An epidemic model with infector-dependent severity

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.

[1]  F. Ball,et al.  The final outcome of an epidemic model with several different types of infective in a large population , 1995, Journal of Applied Probability.

[2]  D. Morley,et al.  Managing measles. Size of infecting dose may be important. , 1997, BMJ.

[3]  N G Becker,et al.  The effect of random vaccine response on the vaccination coverage required to prevent epidemics. , 1998, Mathematical biosciences.

[4]  I. Saunders.  Epidemics in competition , 1981, Journal of mathematical biology.

[5]  École d'été de probabilités de Saint-Flour,et al.  École d'été de probabilités de Saint-Flour XIII - 1983 , 1985 .

[6]  D. Aldous.  Exchangeability and related topics , 1985 .

[7]  Tom Britton,et al.  Estimating vaccine effects from studies of outbreaks in household pairs. , 2006, Statistics in medicine.

[8]  Gianpaolo Scalia-Tomba.  Epidemic Models, Multi-Strain , 2005 .

[9]  H. Andersson,et al.  Stochastic Epidemic Models and Their Statistical Analysis , 2000 .

[10]  Peter Donnelly,et al.  Strong approximations for epidemic models , 1995 .

[11]  Claude Lefèvre,et al.  A UNIFIED ANALYSIS OF THE FINAL SIZE AND SEVERITY DISTRIBUTION IN COLLECTIVE REED-FROST EPIDEMIC PROCESSES , 1990 .

[12]  A. Igarashi,et al.  Molecular and in vitro analysis of eight dengue type 2 viruses isolated from patients exhibiting different disease severities. , 1998, Virology.

[13]  Mikko Alava,et al.  Branching Processes , 2009, Encyclopedia of Complexity and Systems Science.

[14]  P. Jagers,et al.  The Growth and Stabilization of Populations , 1991 .

[15]  Frank Ball,et al.  Control of transmission with two types of infection. , 2006, Mathematical biosciences.

[16]  Claude Lefèvre,et al.  Stochastic epidemic models for S-I-R infectious diseases: a brief survey of the recent general theory , 1990 .

[17]  Klaus Dietz,et al.  The concept of RO in epidemic theory , 1996 .

[18]  M E Halloran,et al.  Interpretation and estimation of vaccine efficacy under heterogeneity. , 1992, American journal of epidemiology.

[19]  An epidemic model with exposure-dependent severities , 2005 .

[20]  Wilfrid S. Kendall,et al.  Epidemics in Competition II: The General Epidemic , 1983 .

[21]  A. Lambert.  Branching Processes: Variation, Growth and Extinction of Populations , 2006 .

[22]  F. Ball,et al.  Epidemics with two levels of mixing , 1997 .

[23]  S. Ethier,et al.  Markov Processes: Characterization and Convergence , 2005 .

[24]  Søren Asmussen,et al.  Branching Processes: Variation, Growth and Extinction of Populations Edited by P. Haccou, P. Jagers, and V. A. Vatutin , 2006 .