A Mathematical Model for a Single Strain Dengue Disease with Control in Aquatic and Adult Phase

Abstract

Dengue is a mosquito-borne viral infection found in urban and semi-urban areas of the tropical and subtropical regions around the world causes millions of death in every year. Dengue has no proper vaccination; vector control remains the only available strategy to prevent the disease. A mathematical model has been formulated to investigate the control strategies of the disease. The qualitative analysis of the model includes the calculation of basic reproduction number using the next generation operator approach. The method of estimation of the effective reproduction number R(t) for actual epidemic has been explored. The local stability analysis of the disease free and endemic equilibrium points has been studied. It is found that the disease free equilibrium point is stable for R₀ < 1, otherwise it is unstable. The endemic equilibrium point exists for R₀ > 1. The figure of the basic reproduction number versus control parameters in aquatic and adult phase suggests that if the controls increase basic reproduction number (R₀) becomes less than one consequently the disease die out from the system. In this context, the control in aquatic phase is more effective than adult phase.