Sensitivity to model structure: a comparison of compartmental models in epidemiology
Tóm tắt
Compartmental models have provided a framework for understanding disease transmission dynamics for over 100 years. The predictions from these models are often policy relevant and need to be robust to model assumptions, parameter values and model structure. A selection of compartmental models with the same parameter values but different model structures (ranging from simple structures to complex ones) were compared in the absence and presence of several policy interventions to assess sensitivity to model structure. Models were fitted to data to assess if this might reduce this sensitivity. The compartmental models produced wide-ranging estimates of outcome measures but when fitted to data, the estimates obtained were robust to model structure. This finding suggests that there may be an argument for selecting simple models over complex ones, but the complexity of the model should be determined by the purpose of the model and the use to which it will be put.
Tài liệu tham khảo
Anderson RM and May RM (1992) Infectious Diseases of Humans: Dynamics and Control. Oxford University Press, Oxford, ISBN: 019854040X.
Aron JL (1988) Acquired immunity dependent upon exposure in an SIRS epidemic model. Mathematical Biosciences 88(1), 37–47.
Auger P, Kouokam E, Sallet G, Tchuente M and Tsanou B (2008) The Ross-Macdonald model in a patchy environment. Mathematical Biosciences, 216(2), 123–131.
Brauer F (2001) Models for transmission of disease with immigration of infectives. Mathematical Biosciences, 171(2), 143–154.
Brauer F, van den Driessche P and Wu J, (Eds.) (2008) Mathematical Epidemiology. Number 1945. 1st edn, Springer, Berlin. ISBN 3540789103. [WWW document] http://books.google.com/books?id=gcP5l1a22rQC&pgis=1.
Chubb MC and Jacobsen KH (2010) Mathematical modeling and the epidemiological research process. European Journal of Epidemiology, 25(1), 13–19.
Dietz K (1980) Models for vector-borne parasitic diseases. In Vito Volterra Symposium on Mathematical Models in Biology (Caludio Barigozzi, Ed), pp 264–277, Springer, Berlin.
Dowdle WR (1998) The principles of disease elimination and eradication. Bulletin of the World Health Organization 76(Suppl 2), 22–25.
Ferrer J, Albuquerque J, Prats C, Lopez D and Valls J (2012) Agent-based models in malaria elimination strategy design. In EMCSR 2012, February. Creative Commons License. [WWW document] http://is.upc.edu/seminaris-i-jornades/documents/AgentbasedModelsinmalariaeliminationstrategydesign.pdf (accessed 19 August 2013).
Greenwood B (2010) Anti-malarial drugs and the prevention of malaria in the population of malaria endemic areas. Malaria Journal 9(Suppl 3), S2.
Hansen PC, Pereyra V and Scherer G (2012) Least Squares Data Fitting with Applications. JHU Press, Baltimore, ISBN 1421408589.
Hethcote HW (1994) A thousand and one epidemic models. In Frontiers in Mathematical Biology (Simon A levin, Ed), pp 504–515, Springer, Berlin.
Jacquez JA (1996) Compartmental analysis in biology and medicine. BioMedware. [WWW document] http://books.google.com/books?id=U81qAAAAMAAJ&pgis=1 (accessed 19 August 2013).
Juan Z (2006) Global dynamics of an SEIR epidemic model with immigra-tion of different compartments. Acta Mathematica Scientia 26(3), 551–567.
Koella JC and Antia R (2003) Epidemiological models for the spread of anti-malarial resistance. Malaria Journal 2(3).
L’Hospital GF (1696) Analyse des infiniment petits pour l’intellligence des lignes courbes. L’imprimerie Royale, Paris.
Luz PM, Struchiner CJ and Galvani AP (2010) Modeling transmission dynamics and control of vector-borne neglected tropical diseases. PLoS Neglected Tropical Diseases, 4(10), e761.
Mandal S, Sarkar RR and Sinha S (2011) Mathematical models of malaria-a review. Malaria Journal, 10(1), 202.
Murray JD (2003) Mathematical Biology II, Volume 18. Springer, Berlin. ISBN 0387952284. [WWW document] http://www.amazon.com/Mathematical-Biology-II-J-D-Murray/dp/0387952284.
O’Connell KA et al (2012) Souls of the ancestor that knock us out and other tales. A qualitative study to identify demand-side factors influencing malaria case management in Cambodia. Malaria journal, 11(1), 335.
Rahmandad H and Sterman J (2008) Heterogeneity and network Structure in the dynamics of diffusion: Comparing agent-based and differential equation models. Management Science, 54(5), 998–1014.
Ross R (1911) The prevention of Malaria. John Murray, Albemarle Street, London.
R Core Group (2013) [WWW document] www.r-project.org (accessed 19 August 2013).
Smith T et al (2006) Mathe-matical modeling of the impact of malaria vaccines on the clinical epidemiology and natural history of Plasmodium falciparum malaria: Overview. The American Journal of Tropical Medicine and Hygiene 75(suppl 2), 1–10.
The malERA Consultative Group on Modeling (2011) A research agenda for malaria eradication: modeling. PLoS medicine, 8(1), January. ISSN 1549-1676. doi: 10.1371/journal.pmed.1000403. [WWW document] http://journals.plos.org/plosmedicine/article?id=10.1371/journal.pmed.1000403.
Torres-Sorando L and Rodriguez DJ (1997) Models of spatio-temporal dynamics in malaria. Ecological Modelling, 104(2–3), 231–240.
Tumwiine J, Mugisha JYT and Luboobi LS (2010) A host-vector model for malaria with infective immigrants. Journal of Mathematical Analysis and Applications, 361 (1), 139–149.
World Health Organization (1997) Vector control: methods for use by individuals and communities. Technical report. [WWW document] http://www.who.int/malaria/publications/atoz/9241544945/en/index.html (accessed 19 August 2013).
White LJ et al (2009) The role of simple mathematical models in malaria elimination strategy design. Malaria Journal, 8(8), 212.
Yang HM (2000) Malaria transmission model for different levels of acquired immunity and temperature-dependent parameters (vector). Revista de saude publica, 34(3), 223–231.
Yang HM and Ferreira MU (2000) Assessing the effects of global warming and local social and economic conditions on the malaria transmission. Revista de saude publica, 34(3), 214–222.