Abstract
The purpose of this study is to see whether it is possible to eradicate the disease theoretically using mathematical modeling with the aid of numerical simulation when disease occurs in a population by implementing adequate preventive measures. For this, we consider a mathematical model for the transmission dynamics of cholera and its preventive measure as one cohort of individuals, namely, a protected cohort in addition to susceptible, infected, and recovered cohorts of individuals including the concentration ofVibrio choleraein the contaminated aquatic reservoir with small modifications. We calculate the basic reproduction number,ℛ0, and investigate the existence and stability of equilibria. The model possessed forward bifurcation. Moreover, we compute the sensitivity indices of each parameter in relating toℛ0of the model. Numerical simulations are carried out to validate our theoretical results. The result indicates that the disease dies out in areas with adequate preventive measures and widespread and kills more people in areas with the inadequate preventive measures.
Highlights
Introduction e cholera epidemic is a fatal waterborne disease causing diarrhea, dehydration, and vomiting in an individual [1, 2]. It is caused by a bacterium called Vibrio cholerae
Cholera is transmitted through ingesting contaminated drinks and food, contact with cholera patient’s feces, and touching vomit and corpse killed by the bacterium without using protective agents [1,2,3]. e incubation period of cholera is less than 24 hours to 5 days. e infection is frequently asymptomatic
Epidemiologists and other researchers use mathematical modeling and numerical simulation for scientific understanding about the dynamics and preventive method of an infectious disease, for determining sensitivities, changes of parameter values, and to forecasting [5, 9,10,11,12,13,14,15,16,17,18,19]. e models are based on cohorts, International Journal of Mathematics and Mathematical Sciences namely, susceptible, infected, and recovered, for individual population incorporated with some preventive measures such as treatment, vaccination, chlorination, hygienic, and sanitation through education
Summary
We divided the population denoted by N(t) according to the infection status into S(t)- susceptible, I(t)- infected, R(t)- recovered, and U(t)- prevented individuals at given time t. We assumed that the adequate preventing measures are using of safe water for drinking, washing, and food preparation; disposing feces in a sanitary manner; removing or washing any bedding or clothing that might have contact with cholera-infected people; restraining a cholera-infected person from swimming even until two weeks after individuals recover; washing hands always with soap and clean water before preparing food, eating, feeding children, after using a latrine, and taking care of patients with diarrhea; cleaning food preparation areas; and storing treated water and food in clean and covered containers Based on these assumptions and the flow diagram, we formulate the following SIRUB model, which is a system of nonlinear autonomous ordinary differential equations: dS bN +(1 − p)ρR − (1 − p)β B + pα + μS, dt. The domain of biological significance is positively invariant and attracting. erefore, the dynamical system in equation (1) has a unique bounded positive solution in Ω
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