Modeling global asymptotic stability of malaria dynamics with structured infectious population

Abstract

Over the last few decades, malaria has become a serious risk to public health, particularly in tropical and sub-tropical areas where the climate is favorable for mosquito breeding. These insects are the primary carriers of the disease, transmitting it to humans through their bites. Here, we have formulated a mathematical framework that explores malaria transmission, incorporating a structured infectious population. Numerous dynamical system methodologies are instrumentalized in studying the malaria model in human-vector interacting populations. Firstly, we have proved that the model state variables has non-negative and bounded solutions throughout time. Then, we have obtained the threshold parameter \({\mathcal {R}}_m,\) by employing the next generation operator approach. We have proved that the proposed malaria model is stable locally and globally in an asymptotic manner by calculating the Jacobian matrix and Lyapunov function theory if \({\mathcal {R}}_m<1\). The malaria model is shown to have a unique endemic equilibrium point whenever the basic reproductive number \({\mathcal {R}}_m>1\). Consequently, the unique malaria-endemic steady point of the proposed malaria model is proven to be globally stable provided that \({\mathcal {R}}_m>1\). Sensitivity analysis is conducted to capture the most significant parameter causing malaria transmission and controlling in the human population. Furthermore, simulations are performed to support the qualitative results of the study, and the results are graphically presented.