Analysis of the transmission dynamics and effects of containment strategies on the eradication of malaria

A debilitating disease such as malaria has been a global health challenge for a long time. Mathematical models have provided insights on how best to control, prevent, or eradicate the disease. Most of the models used parameters to represent control strategies. The current research aims at using control strategies as disease compartments for both vector control and human-protection. By this, the long-time evolution of containment measures can be assessed. Consequently, a model of nine disease compartments is constructed using first-order ordinary differential equations. A qualitative analysis of the malaria-free equilibrium was carried out. The results indicate that the malaria-free equilibrium state is locally and globally asymptotically stable when $R_{0HV}<1$, which implies that the disease-free state will always be attained from any initial conditions. A bifurcation analysis also shows that the malaria-endemic and malaria-free equilibria cannot overlap. Numerical simulations show that vector control is more effective in the containment of malaria than human-protection, which confirms the findings of Ross 53 years ago. Numerical results also show that solutions attain a disease-free steady state with time, which agrees with the theoretical results. The implication of the findings is that more attention should be paid to vector control if malaria is to be eradicated.