Exploring Lie Symmetry Analysis within a Nonlinear System Characterizing Endemic Malaria

This book chapter delves into the integrability of a nonlinear system characterized by the emergence of endemic Malaria, utilizing Prelle-Singer and Lie symmetry analysis techniques. The model involves three nonlinear differential equations representing interactions among susceptible humans, infected humans, and infected mosquitoes. Through examining the biological plausibility of the proposed model and scrutinizing the integrability of the nonlinear system, this study sheds light on its dynamics. Furthermore, it showcases the integrability of the model through the presentation of an explicit solution. Additionally, exact invariant solutions of the model are derived by employing the obtained infinitesimal generators and corresponding similarity reduction equations, enriching our comprehension of the system’s behaviour and potential strategies for combating Malaria.