Mathematical transmission analysis of SEIR tuberculosis disease model

Das, Kalyan; Murthy, B. S.; Samad, Sk. Abdus; Biswas, Md. Haider Ali

doi:10.1016/j.sintl.2021.100120

Cited by 20 publications

(10 citation statements)

References 30 publications

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“…We employed a compartmental susceptible-exposed-infectious-recovered (SEIR) model and the system dynamics (SD) model to frame the analysis [ 15 , 16 ]. The SEIR model was commonly used to explain the epidemic force in many diseases (such as HIV, influenza, and tuberculosis) long before the COVID-19 pandemic [ 17 , 18 , 19 ]. The model simply explains the rate of change of the unit of interest from one stage to another.…”

Section: Methodsmentioning

confidence: 99%

Forecasted Trends of the New COVID-19 Epidemic Due to the Omicron Variant in Thailand, 2022

et al. 2022

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Thailand is among many countries severely affected by COVID-19 since the beginning of the global pandemic. Thus, a deliberate planning of health care resource allocation against health care demand in light of the new SARS-CoV-2 variant, Omicron, is crucial. This study aims to forecast the trends in COVID-19 cases and deaths from the Omicron variant in Thailand. We used a compartmental susceptible-exposed-infectious-recovered model combined with a system dynamics model. We developed four scenarios with differing values of the reproduction number (R) and vaccination rates. In the most pessimistic scenario (R = 7.5 and base vaccination rate), the number of incident cases reached a peak of 49,523 (95% CI: 20,599 to 99,362) by day 73, and the peak daily deaths grew to 270 by day 50. The predicted cumulative cases and deaths at the end of the wave were approximately 3.7 million and 22,000, respectively. In the most optimistic assumption (R = 4.5 and speedy vaccination rate), the peak incident cases was about one third the cases in the pessimistic assumption (15,650, 95% CI: 12,688 to 17,603). In the coming months, Thailand may face a new wave of the COVID-19 epidemic due to the Omicron variant. The case toll due to the Omicron wave is likely to outnumber the earlier Delta wave, but the death toll is proportionately lower. Vaccination campaigns for the booster dose should be expedited to prevent severe illnesses and deaths in the population.

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Section: Methodsmentioning

confidence: 99%

Forecasted Trends of the New COVID-19 Epidemic Due to the Omicron Variant in Thailand, 2022

et al. 2022

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“…In addition, we consider here a more general class of Kermack–McKendrick models than the one considered in Adimy et al [23], adding the compartment of exposed individuals

E

. Indeed, for many infections, such as influenza [38] and tuberculosis [39], there is a more or less long latency period during which individuals have been infected but are not yet infectious themselves. During the period

1/\mu

, infected individuals are in the compartment

E

but are not yet infectious (see also Martcheva [3] for other cases of infectious diseases with a latency period).…”

Section: Discussion and Numerical Simulationsmentioning

confidence: 99%

Global stability of a SEIR discrete delay differential‐difference system with protection phase

Adimy,

Chekroun,

Kuniya

et al. 2023

Math Methods in App Sciences

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We consider an epidemiological model with the four classical compartments of susceptible, exposed, infected, and recovered population. We add a new compartment that is supposed to describe, for a limited time, individuals that are protected from the epidemic through vaccination or medication, for instance. We model the protection phase by an age‐structured partial differential equation. The age is the time since an individual entered the protection phase. The model is then reduced by integration on the characteristics to a differential‐difference system with delay. The discrete delay represents the limited duration of the protection phase. After establishing the basic properties of the model, we show that the disease‐free equilibrium (DFE) is globally asymptotically stable when the basic reproduction number is less than one and is unstable when this number is greater than one. Furthermore, we show that even if there is no mortality during the protection phase and the basic reproduction number is greater than one, the endemic equilibrium is globally asymptotically stable. The proofs of the global asymptotic stability of both equilibria are based on carefully constructed Lyapunov functions. To complete this study on the global dynamics, we discuss some results on weak and strong uniform persistence of the disease. Finally, numerical simulations are performed to illustrate and complete our main results.

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“…In 1970, the authors in [51] developed a TB model with aim to minimize the cost of TB related control interventions. In due course of times several works based on classic SIR model [27] were built to analyse the dynamics of TB disease transmission, some of which are [13] , [18] , [22] , [38] , [53] , in which along with study of the disease prevalence, different controls strategies are also incorporated. In the studies [16] , [17] , the authors worked on TB model with multiple reinfection and media impact respectively.…”

Section: Introductionmentioning

confidence: 99%

A co-infection model on TB - COVID-19 with optimal control and sensitivity analysis

Bandekar

Ghosh

2022

Mathematics and Computers in Simulation

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Mathematical transmission analysis of SEIR tuberculosis disease model

Cited by 20 publications

References 30 publications

Forecasted Trends of the New COVID-19 Epidemic Due to the Omicron Variant in Thailand, 2022

Forecasted Trends of the New COVID-19 Epidemic Due to the Omicron Variant in Thailand, 2022

Global stability of a SEIR discrete delay differential‐difference system with protection phase

A co-infection model on TB - COVID-19 with optimal control and sensitivity analysis

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