Optimal Control of Interventions for Lymphatic Filariasis Disease Incorporating Resistant Strains

Abstract

A deterministic model for controlling the neglected tropical filariasis disease known as elephantiasis, caused by a filarial worm, is developed. The model incorporates drug resistance in human and insecticide-resistant vector populations. An investigation into whether the model is of biological importance reveals that it is positively invariant, mathematically well posed, and tractable for epidemiological studies. The filariasis-free and filariasis-present equilibrium points were obtained. The next-generation matrix technique is used to derive the basic reproduction number R0, which is then used to determine the local stability analysis of the model. It is established that the system is locally asymptotically stable when R0<1. The technique by Castillo-Chavez and a Lyapunov function were employed to prove the global stability of the model’s fixed points. The results of this analysis of filariasis-free equilibrium show that the system is globally asymptotically stable when R0<1 and unstable when R0>1. Similarly, the filariasis-present equilibrium point is proved to be globally asymptotically stable when R0>1 and unstable otherwise. This indicates that the fight against the spread of the disease is achievable. It is observed that increasing human-infected mosquito contacts or mosquito-infected human contacts raises the value of R0, whereas decreasing the progression of micro-filaria into infective larva and killing more mosquitoes will decrease the R0 value according to the sensitivity analysis of the model. The variable precision arithmetic technique executed in MATLAB R2014a was used to determine the elasticity indices of the parameters of R0, which showed that the value of R0=0.94639. Further investigations revealed that ω2 has a significant influence on the reproduction number, suggesting that treatment of acute infections is crucial in the control of the disease. Pontryagin’s Maximum Principle (PMP) is used for optimal control analysis. The numerical result revealed that strategy D is the most effective based on the infection averted ratio (IAR) value.