A unified approach to the distribution of total size and total area under the trajectory of infectives in epidemic models

We provide a unified probabilistic approach to the distribution of total size and total area under the trajectory of infectives for a general stochastic epidemic with any specified distribution of the infectious period. The key tool is a Wald&s identity for the epidemic process. The generalisation of our results to epidemics spreading amongst a heterogeneous population is straightforward.

[1]  F. Ball.  Deterministic and stochastic epidemics with several kinds of susceptibles , 1985, Advances in Applied Probability.

[2]  Thomas Sellke,et al.  On the asymptotic distribution of the size of a stochastic epidemic , 1983, Journal of Applied Probability.

[3]  Frank Ball,et al.  A threshold theorem for the Reed-Frost chain-binomial epidemic , 1983, Journal of Applied Probability.

[4]  R. Watson.  On the size distribution for some epidemic models , 1980, Journal of Applied Probability.

[5]  R. Dunstan.  A note on the moments of the final size of the general epidemic model , 1980, Journal of Applied Probability.

[6]  Anders Martin-Löf,et al.  Threshold limit theorems for some epidemic processes , 1980, Advances in Applied Probability.

[7]  N. Becker,et al.  The uses of epidemic models. , 1979, Biometrics.

[8]  C. Lefèvre.  The expected ultimate size of a carrier-borne epidemic , 1978, Journal of Applied Probability.

[9]  N. Ling.  The Mathematical Theory of Infectious Diseases and its applications , 1978 .

[10]  D. Ludwig.  Stochastic Population Theories , 1976 .

[11]  A. Abakuks.  An optimal isolation policy for an epidemic , 1973, Journal of Applied Probability.

[12]  F. Downton.  A correction to “The area under the infectives trajectory of the general stochastic epidemic” , 1972, Journal of Applied Probability.

[13]  F. Downton.  The area under the infectives trajectory of the general stochastic epidemic , 1972, Journal of Applied Probability.

[14]  J. Gani,et al.  The cost of a general stochastic epidemic , 1972, Journal of Applied Probability.

[15]  R. Watson,et al.  On an epidemic in a stratified population , 1972, Journal of Applied Probability.

[16]  F. Downton.  A note on the ultimate size of a general stochastic epidemic. , 1967, Biometrika.

[17]  V. Cane.  A Note on the Size of Epidemics and the Number of People Hearing a Rumour , 1966 .

[18]  P. Whittle.  THE OUTCOME OF A STOCHASTIC EPIDEMIC—A NOTE ON BAILEY'S PAPER , 1955 .

[19]  S. Rushton,et al.  THE DETERMINISTIC MODEL OF A SIMPLE EPIDEMIC FOR MORE THAN ONE COMMUNITY , 1955 .

[20]  Gianpaolo Scalia-Tomba.  Extensions of the Reed-Frost process , 1983 .

[21]  J. Metz,et al.  The epidemic in a closed population with all susceptibles equally vulnerable; some results for large susceptible populations and small initial infections , 1978, Acta biotheoretica.

[22]  Alexander Grey,et al.  The Mathematical Theory of Infectious Diseases and Its Applications , 1977 .

[23]  H. E. Daniels,et al.  The distribution of the total size of an epidemic , 1967 .