MATHEMATICAL MODELING OF CHOLERA TRANSMISSION IN EPIDEMIC AND ENDEMIC SETTINGS WITH CONTROL STRATEGIES

Sunday Nwokpoku  Aloke; Patrick Agwu  Okpara; Nnaemeka Majindu; Nelson Nnamdi  Ezieke

Sunday Nwokpoku Aloke Department of Industrial Mathematics and Health Statistics, David Umahi Fed- eral University of Health Sciences, Uburu, Ebonyi State, Nigeria.
Patrick Agwu Okpara Department of Industrial Mathematics and Health Statistics, David Umahi Federal University of Health Sciences, Uburu, Ebonyi State, Nigeria.
Nnaemeka Majindu Department of Industrial Mathematics and Health Statistics, David Umahi Federal University of Health Sciences, Uburu, Ebonyi State, Nigeria.
Nelson Nnamdi Ezieke Department of Industrial Mathematics and Health Statistics, David Umahi Federal University of Health Sciences, Uburu, Ebonyi State, Nigeria.

Keywords: vaccination, water treatment and sanitation, optimal control, Stability

Abstract

One of the most serious health issues in the world today is cholera, particularly in poorer nations with poor access to clean water. We have examined the distribution of cholera in both endemic and epidemic settings in this article. We develop the mathematical model of the dynamics of cholera transmission known as SEIRH with controls. The time-dependent control mechanisms (vaccine, water purication, and sanitation) that govern the disease's transmission and management were incorporated into the model. It was possible to acquire the potential key measure R₀, a threshold value used to forecast the prognosis of a disease. The stability of the endemic disease equilibrium point (EEP) and the cholera-free equilibrium point (DFEP) was examined. If R₀ is less than 1, then DFEP is locally asymptotically stable (LAS), and EEP is globally asymptotically stable (GAS) when R₀ is greater than 1. The impact of control measures on virus spread was investigated, and the optimal control value that minimizes the objective function was also investigated using Pontryagin's maximum principle. The model simulation shows that the methods used have a positive impact on public health by lowering morbidity and mortality. Cholera incidence can be considerably decreased by effective prevention and control measures, which will lower rates of morbidity and mortality.

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