Mathematical Modeling of Lymphatic Filariasis with Quarantine Measures, Treatment Protocols and Drug Resistance in Ghana

Lymphatic filariasis (elephantiasis) is a neglected tropical disease caused by parasitic worms that impair the lymphatic system and lead to severe swelling. To better understand its transmission and control, we formulate a deterministic mathematical model to study the transmission dynamics that incorporates treatment, quarantine, and the emergence of drug resistance. The human population is structured into susceptible, exposed, acutely infected, chronically infected, treated, withdrawal, and three resistance stages, while the mosquito population is divided into susceptible, exposed, and infectious classes. The model admits two main equilibrium states: the disease-free equilibrium and the endemic equilibrium. The basic reproduction number, $\mathcal{R}_0$, is derived using the next-generation matrix method. Analytical results show that the disease-free equilibrium is globally asymptotically stable whenever $\mathcal{R}_0 < 1$, while the endemic equilibrium is stable when $\mathcal{R}_0 > 1$. Using Ghana's post-MDA (MAss Drug Administration) surveillance, we estimate four key parameters and three initial conditions. Sensitivity analysis, carried out using Latin Hypercube Sampling and partial rank correlation, identifies the treatment rate, resistance progression, and mosquito biting rate as the most influential factors affecting transmission. Numerical simulations further demonstrate that treatment alone achieves a greater reduction in prevalence compared to quarantine alone, while a combined intervention of treatment and quarantine yields the most significant impact. These findings suggest that integrated control strategies, particularly those accounting for drug resistance, are vital for the effective and sustainable management of lymphatic filariasis.