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An epidemic model with infector-dependent severity

Part of: Special processes

Published online by Cambridge University Press:  01 July 2016

Frank Ball  and
Tom Britton
Frank Ball*
Affiliation:
The University of Nottingham
Tom Britton*
Affiliation:
Stockholm University
*
∗ Postal address: School of Mathematical Sciences, The University of Nottingham, University Park, Nottingham NG7 2RD, UK. Email address: frank.ball@nottingham.ac.uk
∗∗ Postal address: Department of Mathematics, Stockholm University, SE-106 91 Stockholm, Sweden. Email address: tom.britton@math.su.se
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Abstract

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A stochastic epidemic model is defined in which infected individuals have different severities of disease (e.g. mildly and severely infected) and the severity of an infected individual depends on the severity of the individual he or she was infected by; typically, severe or mild infectives have an increased tendency to infect others severely or, respectively, mildly. Large-population properties of the model are derived, using branching process approximations for the initial stages of an outbreak and density-dependent population processes when a major outbreak occurs. The effects of vaccination are considered, using two distinct models for vaccine action. The consequences of launching a vaccination program are studied in terms of the effect it has on reducing the final size in the event of a major outbreak as a function of the vaccination coverage, and also by determining the critical vaccination coverage above which only small outbreaks can occur.

Keywords

Stochastic epidemicfinal sizebasic reproduction numbervarying severitybranching processdensity dependent population processthreshold behaviour

MSC classification

Primary: 92D30: Epidemiology
Secondary: 60K99: None of the above, but in this section
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 39 , Issue 4 , December 2007 , pp. 949 - 972
Copyright
Copyright © Applied Probability Trust 2007 

References

Aldous, D. J. (1985). Exchangeability and Related Topics (Ecole d'Été de Probabilités de Saint-Flour XIII—1983; Lecture Notes Math. 1117), ed. Hennequin, P. L., Springer, Berlin.Google Scholar
Andersson, H. and Britton, T. (2000). Stochastic Epidemic Models and Their Statistical Analysis. (Lecture Notes Statist. 151). Springer, New York.CrossRefGoogle Scholar
Athreya, K. B. and Ney, P. E. (1972). Branching Processes. Springer, Berlin.CrossRefGoogle Scholar
Ball, F. G. and Becker, N. G. (2006). Control of transmission with two types of infection. Math. Biosci. 200, 170–187.CrossRefGoogle ScholarPubMed
Ball, F. G. and Britton, T. (2005). An epidemic model with exposure-dependent severities. J. Appl. Prob. 42, 932–949.CrossRefGoogle Scholar
Ball, F. G. and Clancy, D. (1995). The final outcome of an epidemic with several different types of infective in a large population. J. Appl. Prob. 32, 579–590.CrossRefGoogle Scholar
Ball, F. G. and Donnelly, P. J. (1995). Strong approximations for epidemic models. Stoch. Process. Appl. 55, 1–21.Google Scholar
Ball, F. G., Mollison, D. and Scalia-Tomba, G. (1997). Epidemics with two levels of mixing. Ann. Appl. Prob. 7, 46–89.CrossRefGoogle Scholar
Becker, N. G. and Starczak, D. N. (1998). The effect of random vaccine response on the vaccination coverage required to prevent epidemics. Math. Biosci. 154, 117–135.Google Scholar
Becker, N. G., Britton, T. and O'Neill, P. D. (2006). Estimating vaccine effects from studies of outbreaks in household pairs. Statist. Medicine 25, 1079–1093.Google Scholar
Ethier, S. N. and Kurtz, T. G. (1986). Markov Processes: Characterization and Convergence. John Wiley, New York.Google Scholar
Haccou, P., Jagers, P. and Vatutin, V. A. (2005). Branching Processes: Variation, Growth, and Extinction of Populations. Cambridge University Press.CrossRefGoogle Scholar
Halloran, M. E., Haber, M. and Longini, I. M. (1992). Interpretation and estimation of vaccine efficacy under heterogeneity. Amer. J. Epidemiol. 136, 328–343.Google Scholar
Heesterbeek, J. A. P. and Dietz, K. (1996). The concept of R 0 in epidemic theory. Statist. Neerlandica 50, 89–110.CrossRefGoogle Scholar
Jagers, P. (1991). The growth and stabilization of populations. Statist. Sci. 6, 269–283.Google Scholar
Kendall, W. S. and Saunders, I. W. (1983). Epidemics in competition. II. The general epidemic. J. R. Statist. Soc. B 45, 238–244.Google Scholar
Lefèvre, C. (1990). Stochastic epidemic models for S-I-R infectious diseases: a brief survey of the recent theory. In Stochastic Processes in Epidemic Theory (Lecture Notes Biomath. 86), eds Gabriel, J.-P. et al., Springer, Berlin, pp. 1–12.Google Scholar
Mangada, M. N. M. and Igarashi, A. (1998). Molecular and in vitro analysis of eight dengue type 2 viruses isolated from patients exhibiting different disease severities. Virology 244, 458–466.Google Scholar
Morley, D. C. and Aaby, P. (1997). Managing measles: size of infecting dose may be important. British Medical J. 314, 1692.CrossRefGoogle ScholarPubMed
Parang, N. M. and Archana, C. (2004). Varicella. eMedicine 15 September 2004. Available at http://www.emedicine. com/ped/topic2385.htm.Google Scholar
Picard, P. and Lefèvre, C. (1990). A unified analysis of the final size and severity distribution in collective Reed–Frost epidemic processes. Adv. Appl. Prob. 22, 269–294.CrossRefGoogle Scholar
Scalia-Tomba, G.-P. (2005). Epidemic models, multi-strain. In Encylopedia of Biostatistics, 2nd edn, eds Armitage, P. and Colton, N., John Wiley, Chichester, pp. 1672–1674.Google Scholar
Scalia-Tomba, G.-P. and Svensson, Å. (2001). Competing epidemics in closed populations. Res. Rep. 2001:8, Department of Mathematical Statistics, Stockholm University.Google Scholar