Vaccination in a two-group epidemic model

Aniţa, Sebastian; Banerjee, Malay; Ghosh, Samiran; Volpert, Vitaly

doi:10.1016/j.aml.2021.107197

Cited by 14 publications

(5 citation statements)

References 7 publications

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“…We compared the final size of the epidemic and maximal number of infected obtained in the Formulas (15), (21), and (23), respectively. Note that these formulae depend on τ and β.…”

Section: Discussionmentioning

confidence: 99%

“…Modern studies in mathematical epidemiology begin with the SIR model developed in the works by W. O. Kermack and A. G. McKendrick [11][12][13], stimulated by the Spanish flu epidemic in 1918-1919. Among many developments of such models, we can cite multi-compartment models [14][15][16], models with a time-varying or nonlinear disease transmission rate [17,18], multi-patch models [19][20][21], multi-group models incorporating the effect of the heterogeneity of the population [22], and epidemic models with vaccination and other control measures [23,24]. Random movement of individuals in the population is considered in spatiotemporal models in order to describe spatial distributions of susceptible and infected individuals [25,26].…”

Section: Introductionmentioning

confidence: 99%

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An Epidemic Model with Time Delay Determined by the Disease Duration

2022

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Immuno-epidemiological models with distributed recovery and death rates can describe the epidemic progression more precisely than conventional compartmental models. However, the required immunological data to estimate the distributed recovery and death rates are not easily available. An epidemic model with time delay is derived from the previously developed model with distributed recovery and death rates, which does not require precise immunological data. The resulting generic model describes epidemic progression using two parameters, disease transmission rate and disease duration. The disease duration is incorporated as a delay parameter. Various epidemic characteristics of the delay model, namely the basic reproduction number, the maximal number of infected, and the final size of the epidemic are derived. The estimation of disease duration is studied with the help of real data for COVID-19. The delay model gives a good approximation of the COVID-19 data and of the more detailed model with distributed parameters.

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“…We compared the final size of the epidemic and maximal number of infected obtained in the Formulas (15), (21), and (23), respectively. Note that these formulae depend on τ and β.…”

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

An Epidemic Model with Time Delay Determined by the Disease Duration

2022

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“…F I G U R E 1 Diagram of one age class dynamics subject to model (1)(2)(3)(4)(5)(6)(7)(8)(9)(10) where…”

Section: Structured Model Descriptionmentioning

confidence: 99%

“…Epidemiological models and optimal control were commonly used to provide information useful for decisions on disease prevention, surveillance, control, treatment and vaccine strategies implementation. This type of models is applied to several infectious diseases ranging from Influenza to Ebola or the ongoing COVID-19 outbreak 6,7,8,9,10,11,12 . And based on the newly-striking Covid-19 pandemic, that showed the importance of quick acting, came the idea of this work.…”

Section: Introductionmentioning

confidence: 99%

Age-optimal vaccination strategy for respiratory infectious disease: a constraint-dependant approach

Kebir,

Bouhali,

Aribi

et al. 2023

Preprint

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After the vaccine implementation for COVID-19, the WHO set a unified vaccination approach to be adopted by all different countries. However, given the various constraints including vaccine availability, heterogeneous age distributions, and differing control measures across countries, questions arise about the optimality of the WHO strategy. In this study, we develop an age-structured SEIR epidemic model with vaccinated and unvaccinated compartments to optimize age-targeted vaccination strategies for COVID-19, incorporating realistic constraints. The model equilibria and the basic reproduction number $R_0$ are checked. Moreover, mathematical formulation and analysis of optimal control problem, are conducted. The model is calibrated to COVID-19 data and simulated to solve the optimal control problem under various vaccination and distancing scenarios. Results demonstrate that the optimal strategy strongly depends on the population age distribution and contact patterns. Findings emphasize the significance of age-specific disease transmission in designing vaccination priorities, particularly when vaccine supplies are constrained. The model provides a quantitative framework to inform optimal allocation strategies in a general way that allows to adapt the model for other infectious diseases exhibiting similar features to Covid-19.

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“…Since the works of Kermack and McKendrick [11,12], motivated by the Spanish influenza epidemic in 1918-1919, many epidemic models have been introduced, such as multicompartment models [13,14], models with a nonlinear disease transmission rate [15,16], multi-patch models [17,18], multi-group models incorporating the effect of the heterogeneity of the population [19], and epidemic models with vaccination and other control measures [20,21]. The random movement of individuals in the population is considered in spatio-temporal models in order to describe spatial distributions of susceptible and infected individuals [22,23].…”

Section: Introductionmentioning

confidence: 99%

Dynamics of Persistent Epidemic and Optimal Control of Vaccination

Saade,

Aniţa,

Volpert

2023

Mathematics

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This paper is devoted to a model of epidemic progression, taking into account vaccination and immunity waning. The model consists of a system of delay differential equations with time delays determined by the disease duration and immunity loss. Periodic epidemic outbreaks emerge as a result of the instability of a positive stationary solution if the basic reproduction number exceeds some critical value. Vaccination can change epidemic dynamics, resulting in more complex aperiodic oscillations confirmed by some data on Influenza A in Norway. Furthermore, the measures of social distancing during the COVID-19 pandemic weakened seasonal influenza in 2021, but increased it during the next year. Optimal control allows for the minimization of epidemic cost by vaccination.

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Vaccination in a two-group epidemic model

Cited by 14 publications

References 7 publications

An Epidemic Model with Time Delay Determined by the Disease Duration

An Epidemic Model with Time Delay Determined by the Disease Duration

Age-optimal vaccination strategy for respiratory infectious disease: a constraint-dependant approach

Dynamics of Persistent Epidemic and Optimal Control of Vaccination

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