Impact of awareness to control malaria disease: a mathematical modeling approach. (English) Zbl 1454.92029
Summary: The mathematical modeling of malaria disease has a crucial role in understanding the insights of the transmission dynamics and corresponding appropriate prevention strategies. In this study, a novel nonlinear mathematical model for malaria disease has been proposed. To prevent the disease, we divided the infected population into two groups, unaware and aware infected individuals. The growth rate of awareness programs impacting the population is assumed to be proportional to the unaware infected individuals. It is further assumed that, due to the effect of awareness campaign, the aware infected individuals avoid contact with mosquitoes. The positivity and the boundedness of solutions have been derived through the completing differential process. Local and global stability analysis of disease-free equilibrium has been investigated via basic reproductive number \(R_0\), if \(R_0 < 1\), the system is stable otherwise unstable. The existence of the unique endemic equilibrium has been also determined under certain conditions. The solution to the proposed model is derived through an iterative numerical technique, the Runge-Kutta method. The proposed model is simulated for different numeric values of the population of humans and anopheles in each class. The results show that a significant increase in the population of susceptible humans is achieved in addition to the decrease in the population of the infected mosquitoes.
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