COVID-19 pandemic models revisited with a new proposal: Plenty of epidemiological models outcast the simple population dynamics solution

Paul, Ayan; Reja, Selim; Kundu, Sayani; Bhattacharya, Sabyasachi

doi:10.1016/j.chaos.2021.110697

Cited by 23 publications

(11 citation statements)

References 65 publications

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“…The global outbreak of the novel coronavirus pneumonia has entered a stage of normalization and has not yet been effectively controlled [ 5 – 7 , 10 , 14 ]. The degree of activity of the new crown virus is highly dependent on temperature.…”

Section: Introductionmentioning

confidence: 99%

The effect of self-limiting on the prevention and control of the diffuse COVID-19 epidemic with delayed and temporal-spatial heterogeneous

Zhu

Jiang

2021

BMC Infect Dis

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Background The global spread of the novel coronavirus pneumonia is still continuing, and a new round of more serious outbreaks has even begun in some countries. In this context, this paper studies the dynamics of a type of delayed reaction-diffusion novel coronavirus pneumonia model with relapse and self-limiting treatment in a temporal-spatial heterogeneous environment. Methods First, focus on the self-limiting characteristics of COVID-19, incorporate the relapse and self-limiting treatment factors into the diffusion model, and study the influence of self-limiting treatment on the diffusion of the epidemic. Second, because the traditional Lyapunov stability method is difficult to determine the spread of the epidemic with relapse and self-limiting treatment, we introduce a completely different method, relying on the existence conditions of the exponential attractor of our newly established in the infinite-dimensional dynamic system to determine the diffusion of novel coronavirus pneumonia. Third, relapse and self-limiting treatment have led to a change in the structure of the delayed diffusion COVID-19 model, and the traditional basic reproduction number $$R_0$$ R 0 no longer has threshold characteristics. With the help of the Krein-Rutman theorem and the eigenvalue method, we studied the threshold characteristics of the principal eigenvalue and found that it can be used as a new threshold to describe the diffusion of the epidemic. Results Our results prove that the principal eigenvalue $$\uplambda ^{*}$$ λ ∗ of the delayed reaction-diffusion COVID-19 system with relapse and self-limiting treatment can replace the basic reproduction number $$R_0$$ R 0 to describe the threshold effect of disease transmission. Combine with the latest official data and the prevention and control strategies, some numerical simulations on the stability and global exponential attractiveness of the diffusion of the COVID-19 epidemic in China and the USA are given. Conclusions Through the comparison of numerical simulations, we find that self-limiting treatment can significantly promote the prevention and control of the epidemic. And if the free activities of asymptomatic infected persons are not restricted, it will seriously hinder the progress of epidemic prevention and control.

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Section: Introductionmentioning

confidence: 99%

The effect of self-limiting on the prevention and control of the diffuse COVID-19 epidemic with delayed and temporal-spatial heterogeneous

Zhu

Jiang

2021

BMC Infect Dis

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“…Therefore, the parameter estimation may not be significant through the nonlinear least-square method. Another well established technique for model fitting is grid-search technique 16,19,44,45 . We perform the entire grid search procedure using the following steps-1.…”

Section: Dataset and Fitting Methodologymentioning

confidence: 99%

A noble extended stochastic logistic model for cell proliferation with density-dependent parameters

Roy

Ghosh

Saha³

et al. 2021

Preprint

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Cell proliferation often experiences a density-dependent intrinsic proliferation rate (IPR) and negative feedback from growth-inhibiting molecules in culture media. The lack of flexible models with explanatory parameters fails to capture such a proliferation mechanism. We propose an extended logistic growth law with the density-dependent IPR and additional negative feedback. The extended parameters of the proposed model can be interpreted as density-dependent cell-cell cooperation and negative feedback on cell proliferation. Moreover, we incorporate further density regulation for flexibility in the model through environmental resistance on cells. The proposed growth law has similarities with the strong Allee model and harvesting phenomenon. We also develop the stochastic analog of the deterministic model by representing possible heterogeneity in growth-inhibiting molecules and environmental perturbation of the culture setup as correlated multiplicative and additive noises. The model provides a maximum sustainable stable cell density (MSSCD) and a new fitness measure for proliferative cells. The proposed model shows superiority to the logistic law after fitting to real cell culture datasets. We illustrate both MSSCD and the new cell fitness for a range of parameters. The cell density distributions reveal the chance of overproliferation, underproliferation, or decay for different parameter sets under the deterministic and stochastic setups.

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“…Meanwhile, historically, the Gompertz equation:

should be recognized as the first model of this class, which was proposed as early as 1825 [2] . This model is not commonly used in describing the dynamics of the epidemic development, although it is mentioned in several papers and books on mathematical biology [ 16 , 17 , 18 , 19 , 20 , 21 ]. We especially note one of the recent papers [20] , where this model was generalized in the same way as the classical logistic model.…”

Section: Introductionmentioning

confidence: 99%

Gompertz model in COVID-19 spreading simulation

Pelinovsky

Kokoulina

Epifanova

et al. 2022

Chaos, Solitons & Fractals

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The paper reports on application of the Gompertz model to describe the growth dynamics of COVID-19 cases during the first wave of the pandemic in different countries. Modeling has been performed for 23 countries: Australia, Austria, Belgium, Brazil, Great Britain, Germany, Denmark, Ireland, Spain, Italy, Canada, China, the Netherlands, Norway, Serbia, Turkey, France, Czech Republic, Switzerland, South Korea, USA, Mexico, and Japan. The model parameters are determined by regression analysis based on official World Health Organization data available for these countries. The comparison of the predictions given by the Gompertz model and the simple logistic model (i.e., Verhulst model) is performed allowing to conclude on the higher accuracy of the Gompertz model.

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COVID-19 pandemic models revisited with a new proposal: Plenty of epidemiological models outcast the simple population dynamics solution

Cited by 23 publications

References 65 publications

The effect of self-limiting on the prevention and control of the diffuse COVID-19 epidemic with delayed and temporal-spatial heterogeneous

The effect of self-limiting on the prevention and control of the diffuse COVID-19 epidemic with delayed and temporal-spatial heterogeneous

A noble extended stochastic logistic model for cell proliferation with density-dependent parameters

Gompertz model in COVID-19 spreading simulation

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