Optimal Strategies for the Control of Cholera with Three Infection Routes

Cholera is an acute intestinal infection and water borne disease that has claimed and continue to claim the lives of millions of people in the developing countries. Its effects on developing countries cannot be ignored since most of the people who get infected or die from the disease are usually children and adults who are in their economically active years. This paper presents an epidemic mathematical model that is aimed at describing the dynamics of the spread of Cholera. In this paper, infection of the disease is considered to be through contact with Infectives or vibrio cholerae in the dry lands and the water bodies. The model is qualitatively analyzed to determine conditions for successful fight against cholera. It is shown that if the basic reproduction number , is less than unity, then the disease-free equilibrium is locally asymptotically stable and the disease dies out and when the basic reproduction number is greater than unity, the vibrio cholerae and the disease will persist in the population. Numerical simulations are also carried out and various combinations of intervention strategies are compared to determine the most effective strategy that should be employed in order to control the spread of the v.cholerae. It is observed that the strategy that adopts education on open defecation, environmental sanitation and water treatment are the most effective strategies in the fight against the spread of the disease Keywords and phrases: Mathematical model, local stability, basic reproduction number, optimal control. DOI: 10.7176/MTM/12-1-02 Publication date: January 31 st 2022