2017
DOI: 10.3934/mbe.2017069
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Global stability in a tuberculosis model of imperfect treatment with age-dependent latency and relapse

Abstract: In this paper, an SEIR epidemic model for an imperfect treatment disease with age-dependent latency and relapse is proposed. The model is well-suited to model tuberculosis. The basic reproduction number R0 is calculated. We obtain the global behavior of the model in terms of R0. If R0< 1, the disease-free equilibrium is globally asymptotically stable, whereas if R0>1, a Lyapunov functional is used to show that the endemic equilibrium is globally stable amongst solutions for which the disease is present.

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Cited by 17 publications
(12 citation statements)
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“…Considering multigroup age-structured subclass is a prominent feature of our model, and the part of investigation for uniform persistence is the novel result of our paper. Of course, other properties, such as general nonlinear incidence, infectivity during latency period (for example, COVID-19, AIDS, tuberculosis, and hepatitis B; see Ren and Cai et al 14,37 ), multigroup SVEIR age-dependent model (decomposes the heterogeneous population into several subgroups on the basis of modes of transmission, contact patterns, or geographic distribution), and age-structured epidemic model with environmental virus infection (for example, SARS, AIDS, Ebola, and COVID-19; see Lu et al 38 ), should be integrated into the model to make it more realistic. We leave this for future research.…”
Section: Discussionmentioning
confidence: 99%
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“…Considering multigroup age-structured subclass is a prominent feature of our model, and the part of investigation for uniform persistence is the novel result of our paper. Of course, other properties, such as general nonlinear incidence, infectivity during latency period (for example, COVID-19, AIDS, tuberculosis, and hepatitis B; see Ren and Cai et al 14,37 ), multigroup SVEIR age-dependent model (decomposes the heterogeneous population into several subgroups on the basis of modes of transmission, contact patterns, or geographic distribution), and age-structured epidemic model with environmental virus infection (for example, SARS, AIDS, Ebola, and COVID-19; see Lu et al 38 ), should be integrated into the model to make it more realistic. We leave this for future research.…”
Section: Discussionmentioning
confidence: 99%
“…Remark 6. It can be easily found that the main research techniques and methods proposed and used in previous studies 14,[16][17][18]21,23 are improved and developed in this paper. Remark 7.…”
Section: Stability Of Endemic Steady Statementioning
confidence: 98%
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“…Model (23) is investigated in the work of Liu et al 8 A similar model is also proposed in the work of Ren. 18 According to (5), ℜ 0 reduces to…”
Section: Examplementioning
confidence: 99%
“…Usually, the introduction of age structure often leads to a system of first-order partial differential equations with appropriate boundary conditions. Such models are called age-structured epidemic models, on which recent works can be found (see other works 1,8,[14][15][16][17][18] and the references therein). Since the latent and removed individuals always become infectious at different rates depending on the time that they have been in their classes, it is interesting to consider models with latent age and relapse age.…”
Section: Introductionmentioning
confidence: 99%