Mathematical Analysis of Basic Reproduction Number for the Spread and Control of Malaria Model with Non-Drug Compliant Humans

Malaria arises when there is an infection of a host by Plasmodium falciparum that causes malaria in humans. Non-drug compliance results from not taking medication as prescribed by doctors. Previous research had concentrated on mathematical modeling of transmission dynamics of malaria without considering some infectious humans who do not comply to drug. This study is therefore designed to model transmission dynamics of malaria taking into consideration some infectious humans who do not comply to drug. The model is formulated using nonlinear ordinary differential equations. The human population is partitioned into Susceptible human $(S_H)$, Exposed Human $E_H$, Infectious human $(I_H)$, Non-drug compliant human $I_{NH}$ and Recovered human $(R_H)$. Using next generation matrix, the reproduction number $R_0$ is obtained. This is used to analyse the global stability of the disease-free equilibria and local stability of the endemic equilibria of the model. The global stability of the disease-free equilibria and the local stability of the endemic equilibrium of the model are established through the construction of suitable Lyapunov function and analysis of characteristic equation. It is shown that the disease-free equilibrium is globally asymptotically stable whenever $R_o< 1$. It is also shown that the endemic equilibrium becomes stable through the Routh-Hurwitz stability criteria