Math Modeling Seminar - Time Infectious Disease Models

Strong Allee Effect and Basins of Attraction in Discrete - Time Infectious Disease Models

Dr. Abdul-Aziz Yakubu
Professor
Howard University

Zoom Registration Link

Abstract:
Motivated by the Feline Immunodeficiency Virus, the virus that causes AIDS in cat populations, in this talk, we will use discrete-time infectious disease models with demographic strong Allee effect to examine the impact ofthe fatal susceptible - infected (SI) infections on two different types of density dependent growth functions: Holling type III or modified Beverton-Holt per-capita growth function (compensatory dynamics), and Ricker per-capita growth function with mating (overcompensatory dynamics). The occurrence of the strong Allee effect in the disease-free equation renders the SI population model bistable, where the two coexisting locally asymptotically stable equilibrium points are the origin (catastrophic extinction state) and either another fixed point or an intrinsically generated demographic period k > 1 population cycle. We will use the basic reproduction number, R0, and the spectral radius, λk, to examine the structures of the coexisting attractors. In particular, we will show that the fatal disease is not only capable of enlarging or shrinking the basin of attraction of the catastrophic extinction state, but it can also fracture the basins of attraction into several disjoint sets. Thus, making it difficult to specify the asymptotic SI disease outcome in terms of all initial infections. The complexity of the basins of attractions appear to increase with an increase in the period of the demographic population cycles.

Speaker Bio:
Dr. Abdul-Aziz Yakubu is a Professor in the Department of Mathematics at Howard University. He has been a faculty member in this department for several years and served as Department Chair from 2004-2014. Yakubu is a leading researcher and expert in mathematical biology. His specific research interests are in mathematical applications to the biological sciences with global applications that include the prevention and control of the spread of infectious diseases, and the sustainability of exploited fisheries. His numerous research publications include papers on analysis and applied dynamical systems. He lectures widely on his research in North America, Africa, Asia, and Europe.
Yakubu has held visiting positions at Cornell University, North Carolina State University, the Ohio State University, and Botswana International University of Science and Technology. He has served and continue to serve as a committee member of several professional mathematicsorganizations and national mathematics institutes. He was the Chair of the World Outreach Committee of the Society for Mathematical Biology from 2007-2016.
To date, Yakubu has directed 7 PhD dissertations to successful completion (all students who belong to underrepresented groups). He is a proponent of diversity and inclusion in the mathematical sciences and the institutional engagement of Historically Black Colleges and Universities (HBCU) in such initiatives. From 2000–2006, Yakubu directed and taught in REU projects at the Mathematical and Theoretical Biology Institute of Cornell University and Los Alamos National Laboratory. In the Fall of 2015, in collaboration with Dr. Avner Friedman of the Ohio State University and Dr. Michael Reed of Duke University, Yakubu initiated the biannual Howard University Mathematical Modeling in Biology and Medicine Workshop Series.

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.