Abstract:
This study has attempted to develop and analyze a mathematical model for the spread of cholera disease
the case of Ethiopia. To achieve this objective, secondary data sources from Minister of Health and some
parameter values are from related published articles. The required data for the study were analyzed by
using a MATLAB computer program or Maple Software and the results are presented in the form of
tables and graphs. The findings of the study revealed that we formulated and analyzed a deterministic
SIBTRS mathematical model by considering indirect contact transmission and extended to a stochastic
SITRS mathematical model by incorporating direct transmission path way for cholera disease dynam ics. The total population of this model consists: susceptible, infected, treated, bacteria concentration and
recovered individuals. First we develop and analyze a deterministic mathematical model of the disease
dynamics. Since, the deterministic model does not consider the randomness process of the disease or
environmental factors; we have extended the deterministic model to stochastic model by considering sto chastic environmental factors. Next, the qualitative behavior of this model is analyzed in both approaches
by comparing deterministic to stochastic approach. The invariant region, existence of equilibrium points
(disease free and endemic equilibrium), basic reproduction number (deterministic and stochastic) and
their stabilities (local as well as global stability) of both models are studied. On the other hand, Simula tion results are done using parameter values to attempt the impact of transmission parameters on cholera
disease dynamics. Our numerical simulation results indicated that reducing contact rate, improvement
in treatment and the environmental sanitation is vital to eradicate cholera disease.
