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A deterministic model for highly contagious diseases: The case of varicella

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  • Acedo, L.
  • Moraño, J.-A.
  • Santonja, F.-J.
  • Villanueva, R.-J.

Abstract

The classic nonlinear Kermack–McKendrick model based upon a system of differential equations has been widely applied to model the rise and fall of global pandemic and also seasonal epidemic by introducing a forced harmonic infectivity which would change throughout the year. These methods work well in their respective domains of applicability, and for certain diseases, but they fail when both seasonality and high infectivity are combined. In this paper we consider a Susceptible–Infected–Recovered, or SIR, model with two latent states to model the propagation and evolutionary history of varicella in humans. We show that infectivity can be calculated from real data and we find a nonstandard seasonal variation that cannot be fitted with a single harmonic. Moreover, we show that infectivity for the present strains of the virus has raised following a sigmoid function in a period of several centuries. This could allow the design of vaccination strategies and the study of the epidemiology of varicella and herpes zoster.

Suggested Citation

  • Acedo, L. & Moraño, J.-A. & Santonja, F.-J. & Villanueva, R.-J., 2016. "A deterministic model for highly contagious diseases: The case of varicella," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 450(C), pages 278-286.
    • Handle: RePEc:eee:phsmap:v:450:y:2016:i:c:p:278-286
    DOI: 10.1016/j.physa.2015.12.153
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    References listed on IDEAS

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    1. X. Lenne & J. Diez Domingo & A. Gil & M. Ridao & J.A. Lluch & B. Dervaux, 2006. "Economic evaluation of varicella vaccination in Spain -Results from a dynamic model," Post-Print hal-00200025, HAL.
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    Cited by:

    1. Calatayud, Julia & Jornet, Marc, 2020. "Mathematical modeling of adulthood obesity epidemic in Spain using deterministic, frequentist and Bayesian approaches," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    2. Calatayud, Julia & Jornet, Marc, 2021. "Modeling of adulthood obesity in Spain using Itô-type stochastic differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    3. Mahajan, Shveta & Kumar, Deepak & Verma, Atul Kumar & Sharma, Natasha, 2023. "Dynamic analysis of modified SEIR epidemic model with time delay in geographical networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 629(C).
    4. A. Corberán-Vallet & F. J. Santonja & M. Jornet-Sanz & R.-J. Villanueva, 2018. "Modeling Chickenpox Dynamics with a Discrete Time Bayesian Stochastic Compartmental Model," Complexity, Hindawi, vol. 2018, pages 1-9, March.
    5. Sharma, Natasha & Gupta, Arvind Kumar, 2017. "Impact of time delay on the dynamics of SEIR epidemic model using cellular automata," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 471(C), pages 114-125.

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