Estimates of Seasonal Probability of Disease Outbreaks in  Stochastic Mosquito- and Water-Borne Epidemic Models


Seasonal changes in temperature, humidity, and rainfall impact pathogen and vector survival which are reflected in the seasonal patterns of vector-borne and water-borne disease outbreaks. Dengue, a mosquito-borne disease, and cholera, a water-borne disease, are subject to strong seasonal patterns of disease outbreaks in various regions of the world. Studies of deterministic and stochastic epidemic models have investigated long-term seasonal patterns. We extend these studies to investigate the probability of a disease outbreak at a given time during the season using dengue and cholera stochastic models with demographic and seasonal variability. In the stochastic model for dengue, adult vectors emerging from the larval stage vary seasonally and in cholera, direct transmission and indirect environmental transmission rates vary seasonally. A multitype branching process approximation of the stochastic models near the disease-free periodic solution is used to calculate the probability of a disease outbreak. This approximation provides a periodic probability of a disease outbreak that depends on the strength of seasonality and the number of initially infected individuals. Numerical examples illustrate that seasonality in epidemic models can drive the patterns of disease outbreaks and that the combined effects of demographic and seasonal variability provide a better understanding of the risk of dengue and cholera outbreaks. This is joint work with Kaniz Fatema Nipa, Sophia Jang, and Xueying Wang.

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Simon A. Levin Mathematical, Computational and Modeling Sciences Center Distinguished Lecture
and SoMSS Math Bio Seminar
Friday, Oct. 7
SCOB 101 (note new location)

Dr. Allen will also be giving a talk about her career journey in the mathematical sciences for the SIAM and Math Bio Student Clubs on Thursday, Oct. 6 at 11:00am in WXLR A206. Students are encouraged to attend this interesting talk, followed by lunch. More details available soon.


Linda J. S. Allen 
P. W. Horn Distinguished Professor Emeritus
Department of Mathematics and Statistics 
Texas Tech University 

SCOB 101 (note new location)