Nine challenges for deterministic epidemic models

doi:10.1016/j.epidem.2014.09.006

. 2015 Mar:10:49-53.

doi: 10.1016/j.epidem.2014.09.006. Epub 2014 Sep 27.

Nine challenges for deterministic epidemic models

Mick Roberts¹, Viggo Andreasen², Alun Lloyd³, Lorenzo Pellis⁴

Affiliations

¹ Infectious Disease Research Centre, Institute of Natural and Mathematical Sciences, and New Zealand Institute for Advanced Study, Massey University, Private Bag 102 904, North Shore Mail Centre, 1311 Auckland, New Zealand. Electronic address: m.g.roberts@massey.ac.nz.
² Department of Science, Roskilde University, 4000 Roskilde, Denmark.
³ Department of Mathematics and Biomathematics Graduate Program, North Carolina State University, Raleigh, NC 27695, USA; Fogarty International Center, National Institutes of Health, Bethesda, MD 20892, USA.
⁴ Warwick Infectious Disease Epidemiology Research Centre (WIDER) and Warwick Mathematics Institute, University of Warwick, Coventry, CV4 7AL, UK.

PMID: 25843383
PMCID: PMC4996659
DOI: 10.1016/j.epidem.2014.09.006

Nine challenges for deterministic epidemic models

Mick Roberts et al. Epidemics. 2015 Mar.

. 2015 Mar:10:49-53.

doi: 10.1016/j.epidem.2014.09.006. Epub 2014 Sep 27.

Authors

Mick Roberts¹, Viggo Andreasen², Alun Lloyd³, Lorenzo Pellis⁴

Affiliations

¹ Infectious Disease Research Centre, Institute of Natural and Mathematical Sciences, and New Zealand Institute for Advanced Study, Massey University, Private Bag 102 904, North Shore Mail Centre, 1311 Auckland, New Zealand. Electronic address: m.g.roberts@massey.ac.nz.
² Department of Science, Roskilde University, 4000 Roskilde, Denmark.
³ Department of Mathematics and Biomathematics Graduate Program, North Carolina State University, Raleigh, NC 27695, USA; Fogarty International Center, National Institutes of Health, Bethesda, MD 20892, USA.
⁴ Warwick Infectious Disease Epidemiology Research Centre (WIDER) and Warwick Mathematics Institute, University of Warwick, Coventry, CV4 7AL, UK.

PMID: 25843383
PMCID: PMC4996659
DOI: 10.1016/j.epidem.2014.09.006

Abstract

Deterministic models have a long history of being applied to the study of infectious disease epidemiology. We highlight and discuss nine challenges in this area. The first two concern the endemic equilibrium and its stability. We indicate the need for models that describe multi-strain infections, infections with time-varying infectivity, and those where superinfection is possible. We then consider the need for advances in spatial epidemic models, and draw attention to the lack of models that explore the relationship between communicable and non-communicable diseases. The final two challenges concern the uses and limitations of deterministic models as approximations to stochastic systems.

Keywords: Deterministic models; Endemic equilibrium; Multi-strain systems; Non-communicable diseases; Spatial models.

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References

1. Anderson RM, May RM. Infectious Diseases of Humans: Dynamics and Control. Oxford: Oxford Univ. Press; 1991.
1. Andreasen V. The effect of age-dependent host mortality on the dynamics of an endemic disease. Math. Biosci. 1993;114:29–58. - PubMed
1. Bailey NTJ. The Biomathematics of Malaria. London: Charles Griffin; 1982.
1. Ball F, Neal P. Network epidemic models with two levels of mixing. Math. Biosci. 2008;212:69–87. - PubMed
1. Baussano I, Ronco G, Segnan N, French K, Vineis P, Garnett GP. HPV-16 infection and cervical cancer: modeling the influence of duration of infection and precancerous lesions. Epidemics. 2010;2:21–28. - PubMed

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[1] Anderson RM, May RM. Infectious Diseases of Humans: Dynamics and Control. Oxford: Oxford Univ. Press; 1991.

[2] Anderson RM, May RM. Infectious Diseases of Humans: Dynamics and Control. Oxford: Oxford Univ. Press; 1991.

[3] Andreasen V. The effect of age-dependent host mortality on the dynamics of an endemic disease. Math. Biosci. 1993;114:29–58. - PubMed

[4] Andreasen V. The effect of age-dependent host mortality on the dynamics of an endemic disease. Math. Biosci. 1993;114:29–58. - PubMed

[5] Bailey NTJ. The Biomathematics of Malaria. London: Charles Griffin; 1982.

[6] Bailey NTJ. The Biomathematics of Malaria. London: Charles Griffin; 1982.

[7] Ball F, Neal P. Network epidemic models with two levels of mixing. Math. Biosci. 2008;212:69–87. - PubMed

[8] Ball F, Neal P. Network epidemic models with two levels of mixing. Math. Biosci. 2008;212:69–87. - PubMed

[9] Baussano I, Ronco G, Segnan N, French K, Vineis P, Garnett GP. HPV-16 infection and cervical cancer: modeling the influence of duration of infection and precancerous lesions. Epidemics. 2010;2:21–28. - PubMed

[10] Baussano I, Ronco G, Segnan N, French K, Vineis P, Garnett GP. HPV-16 infection and cervical cancer: modeling the influence of duration of infection and precancerous lesions. Epidemics. 2010;2:21–28. - PubMed

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Nine challenges for deterministic epidemic models

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Nine challenges for deterministic epidemic models

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