Mathematical modeling for the transmission dynamics of cholera with an optimal control strategy

Cholera is an acute diarrheal disease caused by Vibrio cholera, its prevalence occurs in almost all the continents of the world, annually there are about 1.3 to 4.0 million cases of cholera and 21,000 to 143,000 deaths worldwide. In this paper, we propose a deterministic model for the transmission dynamics of cholera to assess the impact of vaccines in decreasing the spread of cholera infection in Nigeria. Moreover, we develop an optimal control strategy, in which we consider personal hygiene a control strategy on infection class, with u(t) as the control function. The best values of the fitting parameters have been obtained using least square minimization to validate the model with the help of experimental data obtained from Nigeria. We perform sensitivity analysis to determine the key parameters that have impacts on the control of the spread of cholera infections in the population. In addition, the numerical simulation of the model reveals that the use of vaccines and personal hygiene will effectively control the spread of cholera infection.