Mathematical modelling of typhoid fever disease incorporating delay caused by false negative diagnosis

Abstract

We developed a mathematical model based on a system of ordinary differential equations to explore the dynamics of typhoid fever sickness, taking into account the delay caused by false negative diagnosis. Typhoid fever continues to be a significant public health problem in a number of countries, particularly developing countries. Typhoid fever, for example, has been classified among the top twenty illnesses in Ghana, accounting for approximately 0.92 percent of hospital admissions. An epidemiological model was developed to determine the impact of delay caused by false negative diagnosis in the spread and treatment dynamics of the disease. Protected (P), Susceptible (S), Infected (I), Delayed (D), and Treated (T) classes were established. The next generation technique was used to calculate the basic reproduction number \(R_{0}\). Additionally, it was demonstrated that for \(R_0 < 1\), the disease-free equilibrium points were both locally and globally asymptotically stable, whereas the endemic equilibrium points were locally asymptotically stable. Having done numerical simulations, it was found that the delay caused by false negative diagnosis significantly contributes to the spread dynamics and also has an effect on treatment. As a result, we determined that delays caused by false negative diagnoses should be kept to a minimum in order to minimize disease spread.