Dynamic model of tuberculosis considering multi-drug resistance and their applications

Abstract

Infectious diseases have always been a problem that threatens people's health and tuberculosis is one of the major. With the development of medical scientific research, drug-resistant infectious diseases have become a more intractable threat because various drugs and antibiotics are widely used in the process of fighting against infectious diseases. In this paper, an improved dynamic model of infectious diseases considering population dynamics and drug resistance is established. The feasible region, equilibrium points and stability of the model are analyzed. Based on the existing data, this model can predict the development of the epidemic situation through numerical simulation, and put forward some relevant measures and suggestions.

Keywords: Drug-resistant tuberculosis (TB); Dynamic model of infectious disease; Numerical simulation; Stability of the equilibrium points.

Fig. 1

The modified transfer diagram of the SEIS model.

Fig. 2

Simulation of TB cases in 20 years.

Fig. 3

TB cases from 2010 to 2017.

Fig. 4

TB and MDR-TB's development under different $f$.

Fig. 5

TB and MDR-TB's development under different $t_{\gamma }$.

Fig. 6

TB and MDR-TB's development under different c.