Mathematical Modeling and Analysis of the Dynamics of Chikungunya in Bangladesh

Abstract

Chikungunya is one of the major public health problems in Bangladesh and the effect of the disease is more virulent over the country. In this paper, a compartmental mathematical model has been proposed that describes the transmission of chikungunya disease in Bangladesh. Nonlinear incidence rate is considered for disease transmission and the system of nonlinear differential equations is developed to represent the model. Furthermore, the treatment term has been introduced in the model. The basic reproduction number, which is a biological threshold parameter for this disease, has been computed for the model by the method of next generation matrix. Disease free and endemic equilibrium points are calculated and the stability of the model has been analyzed using the basic reproduction number. The global stability has been established using the Lyapunov function theory. In this study, we have calculated the numerical value of the basic reproduction number and performed numerical simulations based on the real data collected from several health institutes of Bangladesh. Both analytical and numerical results provide a pattern about the dynamics of the disease in Bangladesh. Based on the effects, some important policies and insights are provided that might help in reducing the number of infected cases of chikungunya.