Extinction and persistence of a stochastic SIRV epidemic model with nonlinear incidence rate

Rifhat, Ramziya; Teng, Zhidong; Wang, Chunxia

doi:10.1186/s13662-021-03347-3

Cited by 21 publications

(16 citation statements)

References 42 publications

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“…Note that just a moderate decrease of the intensity σ 2 related to superspreaders results in a significant enlargement of R S 0 , which gives the superspreaders an important role in the dynamic of the stochastic model. For analysis of sensitivity of a different stochastic compartmental model for COVID-19 to the noise level we refer to [28]. These arguments can be seen as a justification for use of stochastic differential models for describing and forecasting the course of the epidemic.…”

Section: Sensitivity Analysis Of Basic Reproduction Number Of Deterministic Model and Its Stochastic Model Counterpartmentioning

confidence: 99%

Analysis of stability and sensitivity of deterministic and stochastic models for the spread of the new corona virus SARS-CоV-2

Jovanović

Ðordjevic

Manojlović

et al. 2021

Filomat

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Basic reproduction number for deterministic SEIPHAR model and its stochastic counterpart for the spread of SARS-CoV-2 virus are analyzed and compared. For deterministic version of the model, conditions for stability of the disease-free equilibrium are derived and, in addition, conditions for existence of bifurcation state related to endemic equilibrium are established. For stochastic model, conditions for extinction and persistence in mean of the disease are derived. Complete sensitivity analysis of thresholds between the extinction and mean-persistence are performed for both the deterministic and the stochastic version of the model. Influence of variation in parameter values is illustrated for epidemics in Wuhan in early 2020.

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Section: Sensitivity Analysis Of Basic Reproduction Number Of Deterministic Model and Its Stochastic Model Counterpartmentioning

confidence: 99%

Analysis of stability and sensitivity of deterministic and stochastic models for the spread of the new corona virus SARS-CоV-2

Jovanović

Ðordjevic

Manojlović

et al. 2021

Filomat

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show abstract

“…In several very recent publications 31 – 35 applied to the COVID-19 epidemic, researchers have developed and used SIR and SEIR based models with vaccination to overcome the limitations of the conventional SIR model. The work in 31 presents an investigation of the dynamics of a stochastic SIRV epidemic model with general non-linear incidence and vaccination. The introduced random fluctuations controls the disease outbreak.…”

Section: Introductionmentioning

confidence: 99%

“…SIR and SEIR models with vaccination are used to simulate and predict the development of the COVID-19 spread, e.g. 25,[28][29][30] .In several very recent publications [31][32][33][34][35] applied to the COVID-19 epidemic, researchers have developed and used SIR and SEIR based models with vaccination to overcome the limitations of the conventional SIR model. The work in 31 presents an investigation of the dynamics of a stochastic SIRV epidemic model with general nonlinear incidence and vaccination.…”

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confidence: 99%

Adaptive SIR model with vaccination: simultaneous identification of rates and functions illustrated with COVID-19

Marinov

Marinova

2022

Sci Rep

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An Adaptive Susceptible-Infected-Removed-Vaccinated (A-SIRV) epidemic model with time-dependent transmission and removal rates is constructed for investigating the dynamics of an epidemic disease such as the COVID-19 pandemic. Real data of COVID-19 spread is used for the simultaneous identification of the unknown time-dependent rates and functions participating in the A-SIRV system. The inverse problem is formulated and solved numerically using the Method of Variational Imbedding, which reduces the inverse problem to a problem for minimizing a properly constructed functional for obtaining the sought values. To illustrate and validate the proposed solution approach, the present study used available public data for several countries with diverse population and vaccination dynamics—the World, Israel, The United States of America, and Japan.

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“…COVID-19 country-based simulations (Malaysia [8], Saudi Arabia [9], Spain [10], United States [11], and others) have already been reported. A fast simulation method of differential equations is a susceptible-infected-recovered-vaccination (SIRV) model [12][13][14][15][16]. However, these models can represent only the first dose of the vaccination.…”

Section: Introductionmentioning

confidence: 99%

Theoretical Analysis of SIRVVD Model to Provide Insight on the Target Rate of COVID-19/SARS-CoV-2 Vaccination in Japan

Omae,

Sasaki,

Toyotani

et al. 2022

Preprint

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The effectiveness of the first and second dose vaccinations are different for COVID-19; therefore, a susceptible-infected-recovered-vaccination1-vaccination2-death (SIRVVD) model that can represent the states of the first and second vaccination doses has been proposed. By the previous study, we can carry out simulating the spread of infectious disease considering the effects of the first and second doses of the vaccination based on the SIRVVD model. However, theoretical analysis of the SIRVVD Model is insufficient. Therefore, we obtained an analytical expression of the infectious number, by treating the numbers of susceptible persons and vaccinated persons as parameters. We used the solution to determine the target rate of the vaccination for decreasing the infection numbers of the COVID-19 Delta variant (B.1.617) in Japan. Further, we investigated the target vaccination rates for cases with strong or weak variants by comparison with the COVID-19 Delta variant (B.1.617). This study contributes to the mathematical development of the SIRVVD model and provides insight into the target rate of the vaccination to decrease the number of infections.

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Extinction and persistence of a stochastic SIRV epidemic model with nonlinear incidence rate

Cited by 21 publications

References 42 publications

Analysis of stability and sensitivity of deterministic and stochastic models for the spread of the new corona virus SARS-CоV-2

Analysis of stability and sensitivity of deterministic and stochastic models for the spread of the new corona virus SARS-CоV-2

Adaptive SIR model with vaccination: simultaneous identification of rates and functions illustrated with COVID-19

Theoretical Analysis of SIRVVD Model to Provide Insight on the Target Rate of COVID-19/SARS-CoV-2 Vaccination in Japan

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