Mathematical analysis of typhoid fever transmission dynamics with seasonality and fear

Abstract

With deteriorating infrastructure in many countries on the African continent and declining funding for infrastructure development, diseases such as typhoid fever are a problem. In many of these countries, the disease occurs periodically. This disease, which is caused by Salmonella Typhi bacteria, is associated with poor hygiene, poor waste disposal systems and seasonal rains. Recently in Zimbabwe, the infection has been found to exist due to dilapidated infrastructure. The existence of the infection remains a huge public health problem. In this paper, we study the typhoid fever transmission dynamics with fear in periodic environments. We formulate a non-linear system of differential equations in which the infection rate is time dependent. The model’s steady states are determined and the stability analysis carried out. Numerical simulations are carried out to determine the impact of the vital parameters on the course of the disease. Sensitivity analysis is also done to determine parameters that influence disease progression the most. The role of fear and seasonality are discussed and the public health implications of the results are articulated.