Zhilan Feng, NSF and Purdue University

Mathematical modeling of infectious diseases has played an important role in understanding transmission dynamics and influencing disease control policy. In this talk, I will present several examples to demonstrate how various models were used to answer different questions particularly related to disease control and prevention. These models are systems of differential equations. The mathematical results were motivated by specific biological questions. My first example is a very simple 3-dimensional SIR model with exponentially distributed infectious period that was capable of predicting the correct peak time of the second wave of the 2009 H1N1 outbreak in the US. My second shows that, for diseases with longer latent and infectious periods, models with exponentially distributed stages may produce unreliable or misleading evaluations of quarantine and isolation strategies. For the COVID-19 pandemic, questions include evaluation of age- and location-dependent vaccination strategies, so more complex models are needed including non-homogeneous mixing. In my last example, I will describe our descriptive model of seroprevalence by age and time and then our calculation, via first principles, of the age-specific forces of infection, attack rates and - given information from a contact study - probabilities of infection on contact. Because those parameters were not estimated by fitting our transmission model to any observations, others could use them too.