The Role of Control Measures and the Environment in the Transmission Dynamics of Cholera

Abstract

Cholera is an infectious intestinal disease which occurs as a result of poor sanitation and lack of basic education in its transmission. It is characterized by profuse vomiting and severe diarrhea when an individual eats food or drinks water contaminated with the Vibrio cholerae. A dynamic mathematical model that explicitly simulates the transmission mechanism of cholera by taking into account the role of control measures and the environment in the transmission of the disease is developed. e model comprises two populations: the human population and bacteria population. e next-generation method is used to compute the basic reproduction number, R 0 . Both the disease-free and endemic equilibria are shown to be locally and globally stable for R 0 values less than unity and unstable otherwise. Necessary conditions of the optimal control problem were analyzed using Pontryagin's maximum principle with control measures such as educational campaign and treatment of water bodies used to optimize the objective function. Numerical values of model parameters were estimated using the nonlinear least square method. e model simulations confirm the significant role played by control measures (education and treatment of water bodies) and the bacteria in the environment in the transmission dynamics as well as reducing the spread of cholera.

Reliable numerical treatment with Adams and BDF methods for plant virus propagation model by vector with impact of time lag and density

“…Several mathematical models have been established to provide a detailed exposition of how to analyze, interpret, and forecast plant pathogenic farming epidemics as a mechanism for formulating and testing crop countermeasures and control measures [1][2][3][4]. A variety of epidemiology models based upon those used mostly in animal or human epidemiology have been created to assess the population ecosystem of viral infections [5][6][7][8][9][10]. The delay differential equations can be used to define relatively different formulations of epidemic proliferation.…”

A dynamic optimal control model for COVID-19 and cholera co-infection in Yemen

“…Likewise, Kobe et al in [4] suggested a game model of cholera that allows individuals to select one of two programs: vaccinations or clean water consumption. Another related study is that of NKDO Opoku, and Afriyie, C. in [5]. They developed a mathematical model of cholera transmission dynamics of cholera and investigated the following two control measures: education campaign and treatment of water bodies.…”

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