Abstract:
In this paper we develop a stochastic mathematical model of cholera disease
dynamics by considering direct contact transmission pathway. The model considers
four compartments, namely susceptible humans, infectious humans, treated humans,
and recovered humans. Firstly, we develop a deterministic mathematical model of
cholera. Since the deterministic model does not consider the randomness process or
environmental factors, we converted it to a stochastic model. Then, for both types of
models, the qualitative behaviors, such as the invariant region, the existence of a
positive invariant solution, the two equilibrium points (disease-free and endemic
equilibrium), and their stabilities (local as well as global stability) of the model are
studied. Moreover, the basic reproduction numbers are obtained for both models and
compared. From the comparison, we obtained that the basic reproduction number of
the stochastic model is much smaller than that of the deterministic one, which means
that the stochastic approach is more realistic. Finally, we performed sensitivity analysis
and numerical simulations. The numerical simulation results show that reducing
contact rate, improving treatment rate, and environmental sanitation are the most
crucial activities to eradicate cholera disease from the community.
