Mathematical model analysis of malaria transmission dynamics with induced complications

Abstract

This study develops a mathematical model to analyze malaria transmission dynamics. It accounts for complications like severe anemia and organ dysfunction, which impact disease outcomes and healthcare systems. The study includes rigorous analysis to confirm the existence and uniqueness of the solution, positivity, boundedness, and stability of the equilibrium points. Stability analysis is done using the Routh–Hurwitz criteria and the Castillo-Chavez approach. It is verified that the malaria-free equilibrium point is globally asymptotically stable when $R_0$ is below one, with no backward bifurcation. A forward bifurcation exists with a smooth transition to endemic states as $R_0$ crosses one. Local sensitivity analysis justifies a 10% increase in transmission rates ${\beta }_1$ or ${\beta }_2$ raises $R_0$ by 5%, while a 10% increase in recovery rate ${\theta }_c$ or mosquito mortality rate ${\mu }_v$ reduce $R_0$ by 1.3% and 5%, respectively. Global sensitivity analysis was conducted, and it identified that ${\theta }_c$ has strong impact on the model’s output. Among all the parameters, ${\theta }_c$ and the death rate of mosquitoes were found to be the most influential in determining the behavior of the model. We fit the mathematical model to malaria data from Ethiopia and estimate parameters using Matlab’s fminsearch routine. The effect of seasonal malaria transmission rate is also discussed. Simulation analysis show that increasing treatment and mosquito death rates, while reducing transmission rates, can reduce the malaria burden. The findings emphasize the need to control complications and improve vector management for effective malaria interventions in regions like Ethiopia.