, because when a player chooses to defect, the average fitness is lower than when the player decides to cooperate, which results in a social dilemma. For the stag hunt game, Zhang et al. [6] studied the cooperative behavior and various stages in the coevolutionary network dynamics. They found that the status of cooperators can be changed by controlling the payoff parameter r and reconnection probability q. Du and Wu [7] studied the evolutionary dynamics of cooperation based on the co-evolution of strategy and network structure. When the cooperators are active to a certain extent, the cooperation strategy will emerge and remain stable. In an N-player iterative prisoner's dilemma game, the random mobility can improve cooperation and was explored by Chiong and Kirley [8]. Chen et al. [9] proposed a mechanism to promote cooperation on the lattice. This mechanism allowed players to decide whether to keep or delete neighbors by comparing profits. It proved that under this mechanism, if the cost-benefit ratio is small or the temptation of betrayal is small, the level of cooperation would be improved. These studies examined the changes of cooperative strategy in games through different forms.

    In addition, abundant studies have shown that imposing a penalty on defectors can promote cooperative behavior. For example, based on the N-player snowdrift game with peer punishment, Pi et al. [10] assumed that the non-cooperators in the well-mixed population have an individual disguise, and they found that the high cost of disguise and severe punishment inhibit the existence of non-cooperators. Zhu et al. [11] investigated peer punishment and pool punishment together in the spatial public goods game. The influence of penalty-type transfer on evolutionary dynamics was fully analyzed. They showed that peer punishment is more efficacious than collective punishment in promoting players' cooperation. In addition, in a finite population, Catalán et al. [12] assumed that the offspring of players inherit their parents' strategy and can mutate to another strategy. They studied the influence of mutation and selection in the Hawk-dove game with mixed strategies. In[13], Nagatani et al. proposed a metapopulation model of rock paper scissors game under the influence of mutation. The change in mutation rate would cause the dynamic phase transition to occur in three stages: the stable coexistence of three species, the stable phase of two species, and a single-species phase. This study imposes a penalty when both players choose the defective strategy to encourage players to cooperate, and the paper discusses the impact of the mutation.

    Time delay is widely used in biological systems and often leads to bifurcation. It is also essential to discuss time delay in evolutionary game theory. For example, in Wettergren (2021) [14], based on replicator dynamics, a snowdrift game model for N players was constructed. It was found that delay leads to Hopf bifurcation. As the time delay increases, when it is larger than the critical delay, it presents oscillatory replicator dynamics rather than asymptotic stability. Alboszta and Miekisz [15] considered the replicator dynamics models with social and biological delays. When the social delay model is considered, the small delay leads to the asymptotic stability of dynamics. For biological time delay, the dynamics are asymptotically stable for any time delay. Miekisz and Wesołowski [16] discussed the joint influence of stochasticity and time delay. When an individual renewal strategy is randomly selected, the time delay has little influence on dynamics. Burridge et al. [17] showed that memory affects dynamics stability. When the game is stable, long memory is beneficial, but it is different when the game is unstable. Mittal et al. [18] found that mutation does not lead to oscillation of cooperative state, but the delayed information of population state may lead to oscillation. Hu and Qiu [19] studied stochastic delay and fixed delay, in which players in different communities have different delays. However, the impact of mutation time delay has not been fully discussed. We consider that it takes time for players to mutate to another strategy. We study the effects of double delays, i.e., payoff delay and mutation delay, on dynamics.

    The rest of this paper is organized as follows. First, Section 2 considers increasing the penalty for the prisoner's dilemma without mutation. We obtain the stable equilibrium by the replicator equation and prove its stability. The co-existence of cooperators and defectors has emerged. In addition, the change of cooperator ratio under the influence of time delay is studied, and we obtain the critical time delay from stable equilibrium to oscillation. In Section 3, we study the prisoner's dilemma with penalty and mutation and discuss the effects of the time delay of payoff and the time delay of mutation on the game. Section 4 is the conclusion.

    In this paper, we choose the payoff matrix of the prisoner's dilemma

              C         DCD(bccb0), (2.1)

    where bc>0, and a, b, c are positive constants. When both players cooperate, they get bc. When one player cooperates, and the other player defects, the cooperative player bears a cost c. When a player who defects meets a player who cooperates, he immediately gets a payoff of b. When both players defect, they get nothing. At the same time, the classic prisoner's dilemma takes defection as the dominant strategy. To improve players' enthusiasm for cooperation, when two defection strategies meet, a penalty a (a>0) is imposed, and the payoff matrix is given by

    CDCD(bccba) (2.2)

    We see that when a<c, it is still the defection strategy that dominates, so assume that a>c and see what happens.

    In a well-mixed infinite population, x(t) represents the proportion of people who choose to cooperate (that is, to execute strategy C) at time t, and 1x(t) represents the proportion of people who choose to defect (that is, to execute strategy D) at time t. The replicator dynamics' equilibria correspond to the game's optional strategies, so we next study the replicator dynamics of the prisoner's dilemma.

    If time delay is not considered, the expected average payoff of participants who choose to cooperate is

    πc(t)=(bc)x(t)c(1x(t)). (2.3)

    The expected average payoff for the participants who defect is

    πd(t)=bx(t)a(1x(t)). (2.4)

    According to the replicator equation ˙x(t)=x(t)(1x(t))(πcπd), and Eqs (2.3), (2.4), the dynamics for the 2-player prisoner's dilemma with penalty and no time delay is

    ˙x(t)=x(t)(1x(t))[acax(t)]. (2.5)

    Equation (2.5) has three real equilibria x1,x2,x3, given by x1=0, x2=1, x3=aca. The x3 only makes sense if a>c and c>0, where 0<x3<1.

    Lemma 2.1. When ˙x=f(x), f(x)=0. The internal equilibrium point x is a stable equilibrium point if f(x)<0.

    Let f(x)=x(t)(1x(t))[acax(t)], f(0)=c+a>0, and f(1)=c>0. It follows from the stability test that the solutions at x1=0 and x2=1 are unstable, while f(aca)=(ac)ca<0, so the solution at x3 is stable. Thus, in a 2-player prisoner's dilemma with no delay and a penalty, the proportion of cooperators eventually tends to x3=aca regardless of the initial values of cooperators and defectors. Thus, x3 is called the stable equilibrium, denoted by

    x3=x=aca. (2.6)

    From this, we find that when the penalty for defection increases, the proportion of players choosing to cooperate increases, which means that players tend to cooperate to avoid the penalty for defection. Figure 1 shows the proportion of cooperators and defectors over time without the penalty for defection. We can see that no matter what the initial value is, the proportion of cooperators tends to 0, and the proportion of defectors tends to 1. That means the cooperators will disappear, and all that remains are the defectors. However, when the defection penalty is greater than the cheated payoff (a>c), cooperators and defectors coexist regardless of the initial values, and the proportion of cooperators is stable at x3, as shown in Figure 2.

    Figure 1.  Temporal dynamics of nondelay model (2.5) (a=0 and c=2). Over time, x, representing the proportion of cooperators, tends to 0, and y, representing the proportion of defectors, grows to 1.
    Figure 2.  Temporal dynamics of nondelay model (2.5) (a=5 and c=2). Over time, x, representing the proportion of cooperators, tends to 0.6, and y, representing the proportion of defectors, tends to 0.4.

    According to [20,21,22,23,24], we can find that Figure 2 is satisfied with the coexistence of the snowdrift game, which changes the intensity of social dilemma and ensures the existence of cooperation. When the benefits generated by the cooperation of the prisoner's dilemma are available to both players, and the cooperators share the costs, this leads to the so-called snowdrift game [25]. In addition, when sufficient penalty (a>c) is added to the defectors in the prisoner's dilemma, the conditions of snowdrift game are also met, which breaks the dominance of strategy D and ensures the coexistence of strategy C and strategy D.

    We next study the game with time delay, considering that the expected payoffs πdc(t) and πdc(t) depend on the payoffs of the players at the previous time (tτ) (the superscript d denotes payoffs with time delay). The expected average payoffs of the cooperator and the defector with time delay are, respectively,

    πdc(t)=(bc)x(tτ)c(1x(tτ))=bx(tτ)c, (2.7)
    πdd(t)=bx(tτ)a(1x(tτ))=(b+a)x(tτ)a. (2.8)

    The replicator equation of the 2-player prisoner's dilemma with time delay and penalty is

    ˙x(t)=x(t)(1x(t))(πdcπdd) (2.9)
    =x(t)(1x(t))[acax(tτ)]. (2.10)

    Next, we find out the critical delay of Hopf bifurcation through characteristic equation analysis. Let ξ(t)=x(t)x, ξd(t)=x(tτ)x, and replace ξ(t) and ξd(t) with x(t) and x(tτ). Take their linearization and keep only the linear term, and get

     ξ(t)=ax(1x)ξd(t) (2.11)
    =c(ac)aξd(t). (2.12)

    Let ξ(t)=eλt, and let ξd(t)=eλ(tτ). The characteristic equation of (2.9) is

     aλ=(ac)ceλτ. (2.13)

    Let λ=iω (ω>0), and we have

     aiω=(ac)ceiωτ=(ac)c[cos(ωτ)isin(ωτ)]. (2.14)

    The real and the imaginary parts are separated, and we get

    (ac)ccos(ωτ)=0,(ac)csin(ωτ)=aω. (2.15)

    Squaring both sides of (2.15) and adding them together, we get

    ω=(ac)ca. (2.16)

    Substituting (2.16) into (2.15), we obtain

    τc=aπ2(ac)c=π2a(1σ)σ, (2.17)

    where σ=ca.

    According to Eq (2.17), the critical delay τc decreases as the defection penalty a increases. When τ<τc, we have x(t)x, which means the proportion of cooperators is stable at the equilibrium. When τ>τc, the phenomenon of periodic oscillation occurs.

    Figure 3 shows how the equilibrium x3 changes as time increases for different initial values and different time delays. We find that when the time delay is slight (τ=1), it presents a stable dynamic performance with the time change. When the delay is significant (τ=2), the dynamics behave as an oscillation, and the player swings between the two strategies. Figure 4 shows the phase plane of system (2.9). The asymptotically stable dynamics become the behavior of a limit cycle with the increase of time delay. From Figure 5, we can see that for different initial values, the dynamics tend to a stable equilibrium when the delay is small, and a stable limit cycle is formed when the delay is large. In other words, the proportion of cooperators eventually stabilizes at the equilibrium value when the time delay is less than the critical time delay. The stable equilibrium point disappears, and the player swings between cooperative and defective strategies when the time delay exceeds the critical time delay.

    Figure 3.  Temporal dynamics of system (2.9) (a=5 and c=2). When a and c are definite values, when τ is small, the proportion of cooperators tends to be stable, and when τ is large, the oscillation dynamics phenomenon occurs.
    Figure 4.  Phase plane of dynamics of Figure 3 (a=5 and c=2). When a and c are definite values, the phase plane tends to be stable when τ is small, and the limit cycle appears when τ is large.
    Figure 5.  Phase plane of system (2.9) with different initial values (a=5 and c=2). When a and c are definite values, for different initial values, the phase plane tends to be stable when τ is small, and the limit cycle appears when τ is large.

    Figure 6 shows the correlation between critical time delay τc and σ(σ=ca). Since a>0, c>0, and a>c, σ(0,1). When the cheating penalty c is infinitely close to the penalty a when both sides defect, the delay τc becomes larger. When c is small enough, the delay τc becomes larger. Figure 7 is the bifurcation diagram. We can find that the Hopf bifurcation occurs as the time delay increases. The black line indicates that the system is stable when the time delay τ is small, and Hopf bifurcation occurs at the critical time delay. When the time delay increases, the stable equilibrium disappears, generating a stable limit cycle.

    Figure 6.  The graph of aτc and σ, where σ=ca.
    Figure 7.  Bifurcation diagram of x when τ is the time delay parameter. With the increase in delay, bifurcation occurs at the critical delay.
    Figure 8.  The stability of the equilibrium in the four cases. There is at least one point such that g(x)=0.

    Based on Section 2, consider the factors of mutation to observe how the proportion of cooperators changes. Here, we assume that players who choose cooperation or defection have the same probability of u (0<u<1) mutating to each other. For example, ux(t) mutants of these cooperators choose defection, and similarly, u(1x(t)) mutants of some defectors desire cooperation.

    In this case, we can obtain the replicator-mutator equation for the 2-player prisoner's dilemma with penalty and mutation:

    ˙x=x(t)(1x(t))[acax(t)]ux(t)+u(1x(t))=x(t)(1x(t))[acax(t)]+u(12x(t)). (3.1)

    Theorem 3.1. The internal equilibrium x1 of system (3.1) exists and is stable.

    Proof. Let g(x)=x(t)(1x(t))[acax(t)]+u(12x(t)), and we get g(0)=u>0, g(1)=u<0. So, there is at least one point x1 such that g(x1)=0, which means x1 is the equilibrium of Eq (3.1). According to Lemma 2.1, in the following, we want to prove that g(x1)<0. Discussing Figure 7 in four cases, we find that in either case, x1 is between two extreme values (xa and xb) and thus satisfies g(x1)<0.

    Remark 1. Because g(x)=ax3(t)(2ac)x2(t)+(ac2u)x(t)+u, let

    A=(2ac)23a(ac2u),B=(2ac)(ac2u)9au,C=(ac2u)2+3(2ac)u. (3.2)

    According to [26,27], we only discuss cases Δ=B24AC0 and A=B. Δ=B24AC>0, which generates imaginary roots, is not considered.

    Figure 9 shows the temporal dynamics of system (3.1) for different initial values and mutation rates when a=5 and c=2. We find that when a mutation u is added, the co-existence of cooperators and defectors still occurs. The proportion of cooperators increases with the increase of u, but the mutation rate u has little effect on the proportion of cooperators. The mutation u increases, and the percentage of cooperator decreases.

    Figure 9.  Temporal dynamics of nondelay model (3.1). For different initial values and mutation rates, when a and c are definite values, the co-existence of cooperators and defectors still occurs.

    Next, we study how time delays affect games. There are two delays, a payoff delay τ1 (the same as (2.3)) and a mutation delay τ2, considering that player mutation depends on the proportion of cooperators at tτ2. We can obtain the replicator-mutator equation for the 2-player prisoner's dilemma with time delays:

    ˙x(t)=x(t)(1x(t))[acax(tτ1)]+u(12x(tτ2)). (3.3)

    Case 1. τ1=τ2=0. The system (3.3) is the same as system (3.1).

    Case 2. τ1>0,τ2=0. Then, system (3.3) becomes

    ˙x(t)=x(t)(1x(t))[acax(tτ1)]+u(12x(t)). (3.4)

    The characteristic equation of system (3.4) at x1 is

    λ(12x1)[acax1]+2u+a(x1x21)eλτ1=0. (3.5)

    Assuming λ=iω(ω>0) is a pure imaginary solution of Eq (3.5), substituting λ=iω(ω>0) into Eq (3.5), we can get

    iω(12x1)[acax1]+2u+a(x1x21)cos(ωτ1)ia(x1x21)sin(ωτ1)=0. (3.6)

    The real and the imaginary parts are separated, and we get

    a(x1x21)sin(ωτ1)=ω,a(x1x21)cos(ωτ1)=(12x1)[acax1]2u. (3.7)

    According to (3.7), we have

    ω2+[(12x1)(acax1)2u]2=a2(x1x21)2. (3.8)

    Then, we get

    ω1=a2(x1x21)2[(12x1)(acax1)2u]2. (3.9)

    Combining (3.7) and (3.9), the critical time delay is defined as

    τ1c=1ω1arcsin(ω1a(x1x21)). (3.10)

    Theorem 3.2. Suppose ω1>0 holds.

    1) If τ1(0,τ1c), the equilibrium x1 is locally asymptotically stable for system (3.4).

    2) If τ1(τ1c,+), the equilibrium x1 is unstable for system (3.4).

    3) If τ1=τ1c, Hopf bifurcation occurs in the system (3.4) at x1.

    When τ1<τ1c, the internal equilibrium x1 is asymptotically stable. When τ1>τ1c, the internal equilibrium x1 is unstable, showing oscillating dynamics, as shown in Figure 10. Figure 11 shows the phase-portrait of system (3.4). We find that system (3.4) has a Hopf bifurcation when τ1=τ1c and τ2=0 at equilibrium x1. Figure 12 is the bifurcation diagram with τ2=0. We can find that the bifurcation occurs as the time delay increases. The black line indicates that the system has an equilibrium point when the time delay τ1 is slight, and Hopf bifurcation occurs at the critical time delay τ1c. The stable equilibrium point disappears when the time delay increases, and then the system develops a stable limit cycle.

    Figure 10.  Temporal dynamics of delay model (3.4). When a, c and u are definite values, when τ1 is small, the proportion of cooperators tends to be stable, and when τ1 is large, the oscillation dynamics phenomenon occurs.
    Figure 11.  Phase-portrait of delay model (3.4). When a, c and u are definite values, the phase plane tends to be stable when τ1 is small, and the limit cycle appears when τ1 is large.
    Figure 12.  Bifurcation diagram of x when τ1 is the time delay parameter.

    Case 3. τ1=0,τ2>0. Then, system (3.4) becomes

    ˙x(t)=x(t)(1x(t))[acax(t)]+u(12x(tτ2)). (3.11)

    The characteristic equation of system (3.11) at x1 is

    λ(12x1)[acax1]+a(x1x21)+2ueλτ2=0. (3.12)

    Let λ=iω(ω>0) be a root of Eq (3.12), and we get

    iω(12x1)[acax1]+a(xx1)+2ucos(ωτ2)i2usin(ωτ2)=0. (3.13)

    According to (3.13), we obtain

    2usin(ωτ2)=ω,2ucos(ωτ2)=(12x1)[acax1]a(xx21). (3.14)

    Thus, we have

    ω2=4u2[(12x1)(acax1)a(xx21)]2. (3.15)

    We find no explicit solution for satisfying ω1>0 and ω2>0, which means that in most cases, τ1 and τ2 can not work together, that is, τ2 does not affect τ1. Next, we consider the particular case when τ1=τ2>0.

    Case 4. τ1=τ2=τ3>0. The system (3.4) becomes

    ˙x(t)=x(t)(1x(t))[acax(tτ3)]+u(12x(tτ3)). (3.16)

    The characteristic equation of system (3.16) at x1 is

    λ(12x1)[acax1]+[a(x1x21)+2u]eλτ3=0. (3.17)

    Let λ=iω(ω>0) be a root of Eq (3.17), substitute λ=iω(ω>0) into Eq (3.17), and we get

    iω(12x1)[acax1]+[a(x1x21)+2u]cos(ωτ3)[a(x1x21)+2u]sin(ωτ3)=0. (3.18)

    The real and the imaginary parts are separated from Eq (3.18), and we obtain

    [a(x1x21)+2u]sin(ωτ3)=ω,[a(x1x21)+2u]cos(ωτ3)=(12x1)[acax1]. (3.19)

    Thus, we get

    ω3=[a(x1x21)+2u]2[(12x1)(acax1)]2. (3.20)

    From (3.20), we obtain

    τ3c=1ω3arcsinω3[a(x1x21)+2u]. (3.21)

    Theorem 3.3. Suppose ω3>0 holds.

    1) If τ3(0,τ3c), the equilibrium x1 is locally asymptotically stable for system (3.16).

    2) If τ3(τ3c,+), the equilibrium x1 is unstable for system (3.16).

    3) If τ3=τ3c, Hopf bifurcation occurs in system (3.16) at x1.

    When τ1=τ2=τ3, Figure 13 shows the temporal dynamics of delay model (3.16). When the time delay is slight (τ3=0.5), it presents a stable dynamic performance with the time change. When the delay is significant (τ3=0.6), the dynamics behave as oscillation, and the cooperators swing between the two strategies. Figure 14 shows the phase-portrait of system (3.16). The system (3.16) has a Hopf bifurcation when τ3=τ3c at equilibrium x1. Figure 15 is the bifurcation diagram. We find that the bifurcation occurs as the time delay increases. The black line indicates that the equilibrium is stable. The Hopf bifurcation occurs at the critical time delay τ3c. The stable equilibrium point disappears when the time delay increases, and then the system develops a limit cycle.

    Figure 13.  Temporal dynamics of delay model (3.16). When a, c and u are definite values, when τ3 is small, the proportion of cooperators tends to be stable, and when τ3 is large, the oscillation dynamics phenomenon occurs.
    Figure 14.  Phase-portrait of delay model (3.16). When a, c and u are definite values, the phase plane tends to be stable when τ3 is small, and the limit cycle appears when τ3 is large.
    Figure 15.  Bifurcation diagram of x when τ3 is the time delay parameter.

    The classic prisoner's dilemma is dominated by defection, with the percentage of cooperators approaching zero over time. In this paper, we mainly add defection penalty and mutation to the prisoner's dilemma, so that cooperators do not disappear with the change of time. The influence of time delay on the prisoner's dilemma with or without mutation is discussed.

    In Section 2 we study the 2-player prisoner's dilemmas with a penalty. Without considering the time delay, when the given penalty a is greater than the cheated penalty c, the cooperation strategy and defection strategy coexist. The larger a is, the more significant the proportion of final cooperators. Thus, when the penalty for defection is high enough, players tend to cooperate. When time delay is considered, the equilibrium is the same as the replicator equation without time delay. The critical time delay when Hopf bifurcation occurs is obtained. Critical time delay is related to a cheated penalty c and a defect penalty a, and the condition a>c is satisfied. The critical delay τc decreases as the defection penalty a increases. When τ>τc, periodic oscillation occurrs.

    Section 3 considers the case where the mutation is not zero based on penalty and finds that the proportion of cooperators decreases when mutation increases. Then, the system with two delays is studied, in which τ1 is the payoff delay, and τ2 is the mutation delay. Only considering the payoff delay or mutation delay, and in the particular case where the payoff delay and mutation delay are equal, also leads to oscillation. Oscillation due to delay is a general system behavior[28,29].

    Szolnoki and Perc [30] found that the intermediate delay enhances the reciprocity of the network. Wang et al. [31] found that delayed reward supports the spread of cooperation, and the intermediate reward difference between time delays promotes the highest level of cooperation. We find that when the delay is large, the stable state of dynamics is broken, which is not conducive to the stable development of the population.

    This paper considers that players who choose to cooperate or defect have the same probability of mutating to the other player. Considering punishment strategy can help us understand how moral behavior is established and spreads [32,33,34]. In the future, we will consider the evolutionary game dynamics of the prisoner's dilemma with the third strategy to punish defectors under the effect of environmental feedback [35,36], and, on this basis, consider adding mutation affected by environmental interference [37].

    This work is supported by the National Natural Science Foundation of China (No. 12271308), the Shandong Provincial Natural Science Foundation of China (No. ZR2019MA003), the Research Fund for the Taishan Scholar Project of Shandong Province of China.



    [1] Faria T, Almeida-Silva M, Dias A, et al. (2016) Indoor air quality in urban office buildings. Int J Environ Technol Manag 19: 236–256. https://doi.org/10.1504/IJETM.2016.082243. doi: 10.1504/IJETM.2016.082243
    [2] Awad AA, Farag SA (1999) An indoor bio-contaminants air quality. Int J Environ Heal R 9: 313–9. https://doi.org/10.1080/09603129973100. doi: 10.1080/09603129973100
    [3] Gomzi M, Bobic J (2009) Sick building syndrome: Do we live and work in unhealthy environment? Period Biol 111: 1. https://hrcak.srce.hr/35999.
    [4] Budd GM, Warhaft N (1966) Body temperature, shivering, blood pressure and heart rate during a standard cold stress in Australia and Antarctica. J Physiol 186: 216. https://doi.org/10.1113/jphysiol.1966.sp008030. doi: 10.1113/jphysiol.1966.sp008030
    [5] Heinzerling D, Schiavon S, Webster T, et al. (2013) Indoor environmental quality assessment models: a literature review and a proposed weighting and classification scheme. Build Environ 70: 210–222. https://doi.org/10.1016/j.buildenv.2013.08.027. doi: 10.1016/j.buildenv.2013.08.027
    [6] Lan L, Wargocki P, Wyon D.P, et al. (2011) Effects of thermal discomfort in an office on perceived air quality, SBS symptoms, physiological responses, and human performance. Indoor Air 21: 376–390. https://doi.org/10.1111/j.1600-0668.2011.00714.x. doi: 10.1111/j.1600-0668.2011.00714.x
    [7] Spengler JD, Sexton K (1983) Indoor air pollution: a public health perspective. Science 221: 9–17. https://doi.org/10.1126/science.6857273. doi: 10.1126/science.6857273
    [8] Sun YP, Zhu N (2012) Study on assessment of high temperature and humidity in working environment on human health. Adv Mat Res 610: 739–742. https://doi.org/10.4028/www.scientific.net/amr.610-613.739. doi: 10.4028/www.scientific.net/amr.610-613.739
    [9] Vehvil€ainen T, Lindholm H, Rintam€aki H, et al. (2016) High indoor CO< sub> 2< /sub> concentrations in an office environment increases the transcutaneous CO< sub> 2< /sub> level and sleepiness during cognitive work. J Occup Environ Hyg 13: 19–29. https://doi.org/10.1080/15459624.2015.1076160. doi: 10.1080/15459624.2015.1076160
    [10] Xue P, Mak CM, Ai ZT (2016) A structured approach to overall environmental satisfaction in high-rise residential buildings. Energy Build 116: 181–189. https://doi.org/10.1016/j.enbuild.2016.01.006_ doi: 10.1016/j.enbuild.2016.01.006
    [11] Zhang X, Wargocki PZ (2011) Lian, Human responses to carbon dioxide, a follow-up study at recommended exposure limits in non-industrial environments. Build Environ 100: 162–171. https://doi.org/10.1016/j.buildenv.2016.02.014. doi: 10.1016/j.buildenv.2016.02.014
    [12] Pegas PN, Alves CA, Evtyugina MG, et al. (2011) Indoor air quality in elementary schools of Lisbon in spring. Environ Geochem Health 33: 455–468. https://doi.org/10.1007/s10653-010-9345-3. doi: 10.1007/s10653-010-9345-3
    [13] Bradman A, Gaspar F, Castorina R, et al. (2012) Environmental exposures in early childhood education environments. Retrieved on 16 December 2022 from https://ww2.arb.ca.gov/sites/default/iles/classic/research/apr/past/-305.pdf
    [14] Branco PT, Nunes RA, Alvim-Ferraz MC, et al. (2015) Children's exposure to indoor air in urban nurseries–part Ⅱ: gaseous pollutants' assessment. Environ Res 142: 662–670. https://doi.org/10.1016/j.envres.2015.08.026 doi: 10.1016/j.envres.2015.08.026
    [15] Branco P, Alvim-Ferraz MCM, Martins FG, et al. (2019) Quantifying indoor air quality determinants in urban and rural nursery and primary schools. Environ Res 176: 108534. https://doi.org/10.1016/j.envres.2019.108534 doi: 10.1016/j.envres.2019.108534
    [16] Hoang T, Castorina R, Gaspar F, et al. (2017) VOC exposures in California early childhood education environments. Indoor Air 27: 609–621. https://doi.org/10.1111/ina.12340 doi: 10.1111/ina.12340
    [17] Zhang S, Mumovic D, Stamp S, et al. (2021) What do we know about indoor air quality of nurseries? A review of the literature. Build Serv Eng Res Technol 42: 603–632. https://doi.org/10.1177/01436244211009829 doi: 10.1177/01436244211009829
    [18] World Health Organization. Regional Office for E. (2010) WHO guidelines for indoor air quality: selected pollutants. Copenhagen: World Health Organization. Regional Office for Europe https://iris.who.int/handle/10665/260127.
    [19] Krzyzanowski M, Quackenboss JJ, Lebowitz MD (1990) Chronic respiratory effects of indoor formaldehyde exposure. Environ Res 52: 117–125. https://doi.org/10.1016/S0013-9351(05)80247-6. doi: 10.1016/S0013-9351(05)80247-6
    [20] Zomorodian M, Tahsildoost M, Hafezi M (2016) Thermal comfort in educational buildings: A review article. Renewable and Sustainable Energy Revi 59: 895–906. https://doi.org/10.1016/j.rser.2016.01.033. doi: 10.1016/j.rser.2016.01.033
    [21] Gaihre S, Semple S, Miller J, et al. (2014) Classroom carbon dioxide concentration, school attendance, and educational attainment. J Sch Health 84: 569–574. https://doi.org/10.1111/josh.12183. doi: 10.1111/josh.12183
    [22] Aglan HA (2003) Predictive model for CO< sub> 2< /sub> generation and decay in building envelopes. J Appl Phys 93: 1287–1290. https://doi.org/10.1063/1.1529992. doi: 10.1063/1.1529992
    [23] Caruana-Montaldo B, Gleeson K, Zwillich CW (2000) The control of breathing in clinical practice. Chest 117: 205–225. https://doi.org/10.1378/chest.117.1.205. doi: 10.1378/chest.117.1.205
    [24] Cheng C, Matsukawa T, Sessler DI, et al. (1995) Increasing mean skin temperature linearly reduces the core-temperature thresholds for vasoconstriction and shivering in humans. J Am Soc Anesthesiol 82: 1160–1168, https://doi.org/10.1097/00000542-199505000-00011. doi: 10.1097/00000542-199505000-00011
    [25] Evans P, Bristow M, Hucklebridge F, et al. (1994) Stress, arousal, cortisol and secretory immunoglobulin A in students undergoing assessment. Br J Clin Psychol 33: 575–576, https://doi.org/10.1111/j.2044-8260.1994.tb01154.x. doi: 10.1111/j.2044-8260.1994.tb01154.x
    [26] Hamilton M, Rackes A, Gurian PL, et al. (2015) Perceptions in the US building industry of the benefits and costs of improving indoor air quality. Indoor Air 26: 318–330. https://doi.org/10.1111/ina.12192. doi: 10.1111/ina.12192
    [27] H€oppe P, Oohori T, Berglund L, et al. (2000) Vapor resistance of clothing and its effect on human response during and after exercise, in: Proc. CLIMA, 2000, pp. 97–101, 1985.
    [28] Jaggs M, Palmer J (2000) Energy performance indoor environmental quality retrofit—a European diagnosis and decision making method for building refurbishment. Energy Build 31: 97–101. https://doi.org/10.1016/S0378-7788(99)00023-7. doi: 10.1016/S0378-7788(99)00023-7
    [29] Kim J, Hong T, Jeong J, et al. (2016) An optimization model for selecting the optimal green systems by considering the thermal comfort and energy consumption, Appl Energy 169: 682–695. https://doi.org/10.1016/j.apenergy.2016.02.032. doi: 10.1016/j.apenergy.2016.02.032
    [30] McCunney RJ (2001), Health and productivity. J Occup Environ Med 43: 30–34. https://doi.org/10.1097/00043764-200101000-00007. doi: 10.1097/00043764-200101000-00007
    [31] Reynolds SJ, Black DW, Borin SS, et al, (2001) Indoor environmental quality in six commercial office buildings in the Midwest United States. Appl Occup Environ Hyg 16: 1065–1077. https://doi.org/10.1080/104732201753214170. doi: 10.1080/104732201753214170
    [32] Varjo J, Hongisto V, Haapakangas A, et al. (2015) Simultaneous effects of irrelevant speech, temperature and ventilation rate on performance and satisfaction in open-plan offices. J Environ Psychol 44: 16–33. https://doi.org/10.1016/j.jenvp.2015.08.001. doi: 10.1016/j.jenvp.2015.08.001
    [33] Wood TM, Bhat KM (1988) Methods for measuring cellulase activities. Methods Enzymol 160: 87–112. https://doi.org/10.1016/0076-6879(88)60109-1. doi: 10.1016/0076-6879(88)60109-1
    [34] ASHRAE, Standard 62.1. 2013. Ventilation for Acceptable Indoor Air Quality, American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc, Atlanta, GA, 2013.
    [35] Daisey JM, Angell WJ, Apte MG (2003) Indoor air quality, ventilation and health symptoms in schools: an analysis of existing information. Indoor Air 13: 53–64. https://doi.org/10.1034/j.1600-0668.2003.00153.x. doi: 10.1034/j.1600-0668.2003.00153.x
    [36] Kajtar L, Herczeg L. (2012) Influence of carbon-dioxide concentration on human well- being and intensity of mental work. QJ Hung Meteorol Serv 116: 145–169.
    [37] Kim J, de Dear R (2012) Nonlinear relationships between individual IEQ factors and overall workspace satisfaction. Build Environ 49: 33–40. https://doi.org/10.1016/j.buildenv.2011.09.022. doi: 10.1016/j.buildenv.2011.09.022
    [38] Muthuraj K, Othmani C, Krause R, et al. (2024) A convolutional neural network to control sound level for air conditioning units in four different classroom conditions (2024). Energy Build 324: 114913 https://doi.org/10.1016/j.enbuild.2024.114913 doi: 10.1016/j.enbuild.2024.114913
    [39] Othmani C, Sebastian Merchel S, Altinsoy ME, et al. (2023) Acoustic Travel-Time TOMography Technique to Reconstruct the Indoor Temperature: How to Improve the Field Reconstruction Quality? IEEE T Instrum Meas 73 https://doi.org/10.1109/TIM.2023.3335531 doi: 10.1109/TIM.2023.3335531
    [40] Othmani C, Dokhanchi NS, Merchel S, et al. (2023) Acoustic tomographic reconstruction of temperature and flow fields with focus on atmosphere and enclosed spaces: A review. Appl Therm Eng 223: 119953. https://doi.org/10.1016/j.applthermaleng.2022.119953 doi: 10.1016/j.applthermaleng.2022.119953
    [41] Gauderman WJ, Vora H, McConnell R, et al. (2007) Effect of exposure to traffic on lung development from 10 to 18 years of age: a cohort study. Lancet 369: 571–577. https://doi.org/10.1016/S0140-6736(07)60037-3. doi: 10.1016/S0140-6736(07)60037-3
    [42] Fracchia L, Pietronave S, Rinaldi M, et al. (2006). The assessment of airborne bacterial contamination in three composting plants revealed site related biological hazard and seasonal variations. J Appl Microbiol 100: 973–984.
    [43] Gorny R L, Reponen T, Willeke k, et al. (2002). Fungal fragments as indoor air biocontaminnts. Appl Enviro Microbiol 68: 3522–3531.
    [44] Park DU, Yeom JK, Lee WJ, et al. (2013) Assessment of the levels of airborne bacteria, Gram-negative bacteria, and fungi in hospital lobbies. Int J Environ Res Public Health 10: 541–555. https://doi.org/10.3390/ijerph10020541. doi: 10.3390/ijerph10020541
    [45] Stryjakowska-Sekulska M, Piotraszewska-Pająk A, Szyszka A, et al. (2007) Microbiological Quality of Indoor Air in University Rooms. Pol J Environ Stud 16: 623–632.
    [46] Gołofit-Szymczak M, Górny RL (2010) Bacterial and fungal aerosols in air-conditioned office buildings in Warsaw, Poland--the winter season. Int J Occup Saf Ergon. 16: 465–476. https://doi.org/10.1080/10803548.2010.11076861. doi: 10.1080/10803548.2010.11076861
    [47] Diriba L, Kassaye A, Yared M (2016) Identification, Characterization and Antibiotic Susceptibility of Indoor Airborne Bacteria in Selected Wards of Hawassa University Teaching and Referral Hospital, South Ethiopia. OALib 01: 1–12. http://dx.doi.org/10.4236/oalib.preprints.1200012. doi: 10.4236/oalib.preprints.1200012
    [48] Fujiyoshi S, Tanaka D, Maruyama F (2017) Transmission of Airborne Bacteria across Built Environments and Its Measurement Standards: A Review. Front Microbiol 8: 2336. https://doi.org/10.3389/fmicb.2017.02336. doi: 10.3389/fmicb.2017.02336
    [49] Fabian P, Miller S, Reponen T, et al. (2005) Ambient bioaerosol indices for air quality assessments of flood reclamation. J Aerosol Sci 36: 763–783. https://doi.org/10.1016/j.jaerosci.2004.11.018. doi: 10.1016/j.jaerosci.2004.11.018
    [50] Fang X, Zhou Y, Yang Y, et al. (2007) Prevalence and risk factors of trichomoniasis, bacterial vaginosis, and candidiasis for married women of child-bearing age in rural Shandong. Jpn J Infect Dis 60: 257–261.
    [51] Frank W Raumklima, thermische Behaglichkeit (1975) Literaturauswertung durchgeführt im auftrage des Bundesministers für Raumordnung, Bauwesen und Städtebau. Berlin: W Ernst
    [52] Klindworth A, Pruesse E, Schweer T, et al. (2013) Evaluation of general 16S ribosomal RNA gene PCR primers for classical and next-generation sequencing-based diversity studies. Nucleic Acids Res 41: e1. https://doi.org/10.1093/nar/gks808. doi: 10.1093/nar/gks808
    [53] Minot S, Krumm N, Greenfield N (2015) A Sensitive and Accurate Data Platform for Genomic Microbial Identification. bioRxiv https://doi.org/10.1101/027607.
    [54] Siegwald L, Touzet H, Lemoine Y, et al. (2017) Assessment of Common and Emerging Bioinformatics Pipelines for Targeted Metagenomics. PLoS One 12: e0169563. https://doi.org/10.1371/journal.pone.0169563. doi: 10.1371/journal.pone.0169563
    [55] ANSI/ASHRAE (2001) Ventilation for acceptable indoor air quality: American Society of Heating, Refrigerating and Air-Conditioning Engineers.
    [56] Hoffmann B, Boogaard H, de Nazelle A, et al. (2021) WHO Air Quality Guidelines 2021-Aiming for Healthier Air for all: A Joint Statement by Medical, Public Health, Scientific Societies and Patient Representative Organisations. Int J Public Health 66: 1604465. https://doi.org/10.3389/ijph.2021.1604465. doi: 10.3389/ijph.2021.1604465
    [57] Danger R, Moiteaux Q, Feseha Y, et al. (2021) A web application for regular laboratory data analyses. PLOS ONE 16: e0261083. https://doi.org/10.1371/journal.pone.0261083. doi: 10.1371/journal.pone.0261083
    [58] Soares S, Fraga S, Delgado JM, et al. (2015) Influence of Indoor Hygrothermal Conditions on Human Quality of Life in Social Housing. J Public Health Res 4: 589. https://doi.org/10.4081/jphr.2015.589. doi: 10.4081/jphr.2015.589
    [59] He Y, Luo Q, Ge P, et al. (2018) Review on Mould Contamination and Hygrothermal Effect in Indoor Environment. J Environ Prot 09: 100–110. https://doi.org/10.4236/jep.2018.92008. doi: 10.4236/jep.2018.92008
    [60] Wolkoff P, Azuma K, Carrer P (2021) Health, work performance, and risk of infection in office-like environments: The role of indoor temperature, air humidity, and ventilation. Int J Hyg Environ Health 233: 113709. https://doi.org/10.1016/j.ijheh.2021.113709. doi: 10.1016/j.ijheh.2021.113709
    [61] Arar M, Jung C (2021) Improving the Indoor Air Quality in Nursery Buildings in United Arab Emirates. Int J Environ Res Public Health 18: 12091. https://doi.org/10.3390/ijerph182212091. doi: 10.3390/ijerph182212091
    [62] Branco PT, Alvim-Ferraz MC, Martins FG, et al. (2015) Children's exposure to indoor air in urban nurseries-part Ⅰ: CO2 and comfort assessment. Environ Res 140: 1–9. https://doi.org/10.1016/j.envres.2015.03.007. doi: 10.1016/j.envres.2015.03.007
    [63] Branco P, Alvim-Ferraz MCM, Martins FG, et al. (2019) Quantifying indoor air quality determinants in urban and rural nursery and primary schools. Environ Res 176: 108534. https://doi.org/10.1016/j.envres.2019.108534. doi: 10.1016/j.envres.2019.108534
    [64] Mečiarová Ľ, Vilčeková S, Krídlová Burdová E, et al. (2018) The real and subjective indoor environmental quality in schools. Int J Environ Health Res 28: 102–123. https://doi.org/10.1080/09603123.2018.1429579. doi: 10.1080/09603123.2018.1429579
    [65] Ruggieri S, Longo V, Perrino C, et al. (2019) Indoor air quality in schools of a highly polluted south Mediterranean area. Indoor Air 29: 276–290. https://doi.org/10.1111/ina.12529. doi: 10.1111/ina.12529
    [66] Sá JP, Branco P, Alvim-Ferraz MCM, et al. (2017) Evaluation of Low-Cost Mitigation Measures Implemented to Improve Air Quality in Nursery and Primary Schools. Int J Environ Res Public Health 14: 585. https://doi.org/10.3390/ijerph14060585. doi: 10.3390/ijerph14060585
    [67] Vassella CC, Koch J, Henzi A, et al. (2021) From spontaneous to strategic natural window ventilation: Improving indoor air quality in Swiss schools. Int J Hyg Environ Health 234: 113746. https://doi.org/10.1016/j.ijheh.2021.113746. doi: 10.1016/j.ijheh.2021.113746
    [68] Villanueva F, Notario A, Cabañas B, et al. (2021) Assessment of CO(2) and aerosol (PM(2.5), PM(10), UFP) concentrations during the reopening of schools in the COVID-19 pandemic: The case of a metropolitan area in Central-Southern Spain. Environ Res 197: 111092. https://doi.org/10.1016/j.envres.2021.111092. doi: 10.1016/j.envres.2021.111092
    [69] Simoni M, Annesi-Maesano I, Sigsgaard T, et al. (2010) School air quality related to dry cough, rhinitis and nasal patency in children. Eur Respir J 35: 742–749. https://doi.org/10.1183/09031936.00016309. doi: 10.1183/09031936.00016309
    [70] Michelot N, Marchand C, Ramalho O, et al. Monitoring indoor air quality in French schools and day-care centres. Results from the first phase of a pilot survey. Healthy Buildings 2012, 10th International Conference; 2012 2012-07-08; Brisbane, Australia https://hal.archives-ouvertes.fr/hal-00747458/document, https://hal.archives-ouvertes.fr/hal-00747458/file/2012-286_post-print.pdf.
    [71] Clausen G, Toftum J, Andersen B. Indeklima i klasseværelser - resultater af Masseeksperiment 2014. (2014) Indoor Environment in Classrooms - Results of the Mass Experiment.
    [72] Hanoune B, Carteret M (2015) Impact of kerosene space heaters on indoor air quality. Chemosphere 134: 581–587. https://doi.org/10.1016/j.chemosphere.2014.10.083. doi: 10.1016/j.chemosphere.2014.10.083
    [73] Brdarić D, Capak K, Gvozdić V, et al. (2019) Indoor carbon dioxide concentrations in Croatian elementary school classrooms during the heating season. Arh Hig Rada Toksikol 70: 296–302. https://doi.org/10.2478/aiht-2019-70-3343. doi: 10.2478/aiht-2019-70-3343
    [74] Jovanović M, Vučićević B, Turanjanin V, et al. (2014) Investigation of indoor and outdoor air quality of the classrooms at a school in Serbia. Energy 77: 42–48. https://doi.org/10.1016/j.energy.2014.03.080. doi: 10.1016/j.energy.2014.03.080
    [75] Yuan WM, Lu YQ, Wei Z, et al. (2016) An Epistaxis Emergency Associated with Multiple Pollutants in Elementary Students. Biomedical and environmental sciences: BES. 29: 893–897. http://www.besjournal.com/Articles/Archive/2016/No12/201701/t20170112_137315.html.
    [76] Neamtiu IA, Lin S, Chen M, et al. (2019) Assessment of formaldehyde levels in relation to respiratory and allergic symptoms in children from Alba County schools, Romania. Environ Monit Assess 191: 591. https://doi.org/10.1007/s10661-019-7768-6. doi: 10.1007/s10661-019-7768-6
    [77] Zhu YD, Li X, Fan L, et al. (2021) Indoor air quality in the primary school of China-results from CIEHS 2018 study. Environ Pollut 291: 118094. https://doi.org/10.1016/j.envpol.2021.118094. doi: 10.1016/j.envpol.2021.118094
    [78] Santos Catai AS, Petruci JFS, Cardoso AA (2024) Compact colorimetric method for determining formaldehyde in indoor air: Applying to an environment contaminated with hand sanitizer vapor. Build Environ 257: 111546. https://doi.org/10.1016/j.buildenv.2024.111546. doi: 10.1016/j.buildenv.2024.111546
    [79] Matic B, Rakic U, Jovanovic V, et al. (2017) Key Factors Determining Indoor Air PM(10) Concentrations in Naturally Ventilated Primary Schools in Belgrade, Serbia. Zdr Varst 56: 227–235. https://doi.org/10.1515/sjph-2017-0031. doi: 10.1515/sjph-2017-0031
    [80] Branis M, Rezácová P, Domasová M (2005) The effect of outdoor air and indoor human activity on mass concentrations of PM(10), PM(2.5), and PM(1) in a classroom. Environ Res 99: 143–149. https://doi.org/10.1016/j.envres.2004.12.001. doi: 10.1016/j.envres.2004.12.001
    [81] Tran D, Alleman L, Coddeville P, et al. (2012) Elemental characterization and source identification of size resolved atmospheric particles in French classrooms. Atmos Environ 54 : 250–259. https://doi.org/10.1016/j.atmosenv.2012.02.021. doi: 10.1016/j.atmosenv.2012.02.021
    [82] Oliveira M, Slezakova K, Delerue-Matos C, et al. (2019) Children environmental exposure to particulate matter and polycyclic aromatic hydrocarbons and biomonitoring in school environments: A review on indoor and outdoor exposure levels, major sources and health impacts. Environ Int 124: 180–204. https://doi.org/10.1016/j.envint.2018.12.052. doi: 10.1016/j.envint.2018.12.052
    [83] Moriske HJ, Drews M, Ebert G, et al. (1996) Indoor air pollution by different heating systems: coal burning, open fireplace and central heating. Toxicol Lett 88: 349–354. https://doi.org/10.1016/0378-4274(96)03760-5. doi: 10.1016/0378-4274(96)03760-5
    [84] Ruiz PA, Toro C, Cáceres J, et al. (2010) Effect of gas and kerosene space heaters on indoor air quality: a study in homes of Santiago, Chile. J Air Waste Manag Assoc 60: 98–108. https://doi.org/10.3155/1047-3289.60.1.98. doi: 10.3155/1047-3289.60.1.98
    [85] Hong B, Qin H, Jiang R, et al. (2018) How Outdoor Trees Affect Indoor Particulate Matter Dispersion: CFD Simulations in a Naturally Ventilated Auditorium. Int J Environ Res Public Health 15: 2862. https://doi.org/10.3390/ijerph15122862. doi: 10.3390/ijerph15122862
    [86] Reimer LC, Sardà Carbasse J, Koblitz J, et al. (2022) the knowledge base for standardized bacterial and archaeal data. Nucleic Acids Res 50: D741–D746. https://doi.org/10.1093/nar/gkab961. doi: 10.1093/nar/gkab961
    [87] Findley K, Oh J, Yang J, et al. (2013) Topographic diversity of fungal and bacterial communities in human skin. Nature 498: 367–370. https://doi.org/10.1038/nature12171. doi: 10.1038/nature12171
    [88] Madsen AM, Moslehi-Jenabian S, Islam MZ, et al. (2018) Concentrations of Staphylococcus species in indoor air as associated with other bacteria, season, relative humidity, air change rate, and S. aureus-positive occupants. Environ Res 160: 282–291. https://doi.org/10.1016/j.envres.2017.10.001. doi: 10.1016/j.envres.2017.10.001
  • This article has been cited by:

    1. Ahmed Hassouna, Mohammed Hassan, Mohamed Elnaggar, Mohammed Alnahhal, Bader Abd Al Gafoor, Saed Kaware, 2021, Novel Solar Parabolic Trough Collector System for Electrical Generation and Heating/Cooling Purposes, 978-1-6654-1662-7, 24, 10.1109/ICPET53277.2021.00011
    2. Diego A. Flores-Hernández, Alberto Luviano-Juárez, Norma Lozada-Castillo, Octavio Gutiérrez-Frías, César Domínguez, Ignacio Antón, Optimal Strategy for the Improvement of the Overall Performance of Dual-Axis Solar Tracking Systems, 2021, 14, 1996-1073, 7795, 10.3390/en14227795
    3. Soufyane Naaim, Badr Ouhammou, Mohammed Aggour, Brahim Daouchi, El Mahdi El Mers, Miriam Mihi, Multi-Utility Solar Thermal Systems: Harnessing Parabolic Trough Concentrator Using SAM Software for Diverse Industrial and Residential Applications, 2024, 17, 1996-1073, 3685, 10.3390/en17153685
    4. Lalit Mohan Pant, Dali Ramu Burada, Mahendra Pratap Singh, Gufran Sayeed Khan, Chandra Shakher, Investigations on the measurement of freeform optical wavefront using a holo-shear lens, 2025, 64, 1559-128X, 1775, 10.1364/AO.549564
  • Reader Comments
  • © 2025 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Metrics

Article views(521) PDF downloads(105) Cited by(0)

Figures and Tables

Figures(7)  /  Tables(3)

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog