Exploring the effects of awareness and time delay in controlling malaria disease propagation
Fahad Al Basir, Arnab Banerjee, Santanu Ray
Abstract
Abstract In this article, a mathematical model has been derived for studying the dynamics of malaria disease and the influence of awareness-based interventions, for control of the same, that depend on ‘level of awareness’. We have assumed the disease transmission rates from vector to human and from human to vector, as decreasing functions of ‘level of awareness’. The effect of insecticides for controlling the mosquito population is influenced by the level of awareness, modelled using a saturated term. Organizing any awareness campaign takes time. Therefore a time delay has been incorporated in the model. Some basic mathematical properties such as nonnegativity and boundedness of solutions, feasibility and stability of equilibria have been analysed. The basic reproduction number is derived which depends on media coverage. We found two equilibria of the model namely the disease-free and endemic equilibrium. Disease-free equilibrium is stable if basic reproduction number (ℛ 0 ) is less than unity (ℛ 0 < 1). Stability switches occur through Hopf bifurcation when time delay crosses a critical value. Numerical simulations confirm the main results. It has been established that awareness campaign in the form of using different control measures can lead to eradication of malaria.