Modeling the Dynamics of HIV-Pneumonia Coinfections in Nigeria Using Delay Differential Equations (DDE)
Jamilu Karami Lawal
Farouk Tijjani Saad
Abbas Usman
Abstract
In nigeria, which has one of the world's highest hiv burdens, pneumonia is a leading cause of mortality among immune-compromised individuals. This bidirectional relationship where hiv increases susceptibility to pneumonia and pneumonia accelerates hiv progression is poorly captured by traditional models that ignore real world time delays. We develop a delay differential equation (dde) model incorporating critical delays: pneumonia incubation, treatment initiation, and immune recovery. The basic reproduction number (R_0) is derived, and the disease-free equilibrium is shown to be locally and globally stable when R_0<1. Model solutions are proven to be positive and bounded. Sensitivity analysis reveals that transmission rates are the most influential parameters. Numerical simulations demonstrate that time delays significantly elevate infection peaks and prolong epidemic duration. Longer diagnostic and treatment delays increase hiv and pneumonia prevalence by 15% and 25-30%, respectively, while combined delays result in the highest overall burden and slowest convergence to equilibrium. Our findings underscore that reducing delays in diagnosis and treatment is critical for outbreak control. This delay based model provides a more realistic framework for understanding hiv-pneumonia coinfection dynamics and offers validated insights for guiding public health intervention strategies in Nigeria.
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