Analysis of an epidemic model for transmitted diseases in a group of adults and an extension to two age classes

Gölgeli, Meltem; Atay, Fatihcan M.

doi:10.15672/hujms.624042

Cited by 8 publications

(10 citation statements)

References 28 publications

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“…Mathematical modelling of the transmission of infectious diseases has a history of about a hundred years in mathematical epidemiology [ 18 ]. The so-called SIR models have been widely studied for understanding the spread of many infectious diseases and have become an important tool for controlling outbreaks and determining treatment and vaccination policies [ 1 , 4 , 13 , 21 , 34 ]. The current pandemic, coronavirus disease 2019 (COVID-19), has attracted the interest of researchers from different scientific areas and once again highlighted the importance of appropriate mathematical modelling in developing control strategies.…”

Section: Introductionmentioning

confidence: 99%

Modelling personal cautiousness during the COVID-19 pandemic: a case study for Turkey and Italy

2021

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Although policy makers recommend or impose various standard measures, such as social distancing, movement restrictions, wearing face masks and washing hands, against the spread of the SARS-CoV-2 pandemic, individuals follow these measures with varying degrees of meticulousness, as the perceptions regarding the impending danger and the efficacy of the measures are not uniform within a population. In this paper, a compartmental mathematical model is presented that takes into account the importance of personal cautiousness (as evidenced, for example, by personal hygiene habits and carefully following the rules) during the COVID-19 pandemic. Two countries, Turkey and Italy, are studied in detail, as they share certain social commonalities by their Mediterranean cultural codes. A mathematical analysis of the model is performed to find the equilibria and their local stability, focusing on the transmission parameters and investigating the sensitivity with respect to the parameters. Focusing on the (assumed) viral exposure rate, possible scenarios for the spread of COVID-19 are examined by varying the viral exposure of incautious people to the environment. The presented results emphasize and quantify the importance of personal cautiousness in the spread of the disease.

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Section: Introductionmentioning

confidence: 99%

Modelling personal cautiousness during the COVID-19 pandemic: a case study for Turkey and Italy

2021

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“…Especially, it has been concentrated on seeing whether the variations in the models which are studied can lead to significant differences in behaviors related to qualitative and stability, with respect to models in classical type. Hereby, by using the general principles of modeling of epidemics, various models to describe the course of some epidemic diseases have been formulated, [9][10][11][12][13][14][15][16][17][18].…”

Section: Introductionmentioning

confidence: 99%

Local Asymptotic Stability and Sensitivity Analysis of a New Mathematical Epidemic Model Without Immunity

Çakan

2022

Mathematical Sciences and Applications E-Notes

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With this study it is aimed to introduce and analyze a new SIS epidemic model including vaccination effect. Vaccination considered in the model provides a temporary protection effect and is administered to both susceptible and new members of the population. The study provides a different aspect to the SIS models used to express, mathematically, some infectious diseases which are not eradicated by the immune system. The model given this study is designed by considering varying processes from person to person in the disease transmission, the recovery from disease (recovery without immunity) and in the loss of protective effect provided by the vaccine. The processes that change according to individuals are explained by distributed delays used in the relevant differential equations that provide the transition between compartments. The differences in the model are especially evident in these parts. In analyzing the model, firstly, the disease-free and endemic equilibrium points related to the model are determined. Then, the basic reproduction number R 0 is calculated with the next generation matrix method. Next, the dynamics about locally asymptotically stable of the model at the disease-free and endemic equilibriums are examined according to the basic reproduction number R 0 . Attempts intended to reduce the spread of the disease are, of course, in the direction supporting the lowering the value R 0 . In this context, the reducing and enhancing effects of the parameters used in the model on the value R 0 have been interpreted mathematically and suggestions were made to implement control measures in this direction. Also, in order to evaluate the support provided by the vaccine during the spread of the disease, the model has been examined as vaccinated and unvaccinated, and by some mathematical process, it has been seen that the vaccination has a crucial effect on disease control by decreasing the basic reproduction number. In other respects, by explored that the effect of parameters related to vaccination on the change of R 0 , a result about the minimum vaccination ratio of new members required for the elimination of the disease in the population within the scope of the target of R 0 < 1 has been obtained.

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“…Modeling these spread process by dividing the population into distinct compartments indicating the status is known as "compartmental modeling" in the literature. One of the simplest and earliest contributions to these modeling attempts is Kermack and McKendrick [16] model, which is the "SIR (Susceptible-Infected-Recovered) model", and yields important results for epidemics [13]. This model consists of three compartments as "Susceptible", "Infected", and "Recovered".…”

Section: Introductionmentioning

confidence: 99%

“…General compartmental disease transmissions have been modelled by a system of ordinary differential equations by using this reproduction number. Early analytical approaches for modeling these transitions among compartmental states are some mathematical models involving ordinary differential equations and nonlinear analysis [9,13,16,20,26]. The use of differential equations and nonlinear analysis (commonly known as EBM -Equations-Based Modeling in the literature) is still a common way in epidemiology.…”

Section: Introductionmentioning

confidence: 99%

An interaction-oriented multi-agent SIR model to assess the spread of SARS-CoV-2

Altun

Altuntaş

Dereli

2021

Hacettepe Journal of Mathematics and Statistics

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It is important to recognize that the dynamics of each country are different. Therefore, the SARS-CoV-2 (COVID-19) pandemic necessitates each country to act locally, but keep thinking globally. Governments have a responsibility to manage their limited resources optimally while struggling with this pandemic. Managing the trade-offs regarding these dynamics requires some sophisticated models. "Agent-based simulation" is a powerful tool to create such kind of models. Correspondingly, this study addresses the spread of COVID-19 employing an interaction-oriented multi-agent SIR (Susceptible-Infected-Recovered) model. This model is based on the scale-free networks (incorporating 10, 000 nodes) and it runs some experimental scenarios to analyze the main effects and the interactions of "average-node-degree", "initial-outbreak-size", "spread-chance", "recovery-chance", and "gain-resistance" factors on "average-duration (of the pandemic last)", "average-percentage of infected", "maximum-percentage of infected", and "the expected peak-time". Obtained results from this work can assist determining the correct tactical responses of partial lockdown.

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Analysis of an epidemic model for transmitted diseases in a group of adults and an extension to two age classes

Cited by 8 publications

References 28 publications

Modelling personal cautiousness during the COVID-19 pandemic: a case study for Turkey and Italy

Modelling personal cautiousness during the COVID-19 pandemic: a case study for Turkey and Italy

Local Asymptotic Stability and Sensitivity Analysis of a New Mathematical Epidemic Model Without Immunity

An interaction-oriented multi-agent SIR model to assess the spread of SARS-CoV-2

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