Analysis of a SIR model with pulse vaccination and temporary immunity: Stability, bifurcation and a cylindrical attractor

Church, Kevin E. M.; Liu, Xinzhi

doi:10.1016/j.nonrwa.2019.04.015

Cited by 20 publications

(9 citation statements)

References 19 publications

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“…They made concrete contributions to the spread of the virus using control theory. Other similar excellent works can be seen in previous studies 44–46 …”

Section: Introductionsupporting

confidence: 80%

“…Other similar excellent works can be seen in previous studies. [44][45][46] Through the review of existing studies, we can see that significant progress has been made in studying the transmission dynamics behavior of infectious disease models on complex networks, but there are also shortcomings. (1) Studies on existing models often adopt linear incidence rates.…”

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confidence: 99%

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Global stability and control strategies of a SIQRS epidemic model with time delay

Cui

Wang

2022

Math Methods in App Sciences

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“…They made concrete contributions to the spread of the virus using control theory. Other similar excellent works can be seen in previous studies 44–46 …”

Section: Introductionsupporting

confidence: 80%

mentioning

confidence: 99%

Global stability and control strategies of a SIQRS epidemic model with time delay

Cui

Wang

2022

Math Methods in App Sciences

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“…One of the classical variants focuses on an optimal pulse vaccination strategy , others focus on thresholds and bifurcations in the dynamic epidemic model [72][73][74][75], or the analysis of the delayed SIR model [15,16,22,30,51,61,[76][77][78][79]. There are several approaches that investigate the optimal control of the model with time-dependent or nonlinear functions [49,50,55,59,60,62,[67][68][69][70]75,[77][78][79][80][81][82][83][84][85][86][87][88][89][90][91][92][93] and the SIR model had also been applied to networks [34,[94][95][96]. While it is comparably easy to set up a network or agentbased [97][98]<...>…”

Section: Introductionmentioning

confidence: 99%

Analytical Modeling of the Temporal Evolution of Epidemics Outbreaks Accounting for Vaccinations

Schlickeiser

Kröger

2021

Physics

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With the vaccination against Covid-19 now available, how vaccination campaigns influence the mathematical modeling of epidemics is quantitatively explored. In this paper, the standard susceptible-infectious-recovered/removed (SIR) epidemic model is extended to a fourth compartment, V, of vaccinated persons. This extension involves the time t-dependent effective vaccination rate, v(t), that regulates the relationship between susceptible and vaccinated persons. The rate v(t) competes with the usual infection, a(t), and recovery, μ(t), rates in determining the time evolution of epidemics. The occurrence of a pandemic outburst with rising rates of new infections requires k+b<1−2η, where k=μ(0)/a(0) and b=v(0)/a(0) denote the initial values for the ratios of the three rates, respectively, and η≪1 is the initial fraction of infected persons. Exact analytical inverse solutions t(Q) for all relevant quantities Q=[S,I,R,V] of the resulting SIRV model in terms of Lambert functions are derived for the semi-time case with time-independent ratios k and b between the recovery and vaccination rates to the infection rate, respectively. These inverse solutions can be approximated with high accuracy, yielding the explicit time-dependences Q(t) by inverting the Lambert functions. The values of the three parameters k, b and η completely determine the reduced time evolution of the SIRV-quantities Q(τ). The influence of vaccinations on the total cumulative number and the maximum rate of new infections in different countries is calculated by comparing with monitored real time Covid-19 data. The reduction in the final cumulative fraction of infected persons and in the maximum daily rate of new infections is quantitatively determined by using the actual pandemic parameters in different countries. Moreover, a new criterion is developed that decides on the occurrence of future Covid-19 waves in these countries. Apart from in Israel, this can happen in all countries considered.

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“…SIR models with a vaccination component (e.g. [46,47]) demonstrate that the introduction of vaccination decreases the susceptible and infected populations proportional to vaccination rate [46]. Though these models are very useful in determining the intensity of intervention needed to address an epidemic [46], they do not explain fluctuations in vaccination rates or lower-than-expected rates of adoption based on cultural factors.…”

Section: Introductionmentioning

confidence: 99%

The Cultural Evolution of Vaccine Hesitancy: Modeling the Interaction between Beliefs and Behaviors

Anderson

Creanza

2022

Preprint

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In the last decade, despite the proven efficacy of vaccines, the developed world has seen a resurgence of vaccine-preventable diseases (VPDs) such as measles, pertussis, and polio. Vaccine hesitancy, an individual behavior influenced by historical, political, and socio-cultural factors, is believed to be a primary factor responsible for decreasing vaccine coverage, thereby increasing the risk and occurrence of VPD outbreaks. Society, culture, and individual motivations affect human decisions regarding health behavior and preventative care, and health perceptions and health-related behaviors can change at the population level as cultures evolve. In recent years, mathematical models of disease dynamics have begun to incorporate aspects of human behavior, however they do not address how evolving cultures influence these health behaviors. Here, using a mathematical modeling framework, we explore the effects of cultural evolution on vaccine hesitancy and vaccination behavior. With this model, we shed light on the facets of cultural evolution (vertical and oblique transmission, homophily, etc.) that promote the spread of vaccine hesitancy, ultimately affecting levels of vaccination coverage and VPD outbreak risk in a population. In addition, we present our model as a generalizable framework for exploring cultural evolution when beliefs influence, but do not strictly dictate, human behaviors. We show vaccine confidence and vaccine-conferred benefits can be driving forces of vaccine coverage, and we demonstrate that an assortative preference among vaccine-hesitant individuals can lead to increased vaccine hesitancy and lower vaccine coverage. Further, we show that vaccine mandates can lead to a phenomenon in which high vaccine hesitancy co-occurs with high vaccination coverage, and that high vaccine confidence can be maintained even in areas where access to vaccines is limited.

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Analysis of a SIR model with pulse vaccination and temporary immunity: Stability, bifurcation and a cylindrical attractor

Cited by 20 publications

References 19 publications

Global stability and control strategies of a SIQRS epidemic model with time delay

Global stability and control strategies of a SIQRS epidemic model with time delay

Analytical Modeling of the Temporal Evolution of Epidemics Outbreaks Accounting for Vaccinations

The Cultural Evolution of Vaccine Hesitancy: Modeling the Interaction between Beliefs and Behaviors

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