Modeling the Impacts of Diagnosis and Treatment of Snakebite Envenoming Victims with Anti-Snake Venom in a Community

Snakebite envenoming (SBE) is one of the major causes of deaths and disabilities in tropical and subtropical countries especially in the continents of Asia and Africa. Report revealed that on average, 5-8 and about 3,000 cases of SBE are recorded daily and yearly respectively in northeast Nigeria which population are largely agriculturists. Thus, snakebite (SB) led to economy setback and slows down productivity among the workforce as a result of disabilities induced by SBE. Consequently, the revenue generation even including income facing declined. This paper proposes population-based mathematical model for studying the dynamic impacts of diagnosis and treatment of snakebite envenoming victims with anti-snake venom in a community. The model is rigorously analyzed using relevant techniques and theorems in dynamical systems. The model was validated using monthly reported data on snakebite envenoming from 2020–2022, collected from snakebite treatment and research hospital (STRH) Kaltungo in northeast Nigeria. The qualitative study revealed that the model has snakebite-envenoming-free and snakebite-envenoming-endemic equilibrium points. It is shown via the Lyapunov function in conjunction with the Lassale invariance principle that these two equilibrium points are globally asymptotically stable. Furthermore, numerical simulations of the model were carried out to investigate the impact of the diagnosis of snakebite envenoming victims and the treatment of the same on the burden of snakebite envenoming. The results of the simulations revealed that appropriate diagnosis and treatment of snakebite envenoming victims with anti-snake venom could significantly reduce the number of snakebite-induced deaths and disabilities. This work can serve as a framework for making policy and decision in addressing the issues of SBE in the public healthcares in the study region and beyond.