Abstract
The model system of ordinary differential equations considers two classes of latently infected individuals, with different risk of becoming infectious. The system has positive solutions. By constructing a Lyapunov function, it is proved that if the basic reproduction number is less than unity, then the disease-free equilibrium point is globally asymptotically stable. The Routh-Hurwitz criterion is used to prove the local stability of the endemic equilibrium when R 0 > 1 . The model is illustrated using parameters applicable to Ethiopia. A variety of numerical simulations are carried out to illustrate our main results.
Highlights
Tuberculosis (TB) is a contagious disease caused by Mycobacterium tuberculosis and is transmitted from person to person through the air
In most TB endemic countries Bacillus Calmette-Guérin (BCG) vaccination is recommended for tuberculosis prevention and is usually given shortly after birth to prevent TB in infants [3, 4]
The saturation incidence rate is more reasonable than the bilinear saturating incidence rate when we need to include the behavioral change and crowding effect of the infective individuals, in order to curb the contact rate [13, 14]
Summary
Tuberculosis (TB) is a contagious disease caused by Mycobacterium tuberculosis and is transmitted from person to person through the air. The incidence rate plays a very important role in the research of epidemiological models. Many models of TB use this type of incidence rate (see [6,7,8,9,10]). Mathematical modeling fulfills a significant role to examine, explain, and predict the dynamics of infectious disease transmission, including tuberculosis [8, 15, 16]. Ongoing research is aimed at developing more realistic mathematical models for investigating the transmission dynamics of infectious diseases. One of the main issues in mathematical epidemiology is the study of the asymptotic behavior of epidemic models, and for this purpose, we need to analyze steady states and their stability [17]. We present and analyze a basic tuberculosis mathematical model with a saturated incidence rate and TB vaccination
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