Exploring the effects of awareness and time delay in controlling malaria disease propagation

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 (ℛ0) is less than unity (ℛ0 < 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.

Mathematical Modelling and Optimal Control of Malaria Using Awareness-Based Interventions

“…In this research, it is assumed additionally that the infected human recovered by awarenessinduced treatment, and after recovery, they will join the aware human population, which is more realistic. In the proposed model, 'level of awareness' is taken as a model variable, increasing due to awareness campaigns (as adopted by Al Basir et al [22]). The local awareness (due to the information from local people and relatives) and global awareness (due to radio and TV campaigns) are also included in the model.…”

“…To the extent of our familiarity, there needs to be more model-based research on malaria disease dynamics with the influence of awareness campaigns [12,22,23]. In [23], a mathematical model for malaria disease was proposed to avoid the illness by separating the infected population into two groups, unaware and aware infected individuals.…”

“…Besides the effect of the awareness campaign, the aware infected individuals avoid contact with mosquitoes. Authors in [22] resulting a mathematical model for reviewing the dynamics of malaria disease and the influence of awareness-based interventions for control of the same, that depend on 'level of awareness'. They supposed that the disease spread rates, from vector to human and from human to vector, as declining functions of 'level of awareness'.…”

“…The model captures this fact with the term 1 g + H a M . In the modeling development, it is assumed that media movements increase the level of awareness concerning personal protection and the way of controlling mosquito population [22].…”

“…Biological meanings of variables, parameters used in the model(1) and Values of the parameters used for numerical simulations[22,28].…”