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The Impact of Realistic Age Structure in Simple Models of Tuberculosis Transmission

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  • Ellen Brooks-Pollock
  • Ted Cohen
  • Megan Murray

Abstract

Background: Mathematical models of tuberculosis (TB) transmission have been used to characterize disease dynamics, investigate the potential effects of public health interventions, and prioritize control measures. While previous work has addressed the mathematical description of TB natural history, the impact of demography on the behaviour of TB models has not been assessed. Methods: A simple model of TB transmission, with alternative assumptions about survivorship, is used to explore the effect of age structure on the prevalence of infection, disease, basic reproductive ratio and the projected impact of control interventions. We focus our analytic arguments on the differences between constant and exponentially distributed lifespans and use an individual-based model to investigate the range of behaviour arising from realistic distributions of survivorship. Results: The choice of age structure and natural (non-disease related) mortality strongly affects steady-state dynamics, parameter estimation and predictions about the effectiveness of control interventions. Since most individuals infected with TB develop an asymptomatic latent infection and never progress to active disease, we find that assuming a constant mortality rate results in a larger reproductive ratio and an overestimation of the effort required for disease control in comparison to using more realistic age-specific mortality rates. Conclusions: Demographic modelling assumptions should be considered in the interpretation of models of chronic infectious diseases such as TB. For simple models, we find that assuming constant lifetimes, rather than exponential lifetimes, produces dynamics more representative of models with realistic age structure.

Suggested Citation

  • Ellen Brooks-Pollock & Ted Cohen & Megan Murray, 2010. "The Impact of Realistic Age Structure in Simple Models of Tuberculosis Transmission," PLOS ONE, Public Library of Science, vol. 5(1), pages 1-6, January.
  • Handle: RePEc:plo:pone00:0008479
    DOI: 10.1371/journal.pone.0008479
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    Cited by:

    1. Richard Pitman & David Fisman & Gregory S. Zaric & Maarten Postma & Mirjam Kretzschmar & John Edmunds & Marc Brisson, 2012. "Dynamic Transmission Modeling," Medical Decision Making, , vol. 32(5), pages 712-721, September.
    2. Al-arydah, Mo’tassem & Smith̏, Robert, 2011. "An age-structured model of human papillomavirus vaccination," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(4), pages 629-652.
    3. Chu-Chang Ku & Peter J Dodd, 2019. "Forecasting the impact of population ageing on tuberculosis incidence," PLOS ONE, Public Library of Science, vol. 14(9), pages 1-13, September.
    4. Madhu, Kalyanasundaram & Al-arydah, Mo’tassem, 2021. "Optimal vaccine for human papillomavirus and age-difference between partners," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 185(C), pages 325-346.
    5. Chung‐Min Liao & Yi‐Hsien Cheng & Yi‐Jun Lin & Nan‐Hung Hsieh & Tang‐Luen Huang & Chia‐Pin Chio & Szu‐Chieh Chen & Min‐Pei Ling, 2012. "A Probabilistic Transmission and Population Dynamic Model to Assess Tuberculosis Infection Risk," Risk Analysis, John Wiley & Sons, vol. 32(8), pages 1420-1432, August.
    6. Graciani Rodrigues, C.C. & Espíndola, Aquino L. & Penna, T.J.P., 2015. "An agent-based computational model for tuberculosis spreading on age-structured populations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 428(C), pages 52-59.
    7. Md Abdul Kuddus & Michael T Meehan & Lisa J White & Emma S McBryde & Adeshina I Adekunle, 2020. "Modeling drug-resistant tuberculosis amplification rates and intervention strategies in Bangladesh," PLOS ONE, Public Library of Science, vol. 15(7), pages 1-26, July.

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