Mathematical analysis for the dynamics of snakebite envenoming

Abstract

A mechanistic model that incorporates public health enlightenment, treatment, and snake developmental stages is developed and rigorously analyzed. The model is used to gain more insights into the dynamics and control of snakebite envenoming (SBE). Some interesting equilibrium points that demonstrate the presence and absence of snakes in a given population were computed. It has been shown that the existence or extinction of snakes in a given community depends on snake existence threshold (R_S). Whenever the threshold is greater than one, snakes exist in the community, while if the threshold is exactly equal to one, then snakes seize to exist. Furthermore, a rigorous qualitative study of the model revealed that each of the snake-free, SBE-free, and SBE-endemic equilibrium points is globally asymptotically stable. In addition, a sensitivity analysis of the model parameters was conducted in order to identify the most influential parameters on SBE transmission dynamics. It is shown that an effective contact rate is the most important parameter. Therefore, preventive strategies that focus on reducing contact between humans and snakes, such as the use of snakebite repellent and protective gloves, are very important in controlling SBE. Finally, simulations have indicated that public health education on the use of snakebite preventive measures in combination with treatment of SBE victims is critical in reducing the number of new cases and deaths, respectively.