| 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. |