Analysis of a tuberculosis model with undetected and lost-sight cases

Abstract

A deterministic model of tuberculosis (TB) in sub-Saharan Africa including undetected and lost-sight cases is presented and analyzed. The model is shown to exhibit the phenomenon of backward bifurcation, when a stable disease-free equilibrium co-exists with one or more stable endemic equilibrium points when the associated basic reproduction number (R 0 ) is less than unity. Analyzing the model obviously reveals that exogenous reinfection plays a key role on the existence of backward bifurcation. However, an analysis of the ranges of exogenous reinfection suggested that backward bifurcation occurs only for very high and unrealistic ranges of the exogeneous reinfection rate. Random perturbation of reinfection rates was performed to gain insight into the role of this latter on the stability of the disease free equilibrium.

Prevention and Control of Tuberculosis Relying on a Tuberculosis Dynamic Model Based on the Cases of American

“…We can find ψ has a mild effect on the total infected, with its line overlapping with 'without control' approximately. (11) Rate (11) N umber (12) Rate (12) N umber (21) Rate (21) N umber (22) Rate ( Table 2 The definition and value range of parameters for model (1). The data of population from [5] and others from [54].…”

“…In developing countries, the increase of TB cases by a high level of undiagnosed infectious population and incomplete treated population is one of the greatest challenges to control TB. These people are more possible to develop multi-drug resistance relative than the diagnosed infectious population [22,23]. Based on the model proposed by Moualeu et al who considered recurrence of disease, exogenous reinfection, cases of primary active tuberculosis, traditional medicine, natural rehabilitation or self-medication, as well as undiagnosed infectious and lost-sight people [22,24], our model also considers the vaccinated and the relapsed that the recovered population come into susceptible class.…”

“…These people are more possible to develop multi-drug resistance relative than the diagnosed infectious population [22,23]. Based on the model proposed by Moualeu et al who considered recurrence of disease, exogenous reinfection, cases of primary active tuberculosis, traditional medicine, natural rehabilitation or self-medication, as well as undiagnosed infectious and lost-sight people [22,24], our model also considers the vaccinated and the relapsed that the recovered population come into susceptible class. In fact, recovered people have a chance to be infected with TB and even though the state haves cancelled the BCG vaccination for newborns in American, there are also some will be vaccinated to prevent TB.…”

“…We give some definition of the parameters in Table 2, and according to Moualeu et al [22,24] and characteristics of epidemiology, we determined the range of the parameters of Table 2. We propose a mathematical model to understand the transmission dynamics and prevalence of TB which is represented by the following system of ordinary differential equations:…”

Global analysis of a stochastic TB model with vaccination and treatment

“…Mathematical models are powerful tools to gain insights into the transmission of infectious diseases [7,8,9,15,16,21,28,29]. Over the past two decades, there have been a lot of mathematical models to investigate the transmission dynamics of TB [4,10,22,26].…”