Theoretical assessment of the impact of awareness programs on cholera transmission dynamic

Abstract

Abstract 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.