A Discrete Model of TB Dynamics in Khyber Pakhtunkhwa-Pakistan

Abstract

The present paper investigates the theoretical analysis of the tuberculosis (TB) model in the discrete-time case. The model is parameterized by the TB infection cases in the Pakistani province of Khyber Pakhtunkhwa between 2002 and 2017. The model is parameterized and the basic reproduction number is obtained and it is found R₀ ¼ 1:5853. The stability analysis for the model is presented and it is shown that the discrete-time tuberculosis model is stable at the disease-free equilibrium whenever R₀ < 1 and further we establish the results for the endemic equilibria and prove that the model is globally asymptotically stable if R₀ > 1. A discrete fractional model in the sense of Caputo derivative is presented. The numerical results of the model with various parameters and their effect on the model are presented. A comparison of discrete-time method with continuous-time model is presented graphically. A discrete fractional approach is compared with the existing method in literature and some reasonable results are achieved. Finally, a summary of results and conclusion are presented.