Mathematical Modeling of Diarrhea with Vaccination and Treatment Factors

Diarrhea is the second leading cause of death in children under five years old. It is responsible for killing thousands of children globally. It kills more young children than other childhood infectious diseases. Diarrhea illness alone causes more than 1.5 million deaths annually, thereby making it a worse health threat than infectious diseases in terms of death roll. Nonetheless, diarrhea is avoidable and manageable with appropriate treatment. Therefore, this research studied the analysis of a mathematical model of diarrhea dynamics in the presence of vaccination and treatment. To do this, a compartmental mathematical model of (S, V, E, I, R) was considered to investigate the eect of vaccine and treatment in the dynamic spread of diarrhea in the community. The mathematical analysis showed that the disease-free equilibrium point and endemic point of the model exist. Also the basic reproduction Ro was determined through the Next Generation Matrix. The model has a disease-free equilibrium point which is locally asymptotically stable and globally stable over time. The model also has stability of the endemic equilibrium which is stable when Ro > 1. Numerical simulations are given to demonstrate the effects of vaccine and treatment on the spread of diarrhea and the result presented showed that vaccine and treatment have a pronounced effect of reducing diarrhea infection. Moreover, combined with sensitivity analysis, we observe that even though vaccination is adequate but not suffcient in reducing the basic reproduction number, it effectively manages the disease.