A mathematical model of cholera in a periodic environment with control actions

Abstract

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.

Effect of Time Delay in the Stability Analysis of Cholera Epidemic-Endemic Disease Model

“…Under stress, this pathogen assumes a viable but not culturable state, becoming undetectable to traditional bacteriological techniques (Codeco, 2001;Colwell, 1996). Classical control strategies in terms of the sensitization of population and sanitation are integrated through the impulsive differential equations (Kolaye et al, 2020). More recently, (Martins et al, 2022) in their study of mathematical model for prevention and control of cholera transmission in a variable population developed an extended SIRB deterministic epidemiological model for cholera and strictly analyzed it to ascertain the impact of immigration in cholera transmission and to assess the suitability of the various control measures (also see Olaniyi and Ogbonna, 2021).…”

Gaining Profound Knowledge of Cholera Outbreak: The Significance of the Allee Effect on Bacterial Population Growth and Its Implications for Human-Environment Health

“…We also proposed a mathematical model of cholera in a periodic environment with public health worker interventions such as sanitation or campaign awareness. In this study, we combined the bacteria model that we developed and studied in [7] with a S-I-R-S human cholera model in [8]. The findings showed that the control cholera should consider both sensitization and sanitation with a strong focus on sanitation.…”