A geometric analysis of the SIR, SIRS and SIRWS epidemiological models

Jardón-Kojakhmetov, Hildeberto; Kuehn, Christian; Sensi, Mattia

doi:10.1016/j.nonrwa.2020.103220

Cited by 46 publications

(70 citation statements)

References 68 publications

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“…Hence, at this point an acceptable model with greater accuracy is needed. Lower dimensional mathematical models, with lower numbers of parameters and population compartments, that could be better reliably determined by the actual data, are preferable for studying and forecasting the ongoing pandemic [13] . Any model with higher number of dimensions need a large number of parameters to be expressed it, but this large number of parameters are difficult to find with adequate accuracy [14] , [15] .…”

Section: Introductionmentioning

confidence: 99%

Sensitivity analysis and optimal control of COVID-19 dynamics based on SEIQR model

et al. 2021

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It is of great curiosity to observe the effects of prevention methods and the magnitudes of the outbreak including epidemic prediction, at the onset of an epidemic. To deal with COVID-19 Pandemic, an SEIQR model has been designed. Analytical study of the model consists of the calculation of the basic reproduction number and the constant level of disease absent and disease present equilibrium. The model also explores number of cases and the predicted outcomes are in line with the cases registered. By parameters calibration, new cases in Pakistan are also predicted. The number of patients at the current level and the permanent level of COVID-19 cases are also calculated analytically and through simulations. The future situation has also been discussed, which could happen if precautionary restrictions are adopted.

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Section: Introductionmentioning

confidence: 99%

Sensitivity analysis and optimal control of COVID-19 dynamics based on SEIQR model

et al. 2021

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“…This paper aims at introducing methods from Geometric Singular Perturbation Theory (GSPT) to analyse these systems, building on the ideas introduced in Jardón-Kojakhmetov et al. ( 2021 ). The difference in time-scales between epidemic spread and demographic turnover, which can be observed in many diseases, is the motivation for the use of techniques from GSPT.…”

Section: Introductionmentioning

confidence: 99%

A geometric analysis of the SIRS epidemiological model on a homogeneous network

2021

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We study a fast–slow version of an SIRS epidemiological model on homogeneous graphs, obtained through the application of the moment closure method. We use GSPT to study the model, taking into account that the infection period is much shorter than the average duration of immunity. We show that the dynamics occurs through a sequence of fast and slow flows, that can be described through 2-dimensional maps that, under some assumptions, can be approximated as 1-dimensional maps. Using this method, together with numerical bifurcation tools, we show that the model can give rise to periodic solutions, differently from the corresponding model based on homogeneous mixing.

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“…To my knowledge, there have been two previous uses of the entry-exit function in epidemiological models, Li et al (2016) and Jardón-Kojakhmetov et al (2020).…”

Section: Introductionmentioning

confidence: 99%

Geometric singular perturbation theory analysis of an epidemic model with spontaneous human behavioral change

Schecter

2021

J. Math. Biol.

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We consider a model due to Piero Poletti and collaborators that adds spontaneous human behavioral change to the standard SIR epidemic model. In its simplest form, the Poletti model adds one differential equation, motivated by evolutionary game theory, to the SIR model. The new equation describes the evolution of a variable x that represents the fraction of the population following normal behavior. The remaining fraction uses altered behavior such as staying home, social isolation, mask wearing, etc. Normal behavior offers a higher payoff when the number of infectives is low; altered behavior offers a higher payoff when the number is high. We show that the entry–exit function of geometric singular perturbation theory can be used to analyze the model in the limit in which behavior changes on a much faster time scale than that of the epidemic. In particular, behavior does not change as soon as a different behavior has a higher payoff; current behavior is sticky. The delay until behavior changes is predicted by the entry–exit function.

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A geometric analysis of the SIR, SIRS and SIRWS epidemiological models

Cited by 46 publications

References 68 publications

Sensitivity analysis and optimal control of COVID-19 dynamics based on SEIQR model

Sensitivity analysis and optimal control of COVID-19 dynamics based on SEIQR model

A geometric analysis of the SIRS epidemiological model on a homogeneous network

Geometric singular perturbation theory analysis of an epidemic model with spontaneous human behavioral change

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