
Indoor radon exposure poses significant health risks and has prompted testing and mitigation programs in regions such as Europe, North America, Japan, and South Korea. However, African countries have not adopted similar measures on a comparable scale. Limited research on radon exposure in Africa can be attributed to a lack of awareness among policymakers and the public, insufficient expertise in radiation protection and measurements, and restricted access to resources such as laboratories and testing equipment. This review examines existing research articles on radon exposure conducted in African countries, focusing on the efforts made by specific nations, such as Tunisia and Sudan, to address this issue. It analyzes the scope, scale, and impact of these initiatives compared to global efforts in managing radon exposure risks. The findings reveal that the study of radon exposure in Africa is still in its early stages, with limited progress and modest initiatives compared to other regions. While some efforts have been made, they are insufficient to effectively address the significant health risks associated with radon exposure. There is an urgent need for African policymakers and researchers to prioritize radon exposure as a public health issue. Developing frameworks, standards, and mitigation strategies is essential to reduce risks in homes and workplaces. This review emphasizes the importance of addressing radon exposure in African countries and offers recommendations to guide future research and policy development.
Citation: Leonel J.R. Nunes, António Curado. Indoor radon exposure in Africa: A critical review on the current research stage and knowledge gaps[J]. AIMS Public Health, 2025, 12(2): 329-359. doi: 10.3934/publichealth.2025020
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Indoor radon exposure poses significant health risks and has prompted testing and mitigation programs in regions such as Europe, North America, Japan, and South Korea. However, African countries have not adopted similar measures on a comparable scale. Limited research on radon exposure in Africa can be attributed to a lack of awareness among policymakers and the public, insufficient expertise in radiation protection and measurements, and restricted access to resources such as laboratories and testing equipment. This review examines existing research articles on radon exposure conducted in African countries, focusing on the efforts made by specific nations, such as Tunisia and Sudan, to address this issue. It analyzes the scope, scale, and impact of these initiatives compared to global efforts in managing radon exposure risks. The findings reveal that the study of radon exposure in Africa is still in its early stages, with limited progress and modest initiatives compared to other regions. While some efforts have been made, they are insufficient to effectively address the significant health risks associated with radon exposure. There is an urgent need for African policymakers and researchers to prioritize radon exposure as a public health issue. Developing frameworks, standards, and mitigation strategies is essential to reduce risks in homes and workplaces. This review emphasizes the importance of addressing radon exposure in African countries and offers recommendations to guide future research and policy development.
In December 2019, the world is facing the emergence of a new pandemic, which is called coronavirus disease 2019 (COVID-19). Then, COVID-19 spreads to world widely over the first two months in 2020. There were 492,510 confirmed cases of COVID-19 infection and 22,185 dead cases in world [1], [2]. Therefore, it poses a continuing threat to human health because of its high transmission efficiency and serious infection consequences as well, it transmits by direct contact. Many researchers have tried to study and understand the dynamical behavior of COVID-19 through the transmission dynamics and calculate the basic reproduction number of COVID-19. It has become a key quantity to determine the spread of epidemics and control it. For example, in [3], Li et al. conducted a study of the first 425 confirmed cases in Wuhan, China, showing that the reproduction number of COVID-19 was 2.2, and revealed that person to person transmission occurred between close contacts. Other research [4] shows that the reproduction number of COVID-19 becomes 2.90, which is being increasing. In [5], Riou et al. studied pattern of early human to human transmission of COVID-19 in Wuhan, China. In [6], Hellewell et al. investigated the feasibility of controlling 2019-nCoV outbreaks by isolation of cases and contacts. Chen et al.[7], suggested mathematical model for simulation the phase-based transmissibility of novel coronavirus. Bentout et al. [8] developed an susceptible exposed infectious recovered model to estimation and prediction for COVID-19 in Algeria. Belgaid et al.[9] suggested and analysis of a model for Coronavirus spread. Owolabi et al. [10] proposed and analyzed a nonlinear epidemiological model for SARS CoV-2 virus with quarantine class. Flaxman et al. [11] suggested and estimating the effects of non-pharmaceutical interventions on COVID-19 in Europe. Kennedy et al. [12] suggested a mathematical model involving the effects of intervention strategies on COVID-19 transmission dynamics. Feng et al. [13] studied a COVID-19 model with the effects of media and quarantine in UK. In this present study, we will show effects of the quarantine strategy and media reports on the spread of COVID-19.
We propose a mathematical model for COVID-19 transmission dynamics with the quarantine strategy and media effects. We start the model formulation by denoting the total size of the population by N which is classified further into five classes, the susceptible S(t), the exposed E(t), the infected I(t), the hospital quarantined Q(t) and the recovery R(t) at any time t, So,
And the corresponding dynamical model has formulated through the nonlinear differential equations as follows,
with initial conditions
In model (1), the birth rate A is taken into susceptible class and natural death rate of population is given by the parameter d. The susceptible will be infected through sufficient direct contacts with infected people in the absence of media alerts by
It is easy see that the 4th and 5th equations are a linear differential equation with respect to variables I(t) and R(t), which are not appear in the other equations of model (1). Hence model (1) can be reduced to the following model:
In this paper, we will discuss the dynamics of model (3) with initial conditions
This paper is organized as follows. In section 2, we will build the basic properties of model such as (positivity, boundedness of solutions and basic reproduction number). Existence of equilibrium points is presented in section 3. In section, the phenomenon of backward bifurcation is considered. The local and global stability of equilibrium points are studied in sections 4. In section 5, numerical simulation results are given. We conclude this paper with a brief conclusion.
On the positivity of solutions for model (3), we have the following result.
Theorem 2.1 Every solution of (3) with initial values (4) is positive as t > 0.
Proof. Let
which can be written as
thus,
so that
Similarly, it can be shown that E(t) > 0 and I(t) > 0 for all time t > 0. Hence all solutions of the model (3) remain positive for all non-negative initial conditions, as required.
Theorem 2.2 All solutions of model (1) which initiate in
Proof. Define the function
Now, it is easy to verify that the solution of the above linear differential inequalities can be written as
where
and
It is easy to see that model (3) always has a disease-free equilibrium
Consequently, from Theorem 2 of [14], we have the following result.
Theorem 2.3 The disease-free equilibrium
The basic reproduction number for COVID-19 infection
In this section, we consider the number of equilibrium solutions the model (3). To do so, let
here
Since we assume
where
From (15), we can find that
Cases | D1 | D2 | D3 | D4 | D5 | R0 | Number of sign changes | Number of possible positive real roots |
1 | − | + | + | + | + | ℛ0 > 1 | 1 | 1 |
− | + | + | + | − | ℛ0 < 1 | 2 | 0,2 | |
2 | − | + | + | − | + | ℛ0 > 1 | 3 | 1,3 |
− | + | + | − | − | ℛ0 < 1 | 2 | 0,2 | |
3 | − | + | − | + | + | ℛ0 > 1 | 3 | 1,3 |
− | + | − | + | − | ℛ0 < 1 | 4 | 0,2,4 | |
4 | − | + | − | − | + | ℛ0 > 1 | 3 | 1,3 |
− | + | − | − | − | ℛ0 < 1 | 2 | 0,2 | |
5 | − | − | + | + | + | ℛ0 > 1 | 1 | 1 |
− | − | + | + | − | ℛ0 < 1 | 2 | 0,2 | |
6 | − | − | + | − | + | ℛ0 > 1 | 3 | 1,3 |
− | − | + | − | − | ℛ0 < 1 | 2 | 0,2 | |
7 | − | − | − | + | + | ℛ0 > 1 | 1 | 1 |
− | − | − | + | − | ℛ0 < 1 | 2 | 0,2 | |
8 | − | − | − | − | + | ℛ0 > 1 | 1 | 1 |
− | − | − | − | − | ℛ0 < 1 | 0 | 0 |
Theorem 3.1 The model (3)
(i) has a unique endemic equilibrium if
(ii) could have more than one endemic equilibrium if
(iii) could have 2 or more endemic equilibria if
From the 4th and 5th equations of model (1) we can determent the values of Q* and R* through
The existence of multiple endemic equilibria when
Theorem 3.2 The model (3) exhibits backward bifurcation whenever
Proof. To prove existence of backward bifurcation in the model (3) the Center Manifold approach as outlined by Castillo-Chavez and Song in [17] is used.
Firstly, for clarity and understanding of the Center Manifold Theory the model (3) variables are transformed as follows
Now let
With
It is easy to obtain the right eigenvectors of this Jacobian matrix as
First the non-vanishing partial derivatives of the transformed model (17) evaluated at COVID-19 free equilibrium are obtained as
so that
The sign of the bifurcation parameter b is associated with the following non-vanishing partial derivatives of F(X), also evaluated at the disease free equilibrium
The bifurcation coefficient b is obtained as
Obviously, b is always positive. From Theorem 3.2 the system (17) will exhibit backward bifurcation phenomena if the bifurcation coefficient a is positive. The positivity of a in (22) gives the condition for backward bifurcation, which leads to
In this section, the stability analysis of the all equilibrium points of model (3) studied as shown in the following theorems by used some criterion.
Theorem 4.1 The COVID-19 equilibrium point P* of the model (3) is locally asymptotically if the following conditions are hold
Proof. The Jacobian matrix of model (3) at
here
clearly, the characteristics equation of J(P*) is given by
where
furthermore, we have that
Now, according to Routh-huewitz criterion P* will be locally asymptotically stable provided that
The purpose of this section is to investigate the global stability by using Lyapunov function for COVID-19 free equilibrium point and COVID-19 equilibrium point respectively. We obtain the result in the following theorems
Theorem 4.2 The disease-free equilibrium
Proof. Consider the following function
clearly,
now, by doing some algebraic manipulation and using the condition (33), we get
Obviously,
Theorem 4.3 P* in case i of Th. (3.1) is globally asymptotically stable if
Proof. At the COVID-19 equilibrium point
By above equations (4.4) and assumptions
we obtian
now, define the Lyapunov function
clearly, by derivative of
Since the arithmetical mean is greater than, or equal to the geometrical mean, then
For the parameters values of model (1.1), we can chosen the parameters values from real data available sense Feb. 24 2020 to Apr. 5 2020. The total population of the Iraq for the year 2020 is approximately 40 × 106
Parameter | Definition | Value | Source |
A | Birth rate | 1541.8 | [19] |
β1 | Transmission contact rate between S and I | 0.5 | Estimated |
c | Fraction constant | [0–1] | Estimated |
β2 | Awareness rate | 0.1 | Estimated |
m | Half saturation of media constant | 70 | Estimated |
d | Natural death rate | 3.854510−5 | [19],[20] |
k | Fraction denoting the level of exogenous re-infection | 0.05 | Estimated |
ϵ | Quarantined rate | 1/7 | [13] |
γ1 | Recovery rate from infected wihout quarantin strategy | 0.033 | Estimated |
γ2 | Recovery rate from quarantin class | 1/18 | [13] |
µ | Death due to disease rate | 0.38 | [19] |
We plot the solution trajectories of model (1) with initial point (15,20,500,1000,150) which converges to COVID-19 equilibrium point P*=(1,27,2773,5428,19371), shown that in Figure 2.
No. | Date | Government measures | β1 |
1 | Feb. 24 2020 | (1) detection of the first case of COVID-19 in Iraq | 0.3 |
(2) quarantined as preliminary control | |||
2 | Feb. 25 2020 | (1) medical examination for all individuals who are in contact with the affected case | 0.1 |
(2) cancellation of some mass gatherings | |||
(3) increase the awareness programs about prevention measures | |||
3 | Feb. 25-Mar. 24 2020 | (1) cancellation of all religious and social events throughout Iraq | 0.09 |
(2) preventing movement between all provinces | |||
(3) the suspension of attendance at universities and schools | |||
(4) providing a number of hospitals to be places for prevention confirmed cases | |||
4 | Mar. 24-Apr. 5 2020 | (1) close all borders with neighboring countries | 0.08 |
(2) to declare a state of emergency and impose a curfew | |||
(3) medical support from the government | |||
(4) methodological improvement on the diagnosis and treatment strategy | |||
(5) spontaneous household quarantine by citizens | |||
(6) more newly-hospitals put into use | |||
(7) massive online teaching in postponed semester | |||
(8) addition of new diagnosis method clinically diagnosis in Baghdad and some provinces |
In the face of the COVID-19 outbreak, many stringent measures were taken by Iraqi government will show in
The following
Clearly, from above figure for effect of contact rate
No. | Date | Government measures | ϵ |
1 | Feb. 24 2020 | (1) quarantined as preliminary control in Iraq | 0.2 |
2 | Feb. 25 2020 | (1) medical examination for all individuals who are in contact with the affected case | 0.4 |
(2) cancellation of some mass gatherings | |||
(3) increase the awareness programs about prevention measures | |||
3 | Feb. 25-Mar. 24 2020 | (1) direct the media to explain the symptoms of the epidemic | 2.5 |
(2) Preventing movement between all provinces | |||
(3) Providing a number of hospitals to be places for prevention confirmed cases | |||
4 | Mar. 24-Apr. 5 2020 | (1) to declare a state of emergency and impose a curfew to reduce the contact between people | 4.5 |
(2) medical support from the government | |||
(3) methodological improvement on the diagnosis and treatment strategy | |||
(4) spontaneous household quarantine by citizens | |||
(5) addition of new diagnosis method clinically diagnosis in Baghdad and some provinces |
The following
Clearly, from above investigate to impact of the quarantined strategy Table 4, when the quarantine strategy increasing we get the number of infected is decrease and other classes are increase. Here, we ask whether the quarantine strategy is the best solution? The answer is possible, but for specific numbers. Whereas, if the quarantine is more than the capacity of the health institutions. We get the dynamical behavior of model (1.1) lose the stability as shown in Figure 5.
In this research, a mathematical model of COVID-19 transmission has been proposed by compartment the total population into five epidemiological status, namely, susceptible S(t), exposed E(t), infected I(t), quarantine Q(t) and recovered R(t). The model incorporates the impact of social awareness programs conducted by public health officials with quarantine strategy in hospital. It has been noticed that these awareness programs and quarantine strategy result in human behavioral changes in order to avoid risk of disease transmission. The model mainly accounts for the reduction in disease class due to awareness. While we can say the disease goes away due to applied the quarantine it well. The proposed model has two biological equilibrium points are COVID-19 free and COVID-19. The COVID-19 free has been local stability when
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Cases | D1 | D2 | D3 | D4 | D5 | R0 | Number of sign changes | Number of possible positive real roots |
1 | − | + | + | + | + | ℛ0 > 1 | 1 | 1 |
− | + | + | + | − | ℛ0 < 1 | 2 | 0,2 | |
2 | − | + | + | − | + | ℛ0 > 1 | 3 | 1,3 |
− | + | + | − | − | ℛ0 < 1 | 2 | 0,2 | |
3 | − | + | − | + | + | ℛ0 > 1 | 3 | 1,3 |
− | + | − | + | − | ℛ0 < 1 | 4 | 0,2,4 | |
4 | − | + | − | − | + | ℛ0 > 1 | 3 | 1,3 |
− | + | − | − | − | ℛ0 < 1 | 2 | 0,2 | |
5 | − | − | + | + | + | ℛ0 > 1 | 1 | 1 |
− | − | + | + | − | ℛ0 < 1 | 2 | 0,2 | |
6 | − | − | + | − | + | ℛ0 > 1 | 3 | 1,3 |
− | − | + | − | − | ℛ0 < 1 | 2 | 0,2 | |
7 | − | − | − | + | + | ℛ0 > 1 | 1 | 1 |
− | − | − | + | − | ℛ0 < 1 | 2 | 0,2 | |
8 | − | − | − | − | + | ℛ0 > 1 | 1 | 1 |
− | − | − | − | − | ℛ0 < 1 | 0 | 0 |
Parameter | Definition | Value | Source |
A | Birth rate | 1541.8 | [19] |
β1 | Transmission contact rate between S and I | 0.5 | Estimated |
c | Fraction constant | [0–1] | Estimated |
β2 | Awareness rate | 0.1 | Estimated |
m | Half saturation of media constant | 70 | Estimated |
d | Natural death rate | 3.854510−5 | [19],[20] |
k | Fraction denoting the level of exogenous re-infection | 0.05 | Estimated |
ϵ | Quarantined rate | 1/7 | [13] |
γ1 | Recovery rate from infected wihout quarantin strategy | 0.033 | Estimated |
γ2 | Recovery rate from quarantin class | 1/18 | [13] |
µ | Death due to disease rate | 0.38 | [19] |
No. | Date | Government measures | β1 |
1 | Feb. 24 2020 | (1) detection of the first case of COVID-19 in Iraq | 0.3 |
(2) quarantined as preliminary control | |||
2 | Feb. 25 2020 | (1) medical examination for all individuals who are in contact with the affected case | 0.1 |
(2) cancellation of some mass gatherings | |||
(3) increase the awareness programs about prevention measures | |||
3 | Feb. 25-Mar. 24 2020 | (1) cancellation of all religious and social events throughout Iraq | 0.09 |
(2) preventing movement between all provinces | |||
(3) the suspension of attendance at universities and schools | |||
(4) providing a number of hospitals to be places for prevention confirmed cases | |||
4 | Mar. 24-Apr. 5 2020 | (1) close all borders with neighboring countries | 0.08 |
(2) to declare a state of emergency and impose a curfew | |||
(3) medical support from the government | |||
(4) methodological improvement on the diagnosis and treatment strategy | |||
(5) spontaneous household quarantine by citizens | |||
(6) more newly-hospitals put into use | |||
(7) massive online teaching in postponed semester | |||
(8) addition of new diagnosis method clinically diagnosis in Baghdad and some provinces |
No. | Date | Government measures | ϵ |
1 | Feb. 24 2020 | (1) quarantined as preliminary control in Iraq | 0.2 |
2 | Feb. 25 2020 | (1) medical examination for all individuals who are in contact with the affected case | 0.4 |
(2) cancellation of some mass gatherings | |||
(3) increase the awareness programs about prevention measures | |||
3 | Feb. 25-Mar. 24 2020 | (1) direct the media to explain the symptoms of the epidemic | 2.5 |
(2) Preventing movement between all provinces | |||
(3) Providing a number of hospitals to be places for prevention confirmed cases | |||
4 | Mar. 24-Apr. 5 2020 | (1) to declare a state of emergency and impose a curfew to reduce the contact between people | 4.5 |
(2) medical support from the government | |||
(3) methodological improvement on the diagnosis and treatment strategy | |||
(4) spontaneous household quarantine by citizens | |||
(5) addition of new diagnosis method clinically diagnosis in Baghdad and some provinces |
Cases | D1 | D2 | D3 | D4 | D5 | R0 | Number of sign changes | Number of possible positive real roots |
1 | − | + | + | + | + | ℛ0 > 1 | 1 | 1 |
− | + | + | + | − | ℛ0 < 1 | 2 | 0,2 | |
2 | − | + | + | − | + | ℛ0 > 1 | 3 | 1,3 |
− | + | + | − | − | ℛ0 < 1 | 2 | 0,2 | |
3 | − | + | − | + | + | ℛ0 > 1 | 3 | 1,3 |
− | + | − | + | − | ℛ0 < 1 | 4 | 0,2,4 | |
4 | − | + | − | − | + | ℛ0 > 1 | 3 | 1,3 |
− | + | − | − | − | ℛ0 < 1 | 2 | 0,2 | |
5 | − | − | + | + | + | ℛ0 > 1 | 1 | 1 |
− | − | + | + | − | ℛ0 < 1 | 2 | 0,2 | |
6 | − | − | + | − | + | ℛ0 > 1 | 3 | 1,3 |
− | − | + | − | − | ℛ0 < 1 | 2 | 0,2 | |
7 | − | − | − | + | + | ℛ0 > 1 | 1 | 1 |
− | − | − | + | − | ℛ0 < 1 | 2 | 0,2 | |
8 | − | − | − | − | + | ℛ0 > 1 | 1 | 1 |
− | − | − | − | − | ℛ0 < 1 | 0 | 0 |
Parameter | Definition | Value | Source |
A | Birth rate | 1541.8 | [19] |
β1 | Transmission contact rate between S and I | 0.5 | Estimated |
c | Fraction constant | [0–1] | Estimated |
β2 | Awareness rate | 0.1 | Estimated |
m | Half saturation of media constant | 70 | Estimated |
d | Natural death rate | 3.854510−5 | [19],[20] |
k | Fraction denoting the level of exogenous re-infection | 0.05 | Estimated |
ϵ | Quarantined rate | 1/7 | [13] |
γ1 | Recovery rate from infected wihout quarantin strategy | 0.033 | Estimated |
γ2 | Recovery rate from quarantin class | 1/18 | [13] |
µ | Death due to disease rate | 0.38 | [19] |
No. | Date | Government measures | β1 |
1 | Feb. 24 2020 | (1) detection of the first case of COVID-19 in Iraq | 0.3 |
(2) quarantined as preliminary control | |||
2 | Feb. 25 2020 | (1) medical examination for all individuals who are in contact with the affected case | 0.1 |
(2) cancellation of some mass gatherings | |||
(3) increase the awareness programs about prevention measures | |||
3 | Feb. 25-Mar. 24 2020 | (1) cancellation of all religious and social events throughout Iraq | 0.09 |
(2) preventing movement between all provinces | |||
(3) the suspension of attendance at universities and schools | |||
(4) providing a number of hospitals to be places for prevention confirmed cases | |||
4 | Mar. 24-Apr. 5 2020 | (1) close all borders with neighboring countries | 0.08 |
(2) to declare a state of emergency and impose a curfew | |||
(3) medical support from the government | |||
(4) methodological improvement on the diagnosis and treatment strategy | |||
(5) spontaneous household quarantine by citizens | |||
(6) more newly-hospitals put into use | |||
(7) massive online teaching in postponed semester | |||
(8) addition of new diagnosis method clinically diagnosis in Baghdad and some provinces |
No. | Date | Government measures | ϵ |
1 | Feb. 24 2020 | (1) quarantined as preliminary control in Iraq | 0.2 |
2 | Feb. 25 2020 | (1) medical examination for all individuals who are in contact with the affected case | 0.4 |
(2) cancellation of some mass gatherings | |||
(3) increase the awareness programs about prevention measures | |||
3 | Feb. 25-Mar. 24 2020 | (1) direct the media to explain the symptoms of the epidemic | 2.5 |
(2) Preventing movement between all provinces | |||
(3) Providing a number of hospitals to be places for prevention confirmed cases | |||
4 | Mar. 24-Apr. 5 2020 | (1) to declare a state of emergency and impose a curfew to reduce the contact between people | 4.5 |
(2) medical support from the government | |||
(3) methodological improvement on the diagnosis and treatment strategy | |||
(4) spontaneous household quarantine by citizens | |||
(5) addition of new diagnosis method clinically diagnosis in Baghdad and some provinces |