Abstract:
In this study, a mathematical model to analyze the dynamics of a chronic water-borne
disease known as diarrhea is developed. To achieve the objectives of this study work,
secondary data on the population under five years of age from Bishoftu General Hospital
between 2020 and March 2024 is collected. These populations were categorized as newborn,
vaccinated, infected, and treated. Based on the epidemiological behavior of the diarrhea
disease, a deterministic model is formulated by dividing the total population into seven
classes. This model accounts for preventive interventions through vaccination and control
measures through treatment. Since diarrhea is caused by pathogens that can survive and
reproduce in water at specific temperatures and salinities, so we considered the pathogens
as a compartment in the model. Our findings revealed that this water-borne disease can lead
to serious infections. The qualitative behavior of the models, including the existence of
equilibrium points, basic reproductive number of the model, and stability analysis of
equilibrium points were analyzed. Using the collected data, some parameters value were
estimated while value some others parameters were received from related publications, and
based on the behavior of these disease the values left parameters where assumed. To
determine the effect of parameters on the dynamics of the disease, a numerical simulation
was performed and displayed the results in a graph using MATLAB 2019 computer software.
The results show that increasing the rate of vaccination and treatment plays a crucial role
in controlling the dynamics of diarrhea. Therefore, in order to eliminate diarrhea in the
community, it is essential for stakeholders to consider these prevention strategies and
control measures
