Mathematical Model for Dengue Transmission Dynamics

Abstract

Dengue is a rapidly emerging pandemic disease in many parts of the world, especially in tropical and non-tropical areas. The dengue outbreak has a multisectoral impact on the medical, societal, economical, and political sectors. Dengue incidence has increased in Sri Lanka over the past 20 years, with deaths and illnesses. Almost all the districts in Sri Lanka have reported cases and posed a threat to the health of the people. Dengue fever is caused by dengue virus, first recorded in the 1960s in Sri Lanka. In this study, we propose a mathematical model to describe the transmission of dengue with a standard incidence rate for both human and vector populations. The impact of treatment capacity in the case of an epidemic scenario has been studied by using a constant treatment function. The equilibrium points and the basic reproduction number are computed. The conditions leading to the diseasefree and endemic equilibrium are determined. We observed that the reproduction number affects the asymptotic stability for both disease-free and endemic equilibrium points. The Lyapunov function theory is used to discuss the global stability. Based on actual data of infective population gathered from the Institute of Epidemiology Unit Ministry of Health in Sri Lanka, the parameters for infection and disease-related death rates are estimated. Numerical simulations of various compartments are used to investigate the impact of the key parameters affecting the disease’s transmission.