Infection-acquired versus vaccine-acquired immunity in an SIRWS model

Leung, Tiffany; Campbell, Patricia T.; Hughes, Barry D.; Frascoli, Federico; McCaw, James M.

doi:10.1016/j.idm.2018.06.002

“…In the absence of repeated exposure, immunity is known to decline gradually (Leino 2000, Sanderson 2021). This phenomenon was well recognized by previous models, but they still treated it with the binary immunity state assumption (Leung et al 2018). Different components of immunity are known to decline at different rates.…”

Section: Introductionmentioning

confidence: 94%

Epidemiology: Gray Immunity Model Gives Qualitatively Different Predictions

Watve¹,

Bhisikar²,

Kharate³

2021

Preprint

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Compartmental models like the SIR model that dynamically divide the host population in categories such as susceptible, infected and immune form the mainstream of epidemiological modelling. Effectively such models treat infection and immunity as binary variables. We show here that considering immunity as a continuous variable instead of binary and incorporating factors that bring about small changes in immunity lead to qualitatively different epidemiological predictions. The small immunity effects (SIE) constitute cross immunity by other infections, small increments in immunity by sub clinical exposures and slow decay in the absence of repeated exposure. The SIE model explains many epidemiological patterns observed during the Covid-19 pandemic that are not adequately explained by conventional models. In the SIE model repeated waves are possible without the need for new variants. Peak and decline of a wave much before reaching herd immunity threshold, low level apparently stable existence of the pathogen, new surges after variable and unpredictable gaps, new surge after vaccinating majority of population are the common features of the pandemic mimicked by simulations using the SIE model. The model further shows complex interactions of different interventions that can be contextually synergistic as well as antagonistic. As a result, interventions intended to arrest the transmission are not always effective and can turn counterproductive under some conditions. Interventions that are beneficial in the short run can be potentially hazardous in the long run. In the absence of empirical estimates of many parameters, the model may not be useful to make quantitative predictions at this stage but it certainly challenges traditional wisdom and currently held beliefs behind non-pharmaceutical interventions recommended to control the epidemic. We also suggest testable predictions to differentiate between the causal logic of the SIE model against the prevalent explanations for the same observed phenomena.

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“…In the absence of repeated exposure, immunity is known to decline gradually (Leino 2000, Sanderson 2021). This phenomenon was well recognized by previous models, but they still treated it with the binary immunity state assumption (Leung et al 2018). Different components of immunity are known to decline at different rates.…”

Section: Introductionmentioning

confidence: 94%

Epidemiology: Gray Immunity Model Gives Qualitatively Different Predictions

Watve¹,

Bhisikar²,

Kharate³

2021

Preprint

1

0

View full text Add to dashboard Cite

Compartmental models like the SIR model that dynamically divide the host population in categories such as susceptible, infected and immune form the mainstream of epidemiological modelling. Effectively such models treat infection and immunity as binary variables. We show here that considering immunity as a continuous variable instead of binary and incorporating factors that bring about small changes in immunity lead to qualitatively different epidemiological predictions. The small immunity effects (SIE) constitute cross immunity by other infections, small increments in immunity by sub clinical exposures and slow decay in the absence of repeated exposure. The SIE model explains many epidemiological patterns observed during the Covid-19 pandemic that are not adequately explained by conventional models. In the SIE model repeated waves are possible without the need for new variants. Peak and decline of a wave much before reaching herd immunity threshold, low level apparently stable existence of the pathogen, new surges after variable and unpredictable gaps, new surge after vaccinating majority of population are the common features of the pandemic mimicked by simulations using the SIE model. The model further shows complex interactions of different interventions that can be contextually synergistic as well as antagonistic. As a result, interventions intended to arrest the transmission are not always effective and can turn counterproductive under some conditions. Interventions that are beneficial in the short run can be potentially hazardous in the long run. In the absence of empirical estimates of many parameters, the model may not be useful to make quantitative predictions at this stage but it certainly challenges traditional wisdom and currently held beliefs behind non-pharmaceutical interventions recommended to control the epidemic. We also suggest testable predictions to differentiate between the causal logic of the SIE model against the prevalent explanations for the same observed phenomena.

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“…In former SIRWS model studies, e.g. [5,9,12], the immune waning rates are the same for individuals who move from the recovered compartment to the waning compartment and for those who transition onward to the susceptible compartment. In contrast, we consider an asymmetric partition of the immunity period by introducing the parameters α > 1 and ω > 1 setting the average time spent in R and W to (ακ) −1 and (ωκ) −1 , respectively.…”

Section: Modified Sirws Modelmentioning

confidence: 99%

“…Members of W are still immune to infection and are subject to immune boosting upon re-exposure, the frequency of which is modulated by the boosting force ν. In our analysis, hosts going through boosting are not infectious, such as in [1,5,9,12], as opposed to [17].…”

Section: Modified Sirws Modelmentioning

confidence: 99%

Dynamics of an SIRWS model with waning of immunity and varying immune boosting period

Opoku-Sarkodie¹,

Bartha²,

Polner³

et al. 2022

Preprint

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SIRS models capture transmission dynamics of infectious diseases for which immunity is not lifelong. Extending these models by a W compartment for individuals with waning immunity, the boosting of the immune system upon repeated exposure may be incorporated. Previous analyses assumed identical waning rates from R to W and from W to S. This implicitly assumes equal length for the period of full immunity and of waned immunity. We relax this restriction, and allow an asymmetric partitioning of the total immune period. Stability switches of the endemic equilibrium are investigated with a combination of analytic and numerical tools. Then, continuation methods are applied to track bifurcations along the equilibrium branch. We find rich dynamics: Hopf bifurcations, endemic double bubbles, and regions of bistability. Our results highlight that the length of the period in which waning immunity can be boosted is a crucial parameter significantly influencing long term epidemiological dynamics.

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Infection-acquired versus vaccine-acquired immunity in an SIRWS model

Cited by 16 publications

References 57 publications

Epidemiology: Gray Immunity Model Gives Qualitatively Different Predictions

Epidemiology: Gray Immunity Model Gives Qualitatively Different Predictions

Epidemiology: Gray Immunity Model Gives Qualitatively Different Predictions

Dynamics of an SIRWS model with waning of immunity and varying immune boosting period

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