Premium
A Stochastic Epidemic Model with Seasonal Variations in Infection Rate
Author(s) -
Gupta C. K.,
Sharma Usha
Publication year - 1986
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.4710280721
Subject(s) - normalization (sociology) , mathematics , scaling , statistical physics , epidemic model , ornstein–uhlenbeck process , nonlinear system , population , econometrics , gaussian , infection rate , stationary distribution , stochastic process , statistics , physics , demography , medicine , geometry , surgery , quantum mechanics , sociology , anthropology , markov chain
In this paper we consider a modification of Bailey's stochastic model for the spread of an epidemic when there are seasonal variations in infection rate. The resulting nonlinear model is analyzed by employing the diffusion approximation technique. We have shown that for a large population the process, on suitable scaling and normalization, converges to a non‐stationary Ornstein‐Uhlenbeck process. Consequently the number of infectives has in the steady state a gaussian distribution.