Math Modeling Seminar: A Network Immuno-epidemiological Model of HIV and Opioid Epidemics

A Network Immuno-epidemiological Model of HIV and Opioid Epidemics

Dr. Maia Martcheva
Professor of Mathematics
Affiliated Professor of Biology
University of Florida

You may attend this lecture in person at 2305 Gosnell Hall or virtually via Zoom.
If you’d like to attend virtually, you may register here for Zoom link.

Abstract:
We introduce a network immuno-epidemiological model of HIV and opioid epidemics where the jointly affected class is structured by the within-host dynamics. We fit the within-host model to data, collected in monkeys. We compute the reproduction numbers of the HIV and opioid epidemics. We show that the disease-free equilibrium is locally stable if both reproduction numbers are below one, and unstable if at least one of the reproduction numbers is above one. The HIV-only equilibrium exists if the reproduction number of HIV is larger than one. The opioid-use only equilibrium exists if the reproduction number of opioid use is larger than one. The HIV-only equilibrium is locally asymptotically stable if the invasion number of the opioid epidemic is below one and unstable if the invasion number of opioid epidemic is above one. The opioid-only equilibrium is locally asymptotically stable if the invasion number of the HIV epidemic is below one and unstable if the invasion number of HIV epidemic is above one. We fit the no-network model to within-host and between host data to determine parameters. We perform structural and practical identifiability of the within-host model. Simulation suggest that that coexistence of HIV infected, opioid affected and co-affected individuals is possible.

Speaker Bio:
Dr. Maia Martcheva is a professor of mathematics at University of Florida. She obtained her PhD at Purdue University in 1998. After that she was a postdoc at IMA, University of Minnesota, Arizona State university and an NSF Advance Fellow at Cornell University in 2002-2003. Since 2003 she has been an Assistant, Associate and Full Professor at the Department of Mathematics, University of Florida. Dr. Martcheva has published around 120 papers. She has also published 3 books: Gender Structured Population Modeling (2005, SIAM), An Introduction to Mathematical Epidemiology (2015, Springer), and Age Structured Population Modeling (2020, Springer). Her research has been supported by the National Science Foundation. In 2016-2018, Dr. Martcheva was a Managing Editor of Journal of Biological Systems. Currently, she serves on the editorial boards of Journal of Biological Systems, Journal of Biological Dynamics and Journal of Difference Equations with Applications.
Read more here.

Intended Audience:
Undergraduates, graduates, and experts. Those with interest in the topic.

The Math Modeling Seminar will recur each week throughout the semester on the same day and time. Find out more about upcoming speakers on the Mathematical Modeling Seminar Series webpage.
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