MATHEMATICAL MODELING OF TYPHOID FEVER WITH DRUG RESISTANCE COMPARTMENT

Abstract

In this thesis work, we formulated a deterministic mathematical model of Typhoid fever to describe the transmission dynamics of Typhoid fever and for the purpose of studying the effects of drug resistance on controlling the dynamics of typhoid fever in the community using a system of non linear ordinary differential equation. The system has two equilibrium points, namely the disease-free equilibrium point and the endemic equilibrium point which exists conditionally. The invariant region of the solution, conditions for positivity of the solution, existence of equilibrium points of the model and their stabilities and also sensitivity analysis are checked. The basic reproduction number that represents the epidemic indicator is obtained by using next generation matrix. Both local and global stability of the disease-free equilibrium and endemic equilibrium point of the model equation was established. The endemic states are considered to exist when the basic reproduction number is greater than one. Finally our numerical findings are illustrated through computer simulations using MAPLE 18 software, which shows the reliability of our model from the practical point of view . It is worth mentioning that the simulation results confirm the conclusion drawn from the qualitative analysis of the model. Hence, we came to realize that the number of infected people keeps decreasing if one carefully decrease effective contact rate and decrease the contact between susceptible and infected individuals. Therefore, we recommend that decreasing contact rate between infected and susceptible individuals by creating awareness to decrease the spreading of the disease , decreasing drug resistance coverage and increasing recovery rate with proper treatment to effectively control Typhoid fever infection.