A mathematical and exploratory data analysis of malaria disease transmission through blood transfusion - Adeniyi, Michael O.; Aderele, Oluwaseun R.; Oludoun, Olajumoke Y.; Ekum, Matthew I.; Matadi, Maba B.; Oke, Segun I.; Ntiamoah, Daniel (Frontiers in Applied Mathematics and Statistics, 2023)
Malaria is a mosquito-borne disease transmitted through an infected vector (infected female Anopheles mosquito) or through transfusion of infected blood with the plasmodium to susceptible individuals. The disease burden has led to high mortality globally, especially in children under age five. Many intervention responses such as Long-Lasting Insecticide bed nets (LLIN), Treatment using an anti-malaria drug, spraying chemical/pesticides on mosquito breeding sites, and indoor residual spray among others has been implemented to control malaria disease transmission. Consequently, a SIR (Susceptible - Infected - Recovered) model was developed to study the impact of the various controls and mitigation strategies to reduce the spread of malaria. The stability analysis of the model equilibrium points is studied using the associated basic reproduction number and stability theory. The global stability of the malaria-free equilibrium is studied by constructing an appropriate Lyapunov function. The implicit function theorem is employed to study the stability of the model endemic equilibrium by determining the direction of bifurcation. The model is fitted to malaria data for Benue State, Nigeria using R and MATLAB. Parameter estimations were performed. Subsequently, an optimal control model is formulated and analyzed based on Pontryaging’s Maximum Principle. Numerical simulations were performed to validate the analytical results of the model.