Abstract
Tuberculosis (TB) is a serious global health threat that is caused by the bacterium Mycobacterium tuberculosis, is extremely infectious, and has a high mortality rate. In this paper, we developed a model of TB infection to predict the impact of saturated recovery. The existence of equilibrium and its stability has been investigated based on the effective reproduction number R C . The model displays interesting dynamics, including backward bifurcation and Hopf bifurcation, which further results in the stable disease-free and stable endemic equilibria to be coexisting. Bifurcation analysis demonstrates that the saturation parameter is accountable for the phenomenon of backward bifurcation. We derive a condition that guarantees that the model is globally asymptotically stable using the Lyapunov function approach to global stability. The numerical simulation also reveals that the extent of saturation of TB infection is the mechanism that is fuelling TB disease in the population.
Highlights
Modeling and simulation are significant decision tools for controlling human diseases [1, 2]
We discovered that recovery from TB infection depends upon numerous factors such as antibiotic treatment and the number of hospital beds. is leads to nonlinearity in the number of recoveries. e nonlinear recovery function rate principle was introduced to reveal some insight into the eradication of TB disease by examining the effect of antibiotic treatment and the number of hospital beds
E main goal of this study is to investigate the qualitative dynamics of the TB infection incorporating saturated recovery of the form cIι/(1 + πIι) into the model proposed in [21, 22] which gives a more realistic model
Summary
Modeling and simulation are significant decision tools for controlling human diseases [1, 2]. The role of treatment function addresses the likelihood of treatment against the disease at a given time for each infected person. When R0 > 1, some different scenarios, for example, Hopf bifurcation and the occurrence of several endemic equilibria, have been observed as a result of saturated recovery or treatment [12, 14, 15, 17]. Cui et al [14] proposed and investigated an SIS model with saturated recovery rate and discovered the occurrence of oscillatory behavior in the population via Hopf bifurcation because of the treatment capacity limitations. E behaviour of SEIR epidemic model with saturated treatment function is investigated by [18], a backward bifurcation that results in bistability emergence, and numerical result work suggested that they should improve the medical conditions to control the epidemic [19]. We incorporated saturated recovery which was excluded in previous four-dimensional SEIR-like models with exogenous infection used to study the phenomenon of backward bifurcation (see [21, 22])
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