A fractional-order SEIAR-SEI model for malaria dynamics incorporating climatic factors

Abstract

This study extends the SEIR-SEI malaria model to a SEIAR-SEI framework, integrating climatic factors such as rainfall and temperature. In conflict-affected regions such as Sudan, malaria, a devastating disease, persists as a significant public health challenge, leading to the loss of thousands of lives annually, with children being disproportionately affected. It is essential to develop innovative tools aimed at combating the mosquitoes that transmit malaria. Additionally, the model is enhanced by including fractional derivatives in the Caputo–Riemann–Liouville sense, effectively capturing memory effects. We employ the Laplace transform to verify the non-negativity conditions of the solutions, utilizing the Mittag-Leffler function. The existence and uniqueness of solutions are established via fixed point theory and the Lipschitz condition. Furthermore, we compute the basic reproduction number and conduct a comprehensive analysis of the stability of the disease-free equilibrium. To derive numerical solutions, we introduce an innovative numerical method based on the Adams–Bashforth scheme, which we implement using MATLAB.