Dynamical System of the Mathematical Model for Tuberculosis with Vaccination

Abstract

This research focused on the modification of deterministic mathematical models for tuberculosis with vaccination. It also aimed to see the effect of giving the vaccine. It was done by adding vaccine compartments to people who were given the vaccine in the susceptible compartment. The population was divided into nine different groups. Those were susceptible individuals (S), vaccine (V), new latently infected (E1), diagnosed latently infected (E2), undiagnosed latently infected (E3), undiagnosed actively infected (l), diagnosed actively infected with prompt treatment (Dr), diagnosed actively infected with delay treatment (Dp), and treated (T). Basic reproduction number was constructed using next-generation matrix. Sensitivity analysis was also conducted. The results show that the model comprises two equilibriums: diseasefree equilibrium (T0) and endemic equilibrium (T*). It also shows that there is a relationship between R0 and two equilibriums. Moreover, the disease-free equilibrium point is asymptotically stable local when it is R0 1. Furthermore, the parameters of β, ρ, and γ are the most important parameter.