UM Math Graduate Students Seminar

Dr. Shigui Ruan
University of Miami

will present

Modeling the Transmission Dynamics of Influenza

Friday, April 26, 2013, 3:45pm
Ungar Building Room 402

Abstract:Influenza viruses infect about 5 million people and cause about 500,000 deaths each year around the world, the reasons for the seasonal influenza epidemics are still not clear. There are two types of changes in influenza A viruses: antigenic drift which occurs all the time and causes the annual influenza epidemics and antigenic shift which happens only occasionally but causes pandemics. In this talk, we first present an age-structured type evolutionary epidemiological model of influenza A drift, in which the susceptible class is continually replenished because the pathogen changes genetically and immunologically from one epidemic to the next, causing previously immune hosts to become susceptible. Applying our recent established center manifold theory for semilinear equations with non-dense domain, we show that Hopf bifurcation occurs in the model. This demonstrates that the age-structured type evolutionary epidemiological model of influenza A drift has an intrinsic tendency to oscillate due to the evolutionary and/or immunological changes of the influenza viruses. We then introduce a model to describe the evolution of a "super-strain" of influenza (i.e., a strain composed of avian, human, and swine strains). By modeling the transmission dynamics of this super-strain between humans and pigs, we determine that the evolution of a super-strain is very likely and show that the transmissibility of a super-strain and the interaction between humans and pigs determine the epidemic outcome. The results emphasize the necessity of global surveillance of influenza activity in pigs to prevent future pandemics.

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