Effect of Environmental Precaution on the Transmission of Typhoid Fever: A Mathematical Modelling Approach

We proposed and analyzed a nonlinear mathematical model for typhoid fever and optimal control in a community with overpopulation. The model considered the effect of environmental precautions on the transmission of typhoid fever. We obtained the basic reproduction number denoting the epidemic indicator. We proved the local and global asymptomatic stability conditions for disease-free and endemic equilibrium. The model exhibits strategies for optimal control of typhoid fever, such as preventive strategies (environmental sanitation, proper hygiene, vaccination) and the treatment strategy. The numerical simulation of typhoid fever disease transmission and its maximum control summarized that prevention and treatment are the best methods for eradicating the disease in society. Since which is less than one, it follows that the disease-free equilibrium is asymptomatically stable, and that the disease will always die out.