The epidemic of Tuberculosis on vaccinated population

Abstract

Abstract. Tuberculosis is an infectious disease which has caused a large number of mortality in Indonesia. This disease is caused by Mycrobacterium tuberculosis. Besides affecting lung, this disease also affects other organs such as lymph gland, intestine, kidneys, uterus, bone, and brain. This article discusses the epidemic of tuberculosis through employing the SEIR model. Here, the population is divided into four compartments which are susceptible, exposed, infected and recovered. The susceptible population is further grouped into two which are vaccinated group and unvaccinated group. The behavior of the epidemic is investigated through analysing the equilibrium of the model. The result shows that administering vaccine to the susceptible population contributes to the reduction of the tuberculosis epidemic rate.

Mathematical model of tuberculosis epidemic with recovery time delay

“…By using Routh-Hurwitz criteria, it indicates that all of the roots are negative giving an asymptotically stable state at the equilibrium point. For,τ 0 the stability of the equilibrium point is determined by the real part of the characteristic equation solution (7). Suppose that λ = η ± iω is the root of the characteristic equation (7), the equilibrium will be stable if η < 0 .…”

“…One way to reduce the rate of infection is to keep the TB-infected individuals from susceptible populations, whereas to boost the healing rate the maximum treatment need to be conducted [1] [6] developed a model of the spread of the epidemic in SIR-type by reviewing the two models consisting of a model with vaccination and a model without vaccination and studied the comparison of the results generated by the models. Tuberculosis transmission was also studied by Syahrini et al [7] by considering the existence of latent group and vaccine administration to the susceptible group. The model was developed in SEIR-type and the results suggested that the vaccination rate would lower the transmission rate of TB disease [7].…”

“…Tuberculosis transmission was also studied by Syahrini et al [7] by considering the existence of latent group and vaccine administration to the susceptible group. The model was developed in SEIR-type and the results suggested that the vaccination rate would lower the transmission rate of TB disease [7]. Delay differential equation is simple functional differential equation and occurs more frequently in real problems.…”

Optimal control problem for a tuberculosis model with multiple infectious compartments and time delays

“…Using a basic SEI model with saturated incidence rate, Baba et al [34] studied the effect of optimal controller and awareness. It is noted that a considerable number of studies that deal with TB modelling use the basic SEI or SEIR model with only a single compartment of infectious people (see [35][36][37][38][39][40][41]). However, considering a single infectious compartment is no longer convenient, as it fails to take into account that some infected individuals can be detected and treated whereas others remain undetected and untreated.…”

Co-infection of Middle Eastern respiratory syndrome coronavirus and pulmonary tuberculosis

“…The obvious reason behind this is that the bacteria causing TB, mycobacterium tuberculosis, is transmitted through the air. Though the disease has been discovered much earlier, yet it remained incurable till the recent times resulting in havoc on large scale, wiping a one third of the world population [1] , [2] .…”