Highlights COVID-19 modeling transmission using known theory concerning the disease transmission and control strategies . Formulation of a mathematical model for the COVID-19 that incorporates some key epidemiological and biological features. Sensitivity analysis of the model. Theoretical studies and numerical simulations.

a b s t r a c tIn this paper, we investigate the impact of environmental factors on the dynamical transmission of cholera within a human community. We propose a mathematical model for the dynamical transmission of cholera that incorporates the virulence of bacteria and the commensalism relationship between bacteria and the aquatic reservoirs on the persistence of the disease. We provide a theoretical study of the model. We derive the basic reproduction number R 0 which determines the extinction and the persistence of the infection. We show that the disease-free equilibrium is globally asymptotically stable whenever R 0 ≤ 1 , while when R 0 > 1 , the disease-free equilibrium is unstable and there exists a unique endemic equilibrium point which is locally asymptotically stable on a positively invariant region of the positive orthant. The sensitivity analysis of the model has been performed in order to determine the impact of related parameters on outbreak severity. Theoretical results are supported by numerical simulations, which further suggest the necessity to implement sanitation campaigns of aquatic environments by using suitable products against the bacteria during the periods of growth of aquatic reservoirs.

In this paper, we propose and analyse a mathematical model of the transmission dynamics of cholera incorporating awareness programs to study the impact of socio-media and education on cholera outbreaks. These programs induce behavioural changes in the population, which divide the susceptible class into two subclasses, aware individuals and unaware individuals. We first provide a basic study of the model. We compute the Disease-Free Equilibrium (DFE) and derive the basic reproduction number R 0 0 ${\mathcal{R}}_{0}^{0}$ that determines the extinction and the persistence of the disease. We show that there exists a threshold parameter ξ such that when R 0 0 ≤ ξ < 1 ${\mathcal{R}}_{0}^{0}\le \xi < 1$ , the DFE is globally asymptotically stable, but when ξ ≤ R 0 0 < 1 $\xi \le {\mathcal{R}}_{0}^{0}< 1$ , the model exhibits the phenomenon of backward bifurcation on a feasible region. The model exhibits one endemic equilibrium locally stable when R 0 0 > 1 ${\mathcal{R}}_{0}^{0} > 1$ and in that condition the DFE is unstable. Various cases for awareness proportions are performed using the critical awareness rate in order to measure the effect of awareness programs on the infected individuals over time. The results we obtained show that the higher implementation of strategies combining awareness programs and therapeutic treatments increase the efficacy of control measures. The numerical simulations of the model are used to illustrate analytical results and give more precision on critical values on the controls actions.

In this paper, we studied the impact of sensitization and sanitation as possible control actions to curtail the spread of cholera epidemic within a human community. Firstly, we combined a model of Vibrio Cholerae with a generic SIRS cholera model. Classical control strategies in terms of the sensitization of population and sanitation are integrated through the impulsive differential equations. Then we presented the theoretical analysis of the model. More precisely, we computed the disease free equilibrium. We derive the basic reproduction number [Formula: see text] which determines the extinction and the persistence of the infection. We show that the trivial disease-free equilibrium is globally asymptotically stable whenever [Formula: see text], while when [Formula: see text], the trivial disease-free equilibrium is unstable and there exists a unique endemic equilibrium point which is globally asymptotically stable. Theoretical results are supported by numerical simulations, which further suggest that the control of cholera should consider both sensitization and sanitation, with a strong focus on the latter.

A mathematical model for Vibrio Cholerae (V. Cholerae) in a closed environment is considered, with the aim of investigating the impact of climatic factors which exerts a direct influence on the bacterial metabolism and on the bacterial reservoir capacity. We first propose a V. Cholerae mathematical model in a closed environment. A sensitivity analysis using the eFast method was performed to show the most important parameters of the model. After, we extend this V. cholerae model by taking account climatic factors that influence the bacterial reservoir capacity. We present the theoretical analysis of the model. More precisely, we compute equilibria and study their stabilities. The stability of equilibria was investigated using the theory of periodic cooperative systems with a concave nonlinearity. Theoretical results are supported by numerical simulations which further suggest the necessity to implement sanitation campaigns of aquatic environments by using suitable products against the bacteria during the periods of growth of aquatic reservoirs.

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