"Seasonal Disease Emergence in Stochastic Epidemic Models"
The timing of disease emergence is influenced by many factors including social behavior and seasonal weather patterns that affect temperature and humidity. We examine how seasonal variation in transmission, recovery, or dispersal rates impact disease emergence in several well-known continuous-time Markov chain (CTMC) SIR, SEIR epidemic models with one or two patches. An ODE framework which incorporates periodic parameters for transmission, recovery, or dispersal serves as a basis for each stochastic model. The basic reproduction numbers and seasonal reproduction numbers from the ODE and branching process approximations of the CTMC are useful in predicting some of the stochastic behavior of the CTMC epidemic models. In particular, we apply these techniques to estimate a time-periodic probability of disease extinction, or equivalently, the probability of no disease emergence at the initiation of an epidemic. We also compute the mean and standard deviation for time to disease extinction and test the branching process approximations against simulations of the full CTMC epidemic models. Our numerical investigations illustrate how the magnitude and seasonal synchrony or asynchrony in transmission, recovery, or dispersal impact the probability of disease extinction. The numerical outcomes show that seasonal variation in transmission, recovery, or dispersal generally increases the probability of disease extinction (reducing disease emergence) and the shape of the seasonal reproduction number provides information about the shape of the periodic probability of disease extinction. However, the time of peak disease emergence precedes that predicted by the peak of the seasonal reproduction number.
Additional authors: Linda J. S. Allen