Modeling and Stability Analysis of the Dynamics of Malaria Disease Transmission with Some Control Strategies - Alemzewde Ayalew; Yezbalem Molla; Amsalu Woldegbreal (Abstract and Applied Analysis)
In this study, we proposed and analyzed a nonlinear deterministic mathematical model of malaria transmission dynamics. In addition to the previous approaches, we incorporated the class of aware people and other control measures. We established the wellposedness of the model, and the asymptotic behavior of the solutions is rigorously studied depending on the basic reproduction number R0. The model system admits two equilibrium points: disease-free and disease-persistent equilibrium points. The analytical result of the model system revealed that the disease-free equilibrium point is both locally as well as globally asymptotically stable whenever R0<1 while the disease-persistence equilibrium point is globally asymptotically stable whenever R0>1. Moreover, the forward bifurcation phenomenon of the model system for R0=1 was analyzed by using center manifold theory. A sensitivity analysis of the basic reproduction number was performed to identify parameters that will cause to trigger the transmission of malaria disease and should be targeted by control strategies. Then, the model was extended to the optimal control problem, with the use of three time-dependent controls, namely, preventive measures(treated bednets and indoor residual spraying), continuous awareness campaigns to susceptible individuals, and treatment for infected individuals. By using Pontryan’s maximum principle, necessary conditions for the transmission of malaria disease were derived. Numerical simulations are illustrated by using MATLAB ode45 to validate the theoretical results of the model. The numerical findings of the optimal model suggested that integrated control strategies are better than a sole intervention to eliminate malaria disease.