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{"work":{"id":45337388,"created_at":"2021-03-03T09:52:12.059-08:00","from_world_paper_id":166899911,"updated_at":"2024-11-30T14:51:43.505-08:00","_data":{"publisher":"Springer Nature","ai_title_tag":"Seasonal Dynamics and Thresholds in Recurrent Epidemics","grobid_abstract":"Seasonality is a driving force that has a major effect on the spatiotemporal dynamics of natural systems and their populations 1-5 . This is especially true for the transmission of common infectious diseases (such as influenza, measles, chickenpox and pertussis), and is of great relevance for host-parasite relationships in general 1-23 . Here we gain further insights into the nonlinear dynamics of recurrent diseases through the analysis of the classical seasonally forced SIR (susceptible, infectious or recovered) epidemic model 6,7 . Our analysis differs from other modelling studies in that the focus is more on post-epidemic dynamics than the outbreak itself. Despite the mathematical intractability of the forced SIR model, we identify a new threshold effect and give clear analytical conditions for predicting the occurrence of either a future epidemic outbreak, or a 'skip'-a year in which an epidemic fails to initiate. The threshold is determined by the population's susceptibility measured after the last outbreak and the rate at which new susceptible individuals are recruited into the population. Moreover, the time of occurrence (that is, the phase) of an outbreak proves to be a useful parameter that carries important epidemiological information. In forced systems, seasonal changes can prevent late-peaking diseases (that is, those having high phase) from spreading widely, thereby increasing population susceptibility, and controlling the triggering and intensity of future epidemics. These principles yield forecasting tools that should have relevance for the study of newly emerging and re-emerging diseases controlled by seasonal vectors.","publication_date":"2007,,","publication_name":"Nature","grobid_abstract_attachment_id":"65876947"},"document_type":"paper","pre_hit_view_count_baseline":null,"quality":"high","language":"en","title":"Seasonal dynamics of recurrent epidemics","broadcastable":true,"draft":null,"has_indexable_attachment":true,"indexable":true}}["work"]; window.loswp.workCoauthors = [2129413]; window.loswp.locale = "en"; window.loswp.countryCode = "SG"; window.loswp.cwvAbTestBucket = ""; window.loswp.designVariant = "ds_vanilla"; window.loswp.fullPageMobileSutdModalVariant = "full_page_mobile_sutd_modal"; window.loswp.useOptimizedScribd4genScript = false; window.loginModal = {}; window.loginModal.appleClientId = 'edu.academia.applesignon'; window.userInChina = "false";</script><script defer="" src="https://accounts.google.com/gsi/client"></script><div class="ds-loswp-container"><div class="ds-work-card--grid-container"><div class="ds-work-card--container js-loswp-work-card"><div class="ds-work-card--cover"><div class="ds-work-cover--wrapper"><div class="ds-work-cover--container"><button class="ds-work-cover--clickable js-swp-download-button" data-signup-modal="{"location":"swp-splash-paper-cover","attachmentId":65876947,"attachmentType":"pdf"}"><img alt="First page of “Seasonal dynamics of recurrent epidemics”" class="ds-work-cover--cover-thumbnail" src="https://0.academia-photos.com/attachment_thumbnails/65876947/mini_magick20210303-7435-te274p.png?1614794172" /><img alt="PDF Icon" class="ds-work-cover--file-icon" src="//a.academia-assets.com/images/single_work_splash/adobe_icon.svg" /><div class="ds-work-cover--hover-container"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">download</span><p>Download Free PDF</p></div><div class="ds-work-cover--ribbon-container">Download Free PDF</div><div class="ds-work-cover--ribbon-triangle"></div></button></div></div></div><div class="ds-work-card--work-information"><h1 class="ds-work-card--work-title">Seasonal dynamics of recurrent epidemics</h1><div class="ds-work-card--work-authors ds-work-card--detail"><a class="ds-work-card--author js-wsj-grid-card-author ds2-5-body-md ds2-5-body-link" data-author-id="2129413" href="https://independent.academia.edu/RonenOlinky"><img alt="Profile image of Ronen Olinky" class="ds-work-card--author-avatar" src="https://0.academia-photos.com/2129413/690896/857621/s65_ronen.olinky.jpg" />Ronen Olinky</a></div><div class="ds-work-card--detail"><p class="ds-work-card--detail ds2-5-body-sm">2007, Nature</p><div class="ds-work-card--work-metadata"><div class="ds-work-card--work-metadata__stat"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">visibility</span><p class="ds2-5-body-sm" id="work-metadata-view-count">…</p></div><div class="ds-work-card--work-metadata__stat"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">description</span><p class="ds2-5-body-sm">4 pages</p></div><div class="ds-work-card--work-metadata__stat"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">link</span><p class="ds2-5-body-sm">1 file</p></div></div><script>(async () => { const workId = 45337388; const worksViewsPath = "/v0/works/views?subdomain_param=api&work_ids%5B%5D=45337388"; const getWorkViews = async (workId) => { const response = await fetch(worksViewsPath); if (!response.ok) { throw new Error('Failed to load work views'); } const data = await response.json(); return data.views[workId]; }; // Get the view count for the work - we send this immediately rather than waiting for // the DOM to load, so it can be available as soon as possible (but without holding up // the backend or other resource requests, because it's a bit expensive and not critical). const viewCount = await getWorkViews(workId); const updateViewCount = (viewCount) => { try { const viewCountNumber = parseInt(viewCount, 10); if (viewCountNumber === 0) { // Remove the whole views element if there are zero views. document.getElementById('work-metadata-view-count')?.parentNode?.remove(); return; } const commaizedViewCount = viewCountNumber.toLocaleString(); const viewCountBody = document.getElementById('work-metadata-view-count'); if (!viewCountBody) { throw new Error('Failed to find work views element'); } viewCountBody.textContent = `${commaizedViewCount} views`; } catch (error) { // Remove the whole views element if there was some issue parsing. document.getElementById('work-metadata-view-count')?.parentNode?.remove(); throw new Error(`Failed to parse view count: ${viewCount}`, error); } }; // If the DOM is still loading, wait for it to be ready before updating the view count. if (document.readyState === "loading") { document.addEventListener('DOMContentLoaded', () => { updateViewCount(viewCount); }); // Otherwise, just update it immediately. } else { updateViewCount(viewCount); } })();</script></div><p class="ds-work-card--work-abstract ds-work-card--detail ds2-5-body-md">Seasonality is a driving force that has a major effect on the spatiotemporal dynamics of natural systems and their populations 1-5 . This is especially true for the transmission of common infectious diseases (such as influenza, measles, chickenpox and pertussis), and is of great relevance for host-parasite relationships in general 1-23 . Here we gain further insights into the nonlinear dynamics of recurrent diseases through the analysis of the classical seasonally forced SIR (susceptible, infectious or recovered) epidemic model 6,7 . Our analysis differs from other modelling studies in that the focus is more on post-epidemic dynamics than the outbreak itself. Despite the mathematical intractability of the forced SIR model, we identify a new threshold effect and give clear analytical conditions for predicting the occurrence of either a future epidemic outbreak, or a 'skip'-a year in which an epidemic fails to initiate. The threshold is determined by the population's susceptibility measured after the last outbreak and the rate at which new susceptible individuals are recruited into the population. Moreover, the time of occurrence (that is, the phase) of an outbreak proves to be a useful parameter that carries important epidemiological information. In forced systems, seasonal changes can prevent late-peaking diseases (that is, those having high phase) from spreading widely, thereby increasing population susceptibility, and controlling the triggering and intensity of future epidemics. These principles yield forecasting tools that should have relevance for the study of newly emerging and re-emerging diseases controlled by seasonal vectors.</p><div class="ds-work-card--button-container"><button class="ds2-5-button js-swp-download-button" data-signup-modal="{"location":"continue-reading-button--work-card","attachmentId":65876947,"attachmentType":"pdf","workUrl":"https://www.academia.edu/45337388/Seasonal_dynamics_of_recurrent_epidemics"}">See full PDF</button><button class="ds2-5-button ds2-5-button--secondary js-swp-download-button" data-signup-modal="{"location":"download-pdf-button--work-card","attachmentId":65876947,"attachmentType":"pdf","workUrl":"https://www.academia.edu/45337388/Seasonal_dynamics_of_recurrent_epidemics"}"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">download</span>Download PDF</button></div><div class="ds-signup-banner-trigger-container"><div class="ds-signup-banner-trigger ds-signup-banner-trigger-control"></div></div><div class="ds-signup-banner ds-signup-banner-control"><div id="ds-signup-banner-close-button"><button class="ds2-5-button ds2-5-button--secondary ds2-5-button--inverse"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">close</span></button></div><div class="ds-signup-banner-ctas" data-impression-entity-id="45337388" data-impression-entity-type="2" data-impression-source="signup-banner"><img src="//a.academia-assets.com/images/academia-logo-capital-white.svg" /><h4 class="ds2-5-heading-serif-sm">Sign up for access to the world's latest research</h4><button class="ds2-5-button ds2-5-button--inverse ds2-5-button--full-width js-swp-download-button" data-signup-modal="{"location":"signup-banner"}">Sign up for free<span class="material-symbols-outlined" style="font-size: 20px" translate="no">arrow_forward</span></button></div><div class="ds-signup-banner-divider"></div><div class="ds-signup-banner-reasons"><div class="ds-signup-banner-reasons-item"><span class="material-symbols-outlined" style="font-size: 24px" translate="no">check</span><span>Get notified about relevant papers</span></div><div class="ds-signup-banner-reasons-item"><span class="material-symbols-outlined" style="font-size: 24px" translate="no">check</span><span>Save papers to use in your research</span></div><div class="ds-signup-banner-reasons-item"><span class="material-symbols-outlined" style="font-size: 24px" translate="no">check</span><span>Join the discussion with peers</span></div><div class="ds-signup-banner-reasons-item"><span class="material-symbols-outlined" style="font-size: 24px" translate="no">check</span><span>Track your impact</span></div></div></div><script>(() => { // Set up signup banner show/hide behavior: // 1. 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Using the seasonally forced SIR epidemic model, we are able to provide new insights into the dynamics of recurrent diseases and, in some cases, specific predictions about individual outbreaks. The analysis reveals a new threshold effect that gives clear conditions for the triggering of future disease outbreaks or their absence. The threshold depends critically on the susceptibility S 0 of the population after an outbreak. We show that in the presence of seasonality, forecasts based on the susceptibility S 0 are more reliable than those based on the classical reproductive number R 0 from the conventional theory.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Seasonal dynamics and thresholds governing recurrent epidemics","attachmentId":65876948,"attachmentType":"pdf","work_url":"https://www.academia.edu/45337384/Seasonal_dynamics_and_thresholds_governing_recurrent_epidemics","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/45337384/Seasonal_dynamics_and_thresholds_governing_recurrent_epidemics"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="1" data-entity-id="47492480" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/47492480/Small_amplitude_long_period_outbreaks_in_seasonally_driven_epidemics">Small amplitude, long period outbreaks in seasonally driven epidemics</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="56135069" href="https://independent.academia.edu/IraSchwartz3">Ira Schwartz</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Journal of Mathematical Biology, 1992</p><p class="ds-related-work--abstract ds2-5-body-sm">It is now documented that childhood diseases such as measles, mumps, and chickenpox exhibit a wide range of recurrent behavior (periodic as well as chaotic) in large population centers in the first world. Mathematical models used in the past (such as the SEIR model with seasonal forcing) have been able to predict the onset of both periodic and chaotic sustained epidemics using parameters of childhood diseases. Although these models possess stable solutions which appear to have the correct frequency content, the corresponding outbreaks require extremely large populations to support the epidemic. This paper shows that by relaxing the assumption of uniformity in the supply of susceptibles, simple models predict stable long period oscillatory epidemics having small amplitude. Both coupled and single population models are considered.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Small amplitude, long period outbreaks in seasonally driven epidemics","attachmentId":66557116,"attachmentType":"pdf","work_url":"https://www.academia.edu/47492480/Small_amplitude_long_period_outbreaks_in_seasonally_driven_epidemics","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/47492480/Small_amplitude_long_period_outbreaks_in_seasonally_driven_epidemics"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="2" data-entity-id="87356287" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/87356287/Realistic_Distributions_of_Infectious_Periods_in_Epidemic_Models_Changing_Patterns_of_Persistence_and_Dynamics">Realistic Distributions of Infectious Periods in Epidemic Models: Changing Patterns of Persistence and Dynamics</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="25528693" href="https://ncsu.academia.edu/AlunLloyd">Alun Lloyd</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Theoretical Population Biology, 2001</p><p class="ds-related-work--abstract ds2-5-body-sm">Most mathematical models used to study the epidemiology of childhood viral diseases, such as measles, describe the period of infectiousness by an exponential distribution. The effects of including more realistic descriptions of the infectious period within SIR (susceptibleÂ infec-tiousÂ recovered) models are studied. Less dispersed distributions are seen to have two important epidemiological consequences. First, less stable behaviour is seen within the model: incidence patterns become more complex. Second, disease persistence is diminished: in models with a finite population, the minimum population size needed to allow disease persistence increases. The assumption made concerning the infectious period distribution is of a kind routinely made in the formulation of mathematical models in population biology. Since it has a major effect on the central issues of population persistence and dynamics, the results of this study have broad implications for mathematical modellers of a wide range of biological systems.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Realistic Distributions of Infectious Periods in Epidemic Models: Changing Patterns of Persistence and Dynamics","attachmentId":91588375,"attachmentType":"pdf","work_url":"https://www.academia.edu/87356287/Realistic_Distributions_of_Infectious_Periods_in_Epidemic_Models_Changing_Patterns_of_Persistence_and_Dynamics","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/87356287/Realistic_Distributions_of_Infectious_Periods_in_Epidemic_Models_Changing_Patterns_of_Persistence_and_Dynamics"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="3" data-entity-id="14235369" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/14235369/First_Principles_Modeling_of_Nonlinear_Incidence_Rates_in_Seasonal_Epidemics">First Principles Modeling of Nonlinear Incidence Rates in Seasonal Epidemics</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="33208088" href="https://florida.academia.edu/Jos%C3%A9Ponciano">José Ponciano</a></div><p class="ds-related-work--metadata ds2-5-body-xs">PLoS Computational Biology, 2011</p><p class="ds-related-work--abstract ds2-5-body-sm">In this paper we used a general stochastic processes framework to derive from first principles the incidence rate function that characterizes epidemic models. We investigate a particular case, the Liu-Hethcote-van den Driessche's (LHD) incidence rate function, which results from modeling the number of successful transmission encounters as a pure birth process. This derivation also takes into account heterogeneity in the population with regard to the per individual transmission probability. We adjusted a deterministic SIRS model with both the classical and the LHD incidence rate functions to time series of the number of children infected with syncytial respiratory virus in Banjul, Gambia and Turku, Finland. We also adjusted a deterministic SEIR model with both incidence rate functions to the famous measles data sets from the UK cities of London and Birmingham. Two lines of evidence supported our conclusion that the model with the LHD incidence rate may very well be a better description of the seasonal epidemic processes studied here. First, our model was repeatedly selected as best according to two different information criteria and two different likelihood formulations. The second line of evidence is qualitative in nature: contrary to what the SIRS model with classical incidence rate predicts, the solution of the deterministic SIRS model with LHD incidence rate will reach either the disease free equilibrium or the endemic equilibrium depending on the initial conditions. These findings along with computer intensive simulations of the models' Poincaré map with environmental stochasticity contributed to attain a clear separation of the roles of the environmental forcing and the mechanics of the disease transmission in shaping seasonal epidemics dynamics.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"First Principles Modeling of Nonlinear Incidence Rates in Seasonal Epidemics","attachmentId":44422003,"attachmentType":"pdf","work_url":"https://www.academia.edu/14235369/First_Principles_Modeling_of_Nonlinear_Incidence_Rates_in_Seasonal_Epidemics","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/14235369/First_Principles_Modeling_of_Nonlinear_Incidence_Rates_in_Seasonal_Epidemics"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="4" data-entity-id="73992897" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/73992897/Destabilization_of_epidemic_models_with_the_inclusion_of_realistic_distributions_of_infectious_periods">Destabilization of epidemic models with the inclusion of realistic distributions of infectious periods</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="25528693" href="https://ncsu.academia.edu/AlunLloyd">Alun Lloyd</a></div><p class="ds-related-work--metadata ds2-5-body-xs">2001</p><p class="ds-related-work--abstract ds2-5-body-sm">Most mathematical models used to understand the dynamical patterns seen in the incidence of childhood viral diseases, such as measles, employ a simple, but epidemiologically unrealistic, description of the infection and recovery process. The inclusion of more realistic descriptions of the recovery process is shown to cause a signi¢cant destabilization of the model. When there is seasonal variation in disease transmission this destabilization leads to the appearance of complex dynamical patterns with much lower levels of seasonality than previously predicted. More generally, this study illustrates how detailed dynamical properties of a model may depend in an important way on the assumptions made in the formulation of the model.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Destabilization of epidemic models with the inclusion of realistic distributions of infectious periods","attachmentId":83818637,"attachmentType":"pdf","work_url":"https://www.academia.edu/73992897/Destabilization_of_epidemic_models_with_the_inclusion_of_realistic_distributions_of_infectious_periods","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/73992897/Destabilization_of_epidemic_models_with_the_inclusion_of_realistic_distributions_of_infectious_periods"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="5" data-entity-id="55426202" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/55426202/Epidemic_oscillations_Interaction_between_delays_and_seasonality">Epidemic oscillations: Interaction between delays and seasonality</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="176215349" href="https://uncu.academia.edu/GAbramson">Guillermo Abramson</a></div><p class="ds-related-work--abstract ds2-5-body-sm">Traditional epidemic models consider that individual processes occur at constant rates. That is, an infected individual has a constant probability per unit time of recovering from infection after contagion. This assumption certainly fails for almost all infectious diseases, in which the infection time usually follows a probability distribution more or less spread around a mean value. We show a general treatment for an SIRS model in which both the infected and the immune phases admit such a description. The general behavior of the system shows transitions between endemic and oscillating situations that could be relevant in many real scenarios. The interaction with the other main source of oscillations, seasonality, is also discussed.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Epidemic oscillations: Interaction between delays and seasonality","attachmentId":71301399,"attachmentType":"pdf","work_url":"https://www.academia.edu/55426202/Epidemic_oscillations_Interaction_between_delays_and_seasonality","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/55426202/Epidemic_oscillations_Interaction_between_delays_and_seasonality"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="6" data-entity-id="14891987" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/14891987/Discrete_Time_SIS_EpidemicModel_in_a_Seasonal_Environment">Discrete-Time SIS EpidemicModel in a Seasonal Environment</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="33873584" href="https://howard.academia.edu/AbdulazizYakubu">Abdul-aziz Yakubu</a></div><p class="ds-related-work--metadata ds2-5-body-xs">SIAM Journal on Applied Mathematics, 2006</p><p class="ds-related-work--abstract ds2-5-body-sm">We study the combined effects of seasonal trends and diseases on the extinction and persistence of discretely reproducing populations. We introduce the epidemic threshold parameter, R 0 , for predicting disease dynamics in periodic environments. Typically, in periodic environments, R 0 > 1 implies disease persistence on a cyclic attractor, while R 0 < 1 implies disease extinction. We also explore the relationship between the demographic equation and the epidemic process. In particular, we show that in periodic environments, it is possible for the infective population to be on a chaotic attractor while the demographic dynamics is nonchaotic.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Discrete-Time SIS EpidemicModel in a Seasonal Environment","attachmentId":43801078,"attachmentType":"pdf","work_url":"https://www.academia.edu/14891987/Discrete_Time_SIS_EpidemicModel_in_a_Seasonal_Environment","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/14891987/Discrete_Time_SIS_EpidemicModel_in_a_Seasonal_Environment"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="7" data-entity-id="48137339" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/48137339/Attack_rates_of_seasonal_epidemics">Attack rates of seasonal epidemics</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="25556021" href="https://independent.academia.edu/GuyKatriel">Guy Katriel</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Mathematical Biosciences, 2012</p><p class="ds-related-work--abstract ds2-5-body-sm">We study the attack rate, that is the total fraction of the population infected each year, for a disease with seasonally varying transmission rate. The attack rate is shown to be governed by both the reproductive number, reflecting the transmissibility of the disease, and the birth rate, which provides a source of new susceptibles. For the case of epidemics which have an annual period (like the seasonality), we prove inequalities which show that the attack rate is close to that of the non-seasonal model, so that it is nearly independent of the strength of the forcing, despite the fact that the shape of the epidemic curve depends strongly on the degree of seasonality of the forcing. Numerical simulations show that this holds to an even stronger extent than is implied by our rigorous results. When the system has subharmonic or chaotic solutions, we show that similar results hold when the attack rate is replaced by the average attack rate over several years. Consequences of these findings for analyzing the effect of vaccination in seasonally-forced models are noted.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Attack rates of seasonal epidemics","attachmentId":66905500,"attachmentType":"pdf","work_url":"https://www.academia.edu/48137339/Attack_rates_of_seasonal_epidemics","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/48137339/Attack_rates_of_seasonal_epidemics"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="8" data-entity-id="99806506" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/99806506/Modelling_Cyclic_Fluctuations_of_SEIR_Epidemic_Diseases">Modelling Cyclic Fluctuations of SEIR Epidemic Diseases</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="108251210" href="https://umutarapolytech.academia.edu/ProjecteHABYARIMANA">Projecte HABYARIMANA</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Zenodo (CERN European Organization for Nuclear Research), 2022</p><p class="ds-related-work--abstract ds2-5-body-sm">Seasonality of infectious disease is an important factor in disease incidence, outbreaks, control and prevention. Many mathematical models that incorporate seasonality in the transmission were formulated and analyzed. In this essay a qualitative analysis is given in terms of the effective reproduction number R0, the existence and stability of the disease-free equilibrium and endemic equilibrium of both the SEIR model and seasonal SEIR model. We perform numerical simulations to validate the model formulation.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Modelling Cyclic Fluctuations of SEIR Epidemic Diseases","attachmentId":100797128,"attachmentType":"pdf","work_url":"https://www.academia.edu/99806506/Modelling_Cyclic_Fluctuations_of_SEIR_Epidemic_Diseases","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/99806506/Modelling_Cyclic_Fluctuations_of_SEIR_Epidemic_Diseases"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="9" data-entity-id="34506985" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/34506985/A_Discrete_SEIRS_Model_for_Pandemic_Periodic_Infectious_Diseases">A Discrete SEIRS Model for Pandemic Periodic Infectious Diseases</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="50397899" href="https://independent.academia.edu/TzipeGovezensky">Tzipe Govezensky</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Advanced Studies in …, 2012</p><p class="ds-related-work--abstract ds2-5-body-sm">A deterministic SEIRS epidemiological model that captures the essential properties of pandemic recurrent diseases is developed here, in terms of a system of delay-difference equations. A non-linear system of difference equations is proposed, based on the assumptions of exponential incidence and of constant periods of latency, infectiousness and immunity. The model is able to reproduce observed data behaviors such as sustained oscillations and seasonality, typical of many childhood epidemics.We explore the stability of the system in parameter space and show its robustness and versatility to be applied to many infectious diseases. This new model is able to exhibit a wider range of dynamics than previous epidemiological models which make it ideal for a wide use in several infectious diseases. In order to illustrate this, we use this model in combination with a deliberately simplified spatially distributed population, and verify that it captures the essential features of communicable disease spread, such asfade-outs, and a great variability in epidemic sizes.We conclude that realistic models of geographical spread of infections could be improved by describing separately the properties of the diseases, from the social and human mobility aspects of the process. This model helps to fill the theoretical gap that exists between the classical compartmental models and the true stochastic nature of the spread of pandemics.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"A Discrete SEIRS Model for Pandemic Periodic Infectious Diseases","attachmentId":54371669,"attachmentType":"pdf","work_url":"https://www.academia.edu/34506985/A_Discrete_SEIRS_Model_for_Pandemic_Periodic_Infectious_Diseases","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/34506985/A_Discrete_SEIRS_Model_for_Pandemic_Periodic_Infectious_Diseases"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div></div></div><div class="ds-sticky-ctas--wrapper js-loswp-sticky-ctas hidden"><div class="ds-sticky-ctas--grid-container"><div class="ds-sticky-ctas--container"><button class="ds2-5-button js-swp-download-button" data-signup-modal="{"location":"continue-reading-button--sticky-ctas","attachmentId":65876947,"attachmentType":"pdf","workUrl":null}">See full PDF</button><button class="ds2-5-button ds2-5-button--secondary js-swp-download-button" data-signup-modal="{"location":"download-pdf-button--sticky-ctas","attachmentId":65876947,"attachmentType":"pdf","workUrl":null}"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">download</span>Download PDF</button></div></div></div><div class="ds-below-fold--grid-container"><div class="ds-work--container js-loswp-embedded-document"><div class="attachment_preview" data-attachment="Attachment_65876947" style="display: none"><div class="js-scribd-document-container"><div class="scribd--document-loading js-scribd-document-loader" style="display: block;"><img alt="Loading..." src="//a.academia-assets.com/images/loaders/paper-load.gif" /><p>Loading Preview</p></div></div><div style="text-align: center;"><div class="scribd--no-preview-alert js-preview-unavailable"><p>Sorry, preview is currently unavailable. 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href="https://independent.academia.edu/PauloRicardo38">Paulo R Protachevicz</a></div><p class="ds-related-work--metadata ds2-5-body-xs">arXiv (Cornell University), 2022</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Unpredictability in seasonal infectious diseases spread","attachmentId":101429365,"attachmentType":"pdf","work_url":"https://www.academia.edu/100673931/Unpredictability_in_seasonal_infectious_diseases_spread","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/100673931/Unpredictability_in_seasonal_infectious_diseases_spread"><span class="ds2-5-text-link__content">View 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Finkenstädt</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Ecological Monographs, 2002</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Dynamics of Measles Epidemics: Scaling Noise, Determinism, and Predictability with the Tsir Model","attachmentId":88165057,"attachmentType":"pdf","work_url":"https://www.academia.edu/82463803/Dynamics_of_Measles_Epidemics_Scaling_Noise_Determinism_and_Predictability_with_the_Tsir_Model","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" 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