Stability analysis of a nonlocal SIHRDP epidemic model with memory effects

Lu, Zhenzhen; Yu, Yongguang; Chen, YangQuan; Ren, Guojian; Xu, Conghui; Wang, Shuhui

doi:10.1007/s11071-022-07286-w

Cited by 9 publications

(5 citation statements)

References 32 publications

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“…However, formulating models for the population dynamics of SARS-CoV-2 can evaluate the adequacy of diverse anticipation and mediation strategies. Some research works on modeling the evolution of infectious diseases are available in the literature [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31] Recently, Alex Viguerie et al [32] introduced a mathematical model based on partial differential equations coupled with a heterogeneous diffusion model for an early version of susceptible, exposed, infected, recovered, and deceased populations. This model describes COVID-19 pandemic, and aims to capture dynamics also based on human habits and geographical features.…”

Section: Introductionmentioning

confidence: 99%

Fractional mathematical modeling for the transmission dynamics of SARS-CoV-2 infection

Thabet

Kendre

2023

Preprint

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This paper presents a mathematical model based on nonlinear PDEs of fractional veritable-order derivatives which describe the host population surviving on the transmission and evolution of the describes severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) pandemic. Five host population groups have been considered, the susceptible, exposed, infected, recovered, and deceased (SEIRD) populations. The proposed model is governed by PDEs with fractional variable-order derivatives. The proposed model is new and has not been introduced before in its current formulation, therefore, the proposed technique is not compared with other techniques or real scenarios for the same model. The advantage of the used fractional partial derivatives of variable order that it can model the rate of change of subpopulation for the debated model. As an efficient tool to obtain the solution of the proposed model, a modified analytical technique based on the Adomian decomposition method is introduced. However, the present study is in general and can be applied to a host population of any country that can help inform public health interventions.

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Section: Introductionmentioning

confidence: 99%

Fractional mathematical modeling for the transmission dynamics of SARS-CoV-2 infection

Thabet

Kendre

2023

Preprint

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“…Therefore, we only review some of those that we believe are important for their applications. For example, Al-Tuwairqi and Al-Harbi (1) proposed a model to investigate the effects of time delay in vaccine production on COVID-19 spread. In addition, Zhenzhen et al (2) studied a model with "long memory" to describe the multi-wave peaks of the COVID-19 dynamics, where "long memory" allows for predicting this last using non-local terms, which means that one can include an arbitrary long history of the disease.…”

Section: Introductionmentioning

confidence: 99%

A general modeling framework for quantitative tracking, accurate prediction of ICU, and assessing vaccination for COVID-19 in Chile

Cumsille

Rojas-Díaz

Conca

2023

Front. Public Health

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BackgroundOne of the main lessons of the COVID-19 pandemic is that we must prepare to face another pandemic like it. Consequently, this article aims to develop a general framework consisting of epidemiological modeling and a practical identifiability approach to assess combined vaccination and non-pharmaceutical intervention (NPI) strategies for the dynamics of any transmissible disease.Materials and methodsEpidemiological modeling of the present work relies on delay differential equations describing time variation and transitions between suitable compartments. The practical identifiability approach relies on parameter optimization, a parametric bootstrap technique, and data processing. We implemented a careful parameter optimization algorithm by searching for suitable initialization according to each processed dataset. In addition, we implemented a parametric bootstrap technique to accurately predict the ICU curve trend in the medium term and assess vaccination.ResultsWe show the framework's calibration capabilities for several processed COVID-19 datasets of different regions of Chile. We found a unique range of parameters that works well for every dataset and provides overall numerical stability and convergence for parameter optimization. Consequently, the framework produces outstanding results concerning quantitative tracking of COVID-19 dynamics. In addition, it allows us to accurately predict the ICU curve trend in the medium term and assess vaccination. Finally, it is reproducible since we provide open-source codes that consider parameter initialization standardized for every dataset.ConclusionThis work attempts to implement a holistic and general modeling framework for quantitative tracking of the dynamics of any transmissible disease, focusing on accurately predicting the ICU curve trend in the medium term and assessing vaccination. The scientific community could adapt it to evaluate the impact of combined vaccination and NPIs strategies for COVID-19 or any transmissible disease in any country and help visualize the potential effects of implemented plans by policymakers. In future work, we want to improve the computational cost of the parametric bootstrap technique or use another more efficient technique. The aim would be to reconstruct epidemiological curves to predict the combined NPIs and vaccination policies' impact on the ICU curve trend in real-time, providing scientific evidence to help anticipate policymakers' decisions.

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“…This is very useful for public health and preventive healthcare. For this 5 reason, in efforts to prevent the COVID-19 epidemic, many mathematicians and epidemiologists have proposed and analyzed a great number of mathematical models describing transmission dynamics of the COVID-19 (see, for example, [6,22,33,34,39,40,49,50,51,54,59,60] and references therein). As an important consequence, mitigation and prevention measures of COVID-19 outbreaks were suggested.…”

Section: Introductionmentioning

confidence: 99%

A dynamically consistent nonstandard finite difference scheme for a generalized SEIR epidemic model

Hoang

2023

Preprint

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Although Coronavirus disease 2019 (COVID-19) pandemic caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has been controlled and prevented, mathematical modeling and analysis of transmission dynamics of COVID-19 still plays an essential role not only in the post COVID-19 era but also in the study of infectious diseases. This is an important foundation to propose effective strategies and measures for controlling diseases and projecting public health. This work is devoted to proposing and analyzing a new mathematical study for transmission dynamics of COVID-19. We first introduce a generalized SEIR epidemic model that use general nonlinear incidence rates to describe the “psychological” effect. After that, a rigorous mathematical analysis for the proposed COVID-19 model is performed. We establish the positivity and boundedness, calculate the basic reproduction number, determine possible (disease-free and endemic-disease) equilibrium points and investigate their asymptotic stability properties of the SEIR model. The obtained results improve and extend an SEIR model constructed in a recent work. For the purpose of numerical simulation, the Mickens’ methodology is applied to construct a dynamically consistent nonstandard finite difference (NSFD) model for the proposed SEIR epidemic model. The constructed NSFD scheme has the ability to provide reliable approximations that not only preserve the dynamical properties of the SEIR model for all the values of the step size but also are easy to be implemented. Finally, a set of illustrative numerical experiments is conducted to support the theoretical findings and to confirm advantages of the NSFD scheme over some well-known standard ones.

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Stability analysis of a nonlocal SIHRDP epidemic model with memory effects

Cited by 9 publications

References 32 publications

Fractional mathematical modeling for the transmission dynamics of SARS-CoV-2 infection

Fractional mathematical modeling for the transmission dynamics of SARS-CoV-2 infection

A general modeling framework for quantitative tracking, accurate prediction of ICU, and assessing vaccination for COVID-19 in Chile

A dynamically consistent nonstandard finite difference scheme for a generalized SEIR epidemic model

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