Modeling Guinea worm disease with time delays: Threshold dynamics, treatments and sensitivity analysis in heterogeneous populations

This paper presents a mathematical investigation of Guinea worm disease (GWD) dynamics using a two-patch model that incorporates discrete delays and treatment interventions. The model accounts for two distinct host populations sharing a common water source, with dynamics described by a system of delay differential equations. We compute the basic reproduction number ${\mathcal{R}}_0^d$ for both the delayed and nondelayed systems and establish threshold conditions for disease eradication and persistence. Analytical results demonstrate that the disease-free equilibrium is globally asymptotically stable (GAS) when ${\mathcal{R}}_0^d\le 1$, while a unique endemic equilibrium exists and is globally stable when ${\mathcal{R}}_0^d>1$. Sensitivity analysis identifies key parameters influencing disease transmission, and numerical simulations explore the impact of time delays and treatment efficacy on disease dynamics. Our findings reveal that both treatment interventions and specific time delays can significantly reduce the basic reproduction number, providing valuable insights for designing effective GWD control strategies.