Bifurcation analysis and global sensitivity index for malaria disease transmission dynamics: Information and treated bed nets control

Abstract

Malaria is known globally as the foremost cause of death in children and adults. Several intervention strategies and controls have been implemented and proposed, among which is Long Lasting Insecticide Treated Nets (LLINs). Malaria cases have been reported to reduce by [Formula: see text] due to the use of LLINs. However, the laid-back behaviors of humans negatively impact its effective use through improper handling and exposure to direct sunlight. To this end, a mathematical model is formulated to investigate the influence of individual response to information on the transmission dynamics of malaria infection in both human and mosquito populations. The threshold for the effective reduction of the prevalence of malaria through a behavioral change in the use of LLINs in response to the created awareness is determined in this study. The point of departure of this study from other studies is that it incorporates information/awareness as a dynamic variable to investigate the impact of LLINs on malaria. The equilibrium points of the model are analyzed using stability theory and the associated basic reproduction number [Formula: see text]. The implicit function theorem is used to determine the direction of bifurcation. We use Latin hypercube sampling (LHS) to test the most sensitive parameters in the basic reproduction number. The correlation between the [Formula: see text] and parameters is displayed using Scatter plots. The mathematical analysis shows that the direction of bifurcation is supercritical, which suggests that we only need to bring [Formula: see text] below unity for disease eradication. The study also revealed that an increase in awareness of the use of LLINs has an impact on reducing malaria transmission.