TY - JOUR
T1 - Probability of a Disease Outbreak in Stochastic Multipatch Epidemic Models
AU - Lahodny, Glenn E.
AU - Allen, Linda J.S.
N1 - Funding Information:
Acknowledgements The research of LJSA was partially supported by a grant from the National Science Foundation, Grant No. DMS-0718302. Summer support of GEL was partially funded by the Paul W. Horn Professorship account of LJSA. We thank two anonymous reviewers for their helpful suggestions that improved the paper.
PY - 2013/7
Y1 - 2013/7
N2 - Environmental heterogeneity, spatial connectivity, and movement of individuals play important roles in the spread of infectious diseases. To account for environmental differences that impact disease transmission, the spatial region is divided into patches according to risk of infection. A system of ordinary differential equations modeling spatial spread of disease among multiple patches is used to formulate two new stochastic models, a continuous-time Markov chain, and a system of stochastic differential equations. An estimate for the probability of disease extinction is computed by approximating the Markov chain model with a multitype branching process. Numerical examples illustrate some differences between the stochastic models and the deterministic model, important for prevention of disease outbreaks that depend on the location of infectious individuals, the risk of infection, and the movement of individuals.
AB - Environmental heterogeneity, spatial connectivity, and movement of individuals play important roles in the spread of infectious diseases. To account for environmental differences that impact disease transmission, the spatial region is divided into patches according to risk of infection. A system of ordinary differential equations modeling spatial spread of disease among multiple patches is used to formulate two new stochastic models, a continuous-time Markov chain, and a system of stochastic differential equations. An estimate for the probability of disease extinction is computed by approximating the Markov chain model with a multitype branching process. Numerical examples illustrate some differences between the stochastic models and the deterministic model, important for prevention of disease outbreaks that depend on the location of infectious individuals, the risk of infection, and the movement of individuals.
KW - Infectious diseases
KW - Markov chain
KW - Multiple patches
KW - Multitype branching process
UR - http://www.scopus.com/inward/record.url?scp=84879715009&partnerID=8YFLogxK
U2 - 10.1007/s11538-013-9848-z
DO - 10.1007/s11538-013-9848-z
M3 - Article
C2 - 23666483
AN - SCOPUS:84879715009
SN - 0092-8240
VL - 75
SP - 1157
EP - 1180
JO - Bulletin of Mathematical Biology
JF - Bulletin of Mathematical Biology
IS - 7
ER -