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  1. Article ; Online: SIRS epidemics with individual heterogeneity of immunity waning.

    El Khalifi, Mohamed / Britton, Tom

    Journal of theoretical biology

    2024  Volume 587, Page(s) 111815

    Abstract: In the current paper we analyse an extended SIRS epidemic model in which immunity at the individual level wanes gradually at exponential rate, but where the waning rate may differ between individuals, for instance as an effect of differences in immune ... ...

    Abstract In the current paper we analyse an extended SIRS epidemic model in which immunity at the individual level wanes gradually at exponential rate, but where the waning rate may differ between individuals, for instance as an effect of differences in immune systems. The model also includes vaccination schemes aimed to reach and maintain herd immunity. We consider both the informed situation where the individual waning parameters are known, thus allowing selection of vaccinees being based on both time since last vaccination as well as on the individual waning rate, and the more likely uninformed situation where individual waning parameters are unobserved, thus only allowing vaccination schemes to depend on time since last vaccination. The optimal vaccination policies for both the informed and uniformed heterogeneous situation are derived and compared with the homogeneous waning model (meaning all individuals have the same immunity waning rate), as well as to the classic SIRS model where immunity at the individual level drops from complete immunity to complete susceptibility in one leap. It is shown that the classic SIRS model requires least vaccines, followed by the SIRS with homogeneous gradual waning, followed by the informed situation for the model with heterogeneous gradual waning. The situation requiring most vaccines for herd immunity is the most likely scenario, that immunity wanes gradually with unobserved individual heterogeneity. For parameter values chosen to mimic COVID-19 and assuming perfect initial immunity and cumulative immunity of 12 months, the classic homogeneous SIRS epidemic suggests that vaccinating individuals every 15 months is sufficient to reach and maintain herd immunity, whereas the uninformed case for exponential waning with rate heterogeneity corresponding to a coefficient of variation being 0.5, requires that individuals instead need to be vaccinated every 4.4 months.
    Language English
    Publishing date 2024-04-12
    Publishing country England
    Document type Journal Article
    ZDB-ID 2972-5
    ISSN 1095-8541 ; 0022-5193
    ISSN (online) 1095-8541
    ISSN 0022-5193
    DOI 10.1016/j.jtbi.2024.111815
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  2. Article: Quantifying the preventive effect of wearing face masks.

    Britton, Tom

    Proceedings. Mathematical, physical, and engineering sciences

    2021  Volume 477, Issue 2251, Page(s) 20210151

    Abstract: An important task in combating the current Covid-19 pandemic lies in estimating the effect of different preventive measures. Here, we focus on the preventive effect of enforcing the use of face masks. Several publications study this effect, however, ... ...

    Abstract An important task in combating the current Covid-19 pandemic lies in estimating the effect of different preventive measures. Here, we focus on the preventive effect of enforcing the use of face masks. Several publications study this effect, however, often using different measures such as: the relative attack rate in case-control studies, the effect on incidence growth/decline in a specific time frame and the effect on the number of infected in a given time frame. These measures all depend on community-specific features and are hence not easily transferred to other community settings. We argue that a more universal measure is the relative reduction in the reproduction number, which we call the
    Language English
    Publishing date 2021-07-07
    Publishing country England
    Document type Journal Article
    ZDB-ID 209241-4
    ISSN 1471-2946 ; 1364-5021 ; 0962-8444 ; 0080-4630 ; 0950-1207
    ISSN (online) 1471-2946
    ISSN 1364-5021 ; 0962-8444 ; 0080-4630 ; 0950-1207
    DOI 10.1098/rspa.2021.0151
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  3. Article ; Online: Extending susceptible-infectious-recovered-susceptible epidemics to allow for gradual waning of immunity.

    El Khalifi, Mohamed / Britton, Tom

    Journal of the Royal Society, Interface

    2023  Volume 20, Issue 206, Page(s) 20230042

    Abstract: Susceptible-infectious-recovered-susceptible (SIRS) epidemic models assume that individual immunity wanes in one leap, from complete immunity to complete susceptibility. For many diseases immunity on the contrary wanes gradually, something that has ... ...

    Abstract Susceptible-infectious-recovered-susceptible (SIRS) epidemic models assume that individual immunity wanes in one leap, from complete immunity to complete susceptibility. For many diseases immunity on the contrary wanes gradually, something that has become even more evident during COVID-19 pandemic where also recently infected have a reinfection risk, and booster vaccines are given to increase immunity. Here, a novel mathematical model is presented allowing for the gradual decay of immunity following linear or exponential waning functions. The two new models and the SIRS model are compared assuming all three models have the same cumulative immunity. When no intervention is put in place, we find that the long-term prevalence is higher for the models with gradual waning. If aiming for herd immunity by continuous vaccination, it is shown that larger vaccine quantities are required when immunity wanes gradually compared with results obtained from the SIRS model, and this difference is the biggest for the most realistic assumption of exponentially waning of immunity. For parameter choices fitting to COVID-19, the critical amount of vaccine supply is about 50% higher if immunity wanes linearly, and more than 150% higher when immunity wanes exponentially, when compared with the classic SIRS epidemic model.
    MeSH term(s) Humans ; Pandemics ; COVID-19/epidemiology ; Communicable Diseases ; Immunity, Herd ; Systemic Inflammatory Response Syndrome
    Language English
    Publishing date 2023-09-13
    Publishing country England
    Document type Journal Article ; Research Support, Non-U.S. Gov't
    ZDB-ID 2156283-0
    ISSN 1742-5662 ; 1742-5689
    ISSN (online) 1742-5662
    ISSN 1742-5689
    DOI 10.1098/rsif.2023.0042
    Database MEDical Literature Analysis and Retrieval System OnLINE

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  4. Article ; Online: Analysing the Effect of Test-and-Trace Strategy in an SIR Epidemic Model.

    Zhang, Dongni / Britton, Tom

    Bulletin of mathematical biology

    2022  Volume 84, Issue 10, Page(s) 105

    Abstract: Consider a Markovian SIR epidemic model in a homogeneous community. To this model we add a rate at which individuals are tested, and once an infectious individual tests positive it is isolated and each of their contacts are traced and tested ... ...

    Abstract Consider a Markovian SIR epidemic model in a homogeneous community. To this model we add a rate at which individuals are tested, and once an infectious individual tests positive it is isolated and each of their contacts are traced and tested independently with some fixed probability. If such a traced individual tests positive it is isolated, and the contact tracing is iterated. This model is analysed using large population approximations, both for the early stage of the epidemic when the "to-be-traced components" of the epidemic behaves like a branching process, and for the main stage of the epidemic where the process of to-be-traced components converges to a deterministic process defined by a system of differential equations. These approximations are used to quantify the effect of testing and of contact tracing on the effective reproduction numbers (for the components as well as for the individuals), the probability of a major outbreak, and the final fraction getting infected. Using numerical illustrations when rates of infection and natural recovery are fixed, it is shown that Test-and-Trace strategy is effective in reducing the reproduction number. Surprisingly, the reproduction number for the branching process of components is not monotonically decreasing in the tracing probability, but the individual reproduction number is conjectured to be monotonic as expected. Further, in the situation where individuals also self-report for testing, the tracing probability is more influential than the screening rate (measured by the fraction infected being screened).
    MeSH term(s) Basic Reproduction Number ; Contact Tracing ; Epidemics/prevention & control ; Humans ; Mathematical Concepts ; Models, Biological
    Language English
    Publishing date 2022-08-24
    Publishing country United States
    Document type Journal Article ; Research Support, Non-U.S. Gov't
    ZDB-ID 184905-0
    ISSN 1522-9602 ; 0007-4985 ; 0092-8240
    ISSN (online) 1522-9602
    ISSN 0007-4985 ; 0092-8240
    DOI 10.1007/s11538-022-01065-9
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    In stock of ZB MED Cologne/Königswinter

    Zs.B 754: Show issues Location:
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  5. Article ; Online: Basic estimation-prediction techniques for Covid-19, and a prediction for Stockholm

    Britton, Tom

    Abstract: An important task during the current Covid-19 pandemic is to predict the remainder of the epidemic, both without preventive measures and with. In the current paper we address this question using a simple estimation-prediction method. The input is the ... ...

    Abstract An important task during the current Covid-19 pandemic is to predict the remainder of the epidemic, both without preventive measures and with. In the current paper we address this question using a simple estimation-prediction method. The input is the observed initial doubling time and a known value of R0. The simple General epidemic model is then fitted, and time calibration to calendar time is done using the observed number of case fatalities, together with estimates of the time between infection to death and the infection fatality risk. Finally, predictions are made assuming no change of behaviour, as well as for the situation where preventive measures are put in place at one specific time-point. The overall effect of the preventive measures is assumed to be known, or else estimated from the observed increased doubling time after preventive measures are put in place. The predictions are highly sensitive to the doubling times without and with preventive measures, sensitive to R0, but less sensitive to the estimates used for time-calibration: observed number of case fatalities, typical time between infection and death, and the infection fatality risk. The method is applied to the urban area of Stockholm, and predictions show that the peak of infections appear in mid-April and infections start settling in May.
    Keywords covid19
    Publisher MedRxiv; WHO
    Document type Article ; Online
    DOI 10.1101/2020.04.15.20066050
    Database COVID19

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  6. Article ; Online: Basic estimation-prediction techniques for Covid-19, and a prediction for Stockholm

    Britton, Tom

    medRxiv

    Abstract: An important task during the current Covid-19 pandemic is to predict the remainder of the epidemic, both without preventive measures and with. In the current paper we address this question using a simple estimation-prediction method. The input is the ... ...

    Abstract An important task during the current Covid-19 pandemic is to predict the remainder of the epidemic, both without preventive measures and with. In the current paper we address this question using a simple estimation-prediction method. The input is the observed initial doubling time and a known value of R0. The simple General epidemic model is then fitted, and time calibration to calendar time is done using the observed number of case fatalities, together with estimates of the time between infection to death and the infection fatality risk. Finally, predictions are made assuming no change of behaviour, as well as for the situation where preventive measures are put in place at one specific time-point. The overall effect of the preventive measures is assumed to be known, or else estimated from the observed increased doubling time after preventive measures are put in place. The predictions are highly sensitive to the doubling times without and with preventive measures, sensitive to R0, but less sensitive to the estimates used for time-calibration: observed number of case fatalities, typical time between infection and death, and the infection fatality risk. The method is applied to the urban area of Stockholm, and predictions show that the peak of infections appear in mid-April and infections start settling in May.
    Keywords covid19
    Language English
    Publishing date 2020-04-17
    Publisher Cold Spring Harbor Laboratory Press
    Document type Article ; Online
    DOI 10.1101/2020.04.15.20066050
    Database COVID19

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  7. Article ; Online: Basic prediction methodology for covid-19: estimation and sensitivity considerations

    Britton, Tom

    medRxiv

    Abstract: The purpose of the present paper is to present simple estimation and prediction methods for basic quantities in an emerging epidemic like the ongoing covid-10 pandemic. The simple methods have the advantage that relations between basic quantities become ... ...

    Abstract The purpose of the present paper is to present simple estimation and prediction methods for basic quantities in an emerging epidemic like the ongoing covid-10 pandemic. The simple methods have the advantage that relations between basic quantities become more transparent, thus shedding light to which quantities have biggest impact on predictions, with the additional conclusion that uncertainties in these quantities carry over to high uncertainty also in predictions. A simple non-parametric prediction method for future cumulative case fatalities, as well as future cumulative incidence of infections (assuming a given infection fatality risk f), is presented. The method uses cumulative reported case fatalities up to present time as input data. It is also described how the introduction of preventive measures of a given magnitude ρ will affect the two incidence predictions, using basic theory of epidemic models. This methodology is then reversed, thus enabling estimation of the preventive magnitude ρ, and of the resulting effective reproduction number R<sub>E</sub>. However, the effects of preventive measures only start affecting case fatalities some 3-4 weeks later, so estimates are only available after this time has elapsed. The methodology is applicable in the early stage of an outbreak, before, say, 10% of the community have been infected. Beside giving simple estimation and prediction tools for an ongoing epidemic, another important conclusion lies in the observation that the two quantities f (infection fatality risk) and ρ (the magnitude of preventive measures) have very big impact on predictions. Further, both of these quantities currently have very high uncertainty: current estimates of f lie in the range 0.2% up to 2% ([9], [7]), and the overall effect of several combined preventive measures is clearly very uncertain. The two main findings from the paper are hence that, a) any prediction containing f, and/or some preventive measures, contain a large amount of uncertainty (which is usually not acknowledged well enough), and b) obtaining more accurate estimates of in particular f, should be highly prioritized. Seroprevalence testing of random samples in a community where the epidemic has ended are urgently needed.
    Keywords covid19
    Language English
    Publishing date 2020-04-07
    Publisher Cold Spring Harbor Laboratory Press
    Document type Article ; Online
    DOI 10.1101/2020.03.27.20045575
    Database COVID19

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  8. Article ; Online: Basic prediction methodology for covid-19: estimation and sensitivity considerations

    Britton, Tom

    Abstract: The purpose of the present paper is to present simple estimation and prediction methods for basic quantities in an emerging epidemic like the ongoing covid-10 pandemic. The simple methods have the advantage that relations between basic quantities become ... ...

    Abstract The purpose of the present paper is to present simple estimation and prediction methods for basic quantities in an emerging epidemic like the ongoing covid-10 pandemic. The simple methods have the advantage that relations between basic quantities become more transparent, thus shedding light to which quantities have biggest impact on predictions, with the additional conclusion that uncertainties in these quantities carry over to high uncertainty also in predictions. A simple non-parametric prediction method for future cumulative case fatalities, as well as future cumulative incidence of infections (assuming a given infection fatality risk f), is presented. The method uses cumulative reported case fatalities up to present time as input data. It is also described how the introduction of preventive measures of a given magnitude ρ will affect the two incidence predictions, using basic theory of epidemic models. This methodology is then reversed, thus enabling estimation of the preventive magnitude ρ, and of the resulting effective reproduction number RE. However, the effects of preventive measures only start affecting case fatalities some 3-4 weeks later, so estimates are only available after this time has elapsed. The methodology is applicable in the early stage of an outbreak, before, say, 10% of the community have been infected. Beside giving simple estimation and prediction tools for an ongoing epidemic, another important conclusion lies in the observation that the two quantities f (infection fatality risk) and ρ (the magnitude of preventive measures) have very big impact on predictions. Further, both of these quantities currently have very high uncertainty: current estimates of f lie in the range 0.2% up to 2% ([9], [7]), and the overall effect of several combined preventive measures is clearly very uncertain. The two main findings from the paper are hence that, a) any prediction containing f, and/or some preventive measures, contain a large amount of uncertainty (which is usually not acknowledged well enough), and b) obtaining more accurate estimates of in particular f, should be highly prioritized. Seroprevalence testing of random samples in a community where the epidemic has ended are urgently needed.
    Keywords covid19
    Publisher MedRxiv; WHO
    Document type Article ; Online
    DOI 10.1101/2020.03.27.20045575
    Database COVID19

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  9. Book ; Online: SIRS epidemics with individual heterogeneity of immunity waning

    Khalifi, Mohamed El / Britton, Tom

    2023  

    Abstract: We analyse an extended SIRS epidemic model in which immunity at the individual level wanes gradually at exponential rate, but where the waning rate may differ between individuals, for instance as an effect of differences in immune systems. The model also ...

    Abstract We analyse an extended SIRS epidemic model in which immunity at the individual level wanes gradually at exponential rate, but where the waning rate may differ between individuals, for instance as an effect of differences in immune systems. The model also includes vaccination schemes aimed to reach and maintain herd immunity. We consider both the informed situation where the individual waning parameters are known, thus allowing selection of vaccinees being based on both time since last vaccination as well as on the individual waning rate, and the more likely uninformed situation where individual waning parameters are unobserved, thus only allowing vaccination schemes to depend on time since last vaccination. The optimal vaccination policies for both the informed and uniformed heterogeneous situation are derived and compared with the homogeneous waning model (meaning all individuals have the same immunity waning rate), as well as to the classic SIRS model where immunity at the individual level drops from complete immunity to complete susceptibility in one leap. It is shown that the classic SIRS model requires least vaccines, followed by the SIRS with homogeneous gradual waning, followed by the informed situation for the model with heterogeneous gradual waning. The situation requiring most vaccines for herd immunity is the most likely scenario, that immunity wanes gradually with unobserved individual heterogeneity. For parameter values chosen to mimic COVID-19 and assuming perfect initial immunity and cumulative immunity of 12 months, the classic homogeneous SIRS epidemic suggests that vaccinating individuals every 15 months is sufficient to reach and maintain herd immunity, whereas the uninformed case for exponential waning with rate heterogeneity corresponding to a coefficient of variation being 0.5, requires that individuals instead need to be vaccinated every 4.4 months.
    Keywords Quantitative Biology - Populations and Evolution ; Physics - Physics and Society
    Subject code 612
    Publishing date 2023-11-01
    Publishing country us
    Document type Book ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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  10. Article ; Online: Modelling preventive measures and their effect on generation times in emerging epidemics.

    Favero, Martina / Scalia Tomba, Gianpaolo / Britton, Tom

    Journal of the Royal Society, Interface

    2022  Volume 19, Issue 191, Page(s) 20220128

    Abstract: We present a stochastic epidemic model to study the effect of various preventive measures, such as uniform reduction of contacts and transmission, vaccination, isolation, screening and contact tracing, on a disease outbreak in a homogeneously mixing ... ...

    Abstract We present a stochastic epidemic model to study the effect of various preventive measures, such as uniform reduction of contacts and transmission, vaccination, isolation, screening and contact tracing, on a disease outbreak in a homogeneously mixing community. The model is based on an infectivity process, which we define through stochastic contact and infectiousness processes, so that each individual has an independent infectivity profile. In particular, we monitor variations of the reproduction number and of the distribution of generation times. We show that some interventions, i.e. uniform reduction and vaccination, affect the former while leaving the latter unchanged, whereas other interventions, i.e. isolation, screening and contact tracing, affect both quantities. We provide a theoretical analysis of the variation of these quantities, and we show that, in practice, the variation of the generation time distribution can be significant and that it can cause biases in the estimation of reproduction numbers. The framework, because of its general nature, captures the properties of many infectious diseases, but particular emphasis is on COVID-19, for which numerical results are provided.
    MeSH term(s) COVID-19/epidemiology ; COVID-19/prevention & control ; Contact Tracing/methods ; Disease Outbreaks/prevention & control ; Epidemics/prevention & control ; Humans
    Language English
    Publishing date 2022-06-15
    Publishing country England
    Document type Journal Article ; Research Support, Non-U.S. Gov't
    ZDB-ID 2156283-0
    ISSN 1742-5662 ; 1742-5689
    ISSN (online) 1742-5662
    ISSN 1742-5689
    DOI 10.1098/rsif.2022.0128
    Database MEDical Literature Analysis and Retrieval System OnLINE

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