An age-structured mathematical model for studying Malaria transmission dynamics: Applications to some areas of Senegal

Abstract

In this work, we formulate an age-structured model for studying the transmission of Malaria for both human and vector populations. First, we perform an analytical study of this model. To do so, we analyze the positivity and boundedness of solutions and study the stability of the Disease-Free Equilibrium (using a matrix-tree theorem). Then, we focus on the study of the Endemic Equilibrium. Applying a methodology grounded in graph theory, we prove that, under certain assumptions, the Endemic Equilibrium is both unique and globally asymptotically stable. We also conjecture that this result holds true even in cases where these assumptions are not met. While this conjecture remains unproven, it is supported by illustrative numerical experiments. Secondly, we illustrate the interest of our approach by considering real data from two specific areas in Senegal affected by Malaria, namely Dielmo and Ndiop. In particular, we estimate some of the model parameters for these zones and illustrate how the proposed model may help to estimate the behavior of Malaria outbreaks.