Sensitivity analysis of a mathematical model for malaria transmission accounting for infected ignorant humans and relapse dynamics

This article presents and analyzes a deterministic model for malaria transmission that incorporates infected individuals who are unaware of their infectious status (ignorant infected humans) and accounts for relapse dynamics. We explore the invariant region and positivity of the model and calculate the effective reproduction number using the next-generation matrix method. We demonstrate the local and global stability of disease-free equilibrium points using the Routh-Hurwitz criterion and Lyapunov function, respectively. The proposed model shows that a disease-free equilibrium point is globally asymptotically stable when the basic reproduction number R-e < 1. We conducted a sensitivity analysis on the effective reproduction number to identify which basic parameter most significantly influences the increase or decrease of malaria cases. This study focuses on individuals who have been treated and cured but continue to carry dormant Plasmodium parasites in their blood, which can potentially cause relapse or reinfection. Additionally, we introduce a protected compartment to carefully evaluate how preventive measures influence the spread and persistence of malaria within the population.