Global Stability of SIR and SEIR Model for Tuberculosis Disease Transmission with Lyapunov Function Method

Side, Syafruddin; Sanusi, Wahidah; Aidid, Muhammad Kasim; Sidjara, Sahlan

doi:10.3923/ajaps.2016.87.96

Cited by 40 publications

(28 citation statements)

References 7 publications

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“…The expression for λ , defined in (1), (2) and 3 λ , given into the expression in (14). Thus, the following has been established.…”

Section: Endemic Equilibrium Point (Eep) Of the Tb Modelmentioning

confidence: 99%

“…The susceptible infected removal (SIR) is a system of ordinary differential equation in three dimensions. SIR model is analyzed by building a mathematical theorem which guarantees the existence of a case of Tuberculosis, the disease free equilibrium phase and stage of disease endemic Tuberculosis [2].…”

Section: Introductionmentioning

confidence: 99%

“…Lemma: The disease free equilibrium 0 ε of the model (1),(2) and(3), is locally asymptotically stable (LAS) if 0 1 R < and unstable if 0 1 R > . The threshold quantity, 0 R , is the reproduction number for the model.…”

mentioning

confidence: 99%

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Mathematical Analysis of the Transmission Dynamics of Tuberculosis

Nayeem¹,

Sultana²

2019

AJCM

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We develop a dynamical model to understand the underlying dynamics of TUBERCULOSIS infection at population level. The model, which integrates the treatment of individuals, the infections of latent and recovery individuals, is rigorously analyzed to acquire insight into its dynamical features. The phenomenon resulted due to the exogenous infection of TUBERCULOSIS disease. The mathematical analysis reveals that the model exhibits a backward bifurcation when TB treatment remains of infected class. It is shown that, in the absence of treatment, the model has a disease-free equilibrium (DEF) which is globally asymptotically stable (GAS) and the associated reproduction threshold is less than unity. Further, the model has a unique endemic equilibrium (EEP), for a special case, whenever the associated reproduction threshold quantity exceeds unity. For a special case, the EEP is GAS using the central manifold theorem of Castillo-Chavez.

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“…The expression for λ , defined in (1), (2) and 3 λ , given into the expression in (14). Thus, the following has been established.…”

Section: Endemic Equilibrium Point (Eep) Of the Tb Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Mathematical Analysis of the Transmission Dynamics of Tuberculosis

Nayeem¹,

Sultana²

2019

AJCM

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“…[10]. The climate changes unpredictability especially in the era of global warming [22,23], which need stochastic approach [24]. Poverty of fishermen will grow, [11] if fisheries development policy is not impartial to fishermen.…”

Section: Introductionmentioning

confidence: 99%

Mapping of Poverty Characteristics, based on the quality of Fisherman’s House, Bajo Tribe, South Halmahera, Indonesia

Maru

Umar

Nyompa

et al. 2018

J. Phys.: Conf. Ser.

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“…A way to decrease the spreading rate is by keeping at a distance of the TB-infected individual from the susceptible population, while to increase the recovery rate, a maximal treatment needs to be conducted. Side et al [8] also developed two models of TB spread, which are SIR and SEIR. By implementing Lyapunov function method, it is obtained that the disease will disappear if the basic reproduction number is less than or equal to one, and vice versa.…”

Section: Introductionmentioning

confidence: 99%

The epidemic of Tuberculosis on vaccinated population

Syahrini

Sriwahyuni

Halfiani

et al. 2017

J. Phys.: Conf. Ser.

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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.

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Global Stability of SIR and SEIR Model for Tuberculosis Disease Transmission with Lyapunov Function Method

Cited by 40 publications

References 7 publications

Mathematical Analysis of the Transmission Dynamics of Tuberculosis

Mathematical Analysis of the Transmission Dynamics of Tuberculosis

Mapping of Poverty Characteristics, based on the quality of Fisherman’s House, Bajo Tribe, South Halmahera, Indonesia

The epidemic of Tuberculosis on vaccinated population

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