Circular Migrations and HIV Transmission Dynamics: A Comparison of Classical Ordinary Differential Equations and Modern Network Modeling

Aditya Khanna, University of Washington
Steven M. Goodreau, University of Washington

The objectives of the current work are to study the role of circular migrations (periodic movement of individuals between two or more locations) in the transmission dynamics of HIV. Specifically, we are interested in impact of migration frequency on the rate of HIV transmission through the population. We use two different types of mathematical models to understand this connection. The first method involves classic ordinary differential equations (ODEs) that build on the classic Susceptible-Infected-Removed (S-I-R) paradigm. We compare the results obtained from these models with modern stochastic network-based models that allow us to more explicitly model the partnership structure and person to person transmission in the model. Our results indicate that given the unique nature of temporal overlap in partnerships in the context of migrations, it is necessary to explicitly model person to person transmission to capture the dynamics of HIV transmission.