The cost of a general stochastic epidemic
- 1 March 1972
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 9 (02) , 257-269
- https://doi.org/10.1017/s0021900200094961
Abstract
This paper is concerned with the cost Cis = aWis + bTis (a, b > 0) of a general stochastic epidemic starting with i infectives and s susceptibles; Tis denotes the duration of the epidemic, and Wis the area under the infective curve. The joint Laplace-Stieltjes transform of (Wis, Tis ) is studied, and a recursive equation derived for it. The duration Tis and its mean Nis are considered in some detail, as are also Wis and its mean Mis . Using the results obtained, bounds are found for the mean cost of the epidemic.Keywords
This publication has 7 references indexed in Scilit:
- The area under the infectives trajectory of the general stochastic epidemicJournal of Applied Probability, 1972
- Joint distributions of random variables and their integrals for certain birth-death and diffusion processesAdvances in Applied Probability, 1971
- A note on the cost of the simple epidemicJournal of Applied Probability, 1970
- Integral Functionals of Birth and Death Processes and Related Limiting DistributionsThe Annals of Mathematical Statistics, 1970
- Some further results on the birth-and-death process and its integralMathematical Proceedings of the Cambridge Philosophical Society, 1968
- On the homogeneous birth-and-death process and its integralBiometrika, 1966
- Equations for stochastic path integralsMathematical Proceedings of the Cambridge Philosophical Society, 1961