Mathematical analysis of malaria transmission in under-five children in the Democratic Republic of the Congo using an age-structured model

Abstract

Malaria is a multifaceted disease influenced by numerous factors, including natural immunity driven by humans, which significantly affects its transmission dynamics. It remains a major public health threat in sub-Saharan Africa, with the Democratic Republic of the Congo (DRC) accounting for approximately 12% of global malaria cases and deaths. This study employs a discrete age-structured model to analyze malaria dynamics in children under five in the DRC. The model incorporates malaria control strategies, such as long-lasting insecticide net (LLINs) coverage and access to treatment for severe (ε 1) and uncomplicated (ε 2) malaria coverage. We analyze the model by examining the existence and uniqueness of solutions using the Cauchy-Lipschitz theorem. The positivity and boundedness of the solutions, as well as the local stability of the disease-free equilibrium, are also investigated. Using the next-generation matrix approach, we derive basic and control reproduction numbers (R 0 and R c) and conduct a sensitivity analysis of R c with respect to intervention measures. The results indicate a basic and control reproduction number in under-five children of 43.779 and 18.169, respectively, confirming the high vulnerability of this age group. Elasticity analysis highlights LLINs coverage (ε 0) as the dominant driver of transmission reduction , with an elasticity index of-0.403 at 50.5% of ε 0 , while ε 1 exerts a smaller, though clinically essential, effect, with an index of-0.084 at 37% of ε 1. The findings provide valuable insights for optimizing intervention strategies in high-burden settings such as the DRC. We conclude that malaria control programs should prioritize increasing LLINs coverage and access to treatment for clinical cases, supported by malaria education and expanded bed-net distribution. Both strategies must be integrated with complementary tools to advance malaria elimination. This work advances discrete age-structured modeling as a generalizable mathematical framework for analyzing age-dependent transmission and intervention strategies across infectious diseases.