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Mathematical Biosciences and Engineering

2013, Volume 10, Issue 5&6: 1475-1497. doi: 10.3934/mbe.2013.10.1475
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Mathematical models of contact patterns between age groups for predicting the spread of infectious diseases

  • 1.
    Los Alamos National Laboratory, Los Alamos, NM 87545
  • 2.
    Tulane University, New Orleans, LA, 70118
  • 3.
    Swiss Tropical and Public Health Institute, 4002 Basel
  • Received: 01 August 2012 Accepted: 29 June 2018 Published: 01 August 2013

  • MSC : Primary: 37N25, 9008; Secondary: 68R01.

  • The spread of an infectious disease is sensitive to the contact patterns in the population and to precautions people take to reduce the transmission of the disease.We investigate the impact that different mixing assumptions have on the spread an infectious disease in an age-structured ordinary differential equation model. We consider the impact of heterogeneity in susceptibility and infectivity within the population on the disease transmission. We apply the analysis to the spread of a smallpox-like disease, derive the formula for the reproduction number, $\Re_{0}$, and based on this threshold parameter, show the level of human behavioral change required to control the epidemic.We analyze how different mixing patterns can affect the disease prevalence, the cumulative number of new infections, and the final epidemic size.Our analysis indicates that the combination of residual immunity and behavioral changes during a smallpox-like disease outbreak can play a key role in halting infectious disease spread; and that realistic mixing patterns must be included in the epidemic model for the predictions to accurately reflect reality.

    Citation: Sara Y. Del Valle, J. M. Hyman, Nakul Chitnis. Mathematical models of contact patterns between age groups for predicting the spread of infectious diseases[J]. Mathematical Biosciences and Engineering, 2013, 10(5&6): 1475-1497. doi: 10.3934/mbe.2013.10.1475

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  • The spread of an infectious disease is sensitive to the contact patterns in the population and to precautions people take to reduce the transmission of the disease.We investigate the impact that different mixing assumptions have on the spread an infectious disease in an age-structured ordinary differential equation model. We consider the impact of heterogeneity in susceptibility and infectivity within the population on the disease transmission. We apply the analysis to the spread of a smallpox-like disease, derive the formula for the reproduction number, $\Re_{0}$, and based on this threshold parameter, show the level of human behavioral change required to control the epidemic.We analyze how different mixing patterns can affect the disease prevalence, the cumulative number of new infections, and the final epidemic size.Our analysis indicates that the combination of residual immunity and behavioral changes during a smallpox-like disease outbreak can play a key role in halting infectious disease spread; and that realistic mixing patterns must be included in the epidemic model for the predictions to accurately reflect reality.


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