Mathematical Biology Seminar Abstract
Oct 30, 2020
Linda Allen
Texas Tech University, Department of Mathematics and Statistics
3:00 pm in Zoom (Math Colloquium, Meeting ID: 979 8270 2645)

Seasonal variability on disease outbreaks in stochastic multi-patch epidemic models

Factors such as seasonality and spatial connectivity affect the spread of an infectious disease. Accounting for these factors in infectious disease models provides useful information on the times and locations of greatest risk for disease outbreaks. In this investigation, stochastic multi-patch epidemic models are formulated with seasonal and demographic variability. The stochastic models are used to investigate the probability of a disease outbreak when infected individuals are introduced into one or more of the patches. Seasonal variation is included through periodic transmission and dispersal rates. Multitype branching process approximation and application of the backward Kolmogorov differential equation lead to an estimate for the probability of a disease outbreak. This estimate is also periodic and depends on the time, the location, and the number of initial infected individuals introduced into the patch system as well as the magnitude of the transmission and dispersal rates and the connectivity between patches. Examples are given for seasonal transmission and dispersal in two and three patches. Application of our modeling framework and methods, coupled with information about travel patterns and seasonal trends on specific diseases (such as seasonal influenza, avian influenza, dengue, malaria, cholera, Ebola, and coronavirus diseases), provide insight about the times and locations for travel restrictions.