Ying Xin
The Mathematical Biology and Dynamical Systems Seminar presents Ying Xin on “Results in Behavioral Epidemiology of infectious diseases” on Tuesday, Jan. 23, from 3:05 to 4 p.m. in Morton 326.
Xin is a graduate student in Mathematics at Ohio University.
Abstract: This talk presents two projects in behavioral epidemiology of infectious diseases.
One is on oscillations in epidemic models with the spread of awareness, which is joint work with Drs. W. Just and J. Saldana. We studied ODE models of epidemic spreading with a preventive behavioral response that is triggered by awareness of the infection. Previous studies of such models had shown that under certain assumptions, awareness may drive the endemic equilibrium to very low levels of disease prevalence. But if such a response is supposed to be considered as an effective control measure, then it should not allow future flare-ups. We focused on the question what conditions would rule out such future flare-ups, which would mathematically translate into sustained oscillations. Our results show that such oscillations are ruled out when there is only a single compartment of aware hosts, but can occur if we consider two distinct such compartments for hosts who differ in their willingness to disseminate the information.
The other project is about modeling vaccination decisions for seasonal influenza. This is joint work with Drs. W. Just and D. Gerberry. Our game-theoretic models share some features of previously published ones, but the strategies permit randomized decisions according to distributions that depend exclusively on the host’s most recent experience. Proportions of the strategies in the population may change over time. This change can be driven by imitation as conceptualized in prior research, by a modified version of imitation, or by a novel adaptive procedure that we provisionally named “unhappiness minimization.” The latter does not explicitly depend on what happened to other hosts but instead depends on comparison with alternative scenarios under other possible strategies. Our results show that under certain conditions, under our modified version of imitation and under “unhappiness minimization,” the population will approach equilibria with much lower overall costs to society than had previously reported for similar models.
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