The Incidence of Infectious Diseases Under the Influence of Seasonal Fluctuations - Analytical Approach

Grossman, Z.; Gumowski, I.; Dietz, Klaus

doi:10.1016/b978-0-12-434150-0.50049-7

Cited by 25 publications

(9 citation statements)

References 4 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Motivated by the fact that both the weather and certain social processes, namely school-recruitment following the yearly school calendar, have one year periodicity, an important strain of the literature has focused on 1 − year periodic β(t) in endemic SIR models. If the corresponding period T β is around 1 year, then nonlinear resonance may appear, inducing phenomena such as biennal and multi-year periodicity, and chaos [91,[93][94][95][96][97][98][99] that partially explain a number of observed epidemiological time-series.…”

Section: Periodic Contact Ratesmentioning

confidence: 99%

Statistical physics of vaccination

et al. 2016

View full text Add to dashboard Cite

Historically, infectious diseases caused considerable damage to human societies, and they continue to do so today. To help reduce their impact, mathematical models of disease transmission have been studied to help understand disease dynamics and inform prevention strategies. Vaccination-one of the most important preventive measures of modern times-is of great interest both theoretically and empirically. And in contrast to traditional approaches, recent research increasingly explores the pivotal implications of individual behavior and heterogeneous contact patterns in populations. Our report reviews the developmental arc of theoretical epidemiology with emphasis on vaccination, as it led from classical models assuming homogeneously mixing (mean-field) populations and ignoring human behavior, to recent models that account for behavioral feedback and/or population spatial/social structure. Many of the methods used originated in statistical physics, such as lattice and network models, and their associated analytical frameworks. Similarly, the feedback loop between vaccinating behavior and disease propagation forms a coupled nonlinear system with analogs in physics. We also review the new paradigm of digital epidemiology, wherein sources of digital data such as online social media are mined for high-resolution information on epidemiologically relevant individual behavior. Armed with the tools and concepts of statistical physics, and further assisted by new sources of digital data, models that capture nonlinear interactions between behavior and disease dynamics offer a novel way of modeling real-world phenomena, and can help improve health outcomes. We conclude the review by discussing open problems in the field and promising directions for future research.

show abstract

Section: Periodic Contact Ratesmentioning

confidence: 99%

Statistical physics of vaccination

et al. 2016

View full text Add to dashboard Cite

show abstract

“…(48), arises for example in SIS/SIR/SIRS epidemic models with a sinusoidal contact rate. If the infectious period is exponentially distributed as in Dietz (1976); Grossman et al (1977); Kuznetsov and Piccardi (1994), then G(x) = a e −bx and it is easily checked that G 0 = a/b, that the term of order ε 2 in Eq. (31) vanishes, so that R 0 a/b.…”

Section: Other Applicationsmentioning

confidence: 99%

Approximation of the Basic Reproduction Number R 0 for Vector-Borne Diseases with a Periodic Vector Population

2007

View full text Add to dashboard Cite

The main purpose of this paper is to give an approximate formula involving two terms for the basic reproduction number R(0) of a vector-borne disease when the vector population has small seasonal fluctuations of the form p(t) = p(0) (1+epsilon cos(omegat - phi)) with epsilon << 1. The first term is similar to the case of a constant vector population p but with p replaced by the average vector population p(0). The maximum correction due to the second term is (epsilon(2)/8)% and always tends to decrease R(0). The basic reproduction number R(0) is defined through the spectral radius of a linear integral operator. Four numerical methods for the computation of R(0) are compared using as example a model for the 2005/2006 chikungunya epidemic in La Réunion. The approximate formula and the numerical methods can be used for many other epidemic models with seasonality.

show abstract

“…LetR 0 be defined as in (15). IfR 0 < 1, then disease extinction occurs in model (13), lim t→∞ I j (t) = 0, j = 1, .…”

Section: Solutions To Equation (13) Are Nonnegative and Boundedmentioning

confidence: 99%

“…Disease models with periodicity in births, deaths, and carrying capacity have been applied to the study of hantavirus in bank voles [31,32,38]. Seasonality has been studied in many types of epidemic models, showing that periodic solutions exist, period doubling and chaos occur, or providing conditions for disease extinction [3,6,[10][11][12]14,15,17,22,23,[24][25][26][27]30,[33][34][35].…”

Section: Introductionmentioning

confidence: 99%

The basic reproduction number in epidemic models with periodic demographics

Wesley

Allen

2009

Journal of Biological Dynamics

View full text Add to dashboard Cite

Patterns of contact in social behaviour and seasonality due to environmental influences often affect the spread and persistence of diseases. Models of epidemics with seasonality and patterns in the contact rate include time-periodic coefficients, making the systems nonautonomous. No general method exists for calculating the basic reproduction number, the threshold for disease extinction, in nonautonomous epidemic models. However, for some epidemic models with periodic coefficients and constant population size, the time-averaged basic reproduction number has been shown to be a threshold for disease extinction. We extend these results by showing that the time-averaged basic reproduction number is a threshold for disease extinction when the population demographics are periodic. The results are shown to hold in epidemic models with periodic demographics that include temporary immunity, isolation, and multiple strains.

show abstract

The Incidence of Infectious Diseases Under the Influence of Seasonal Fluctuations - Analytical Approach

Cited by 25 publications

References 4 publications

Statistical physics of vaccination

Statistical physics of vaccination

Approximation of the Basic Reproduction Number R 0 for Vector-Borne Diseases with a Periodic Vector Population

The basic reproduction number in epidemic models with periodic demographics

Contact Info

Product

Resources

About