In conjunction with the interdisciplinary activities of the National Institute for Mathematical and Biological Synthesis (NIMBioS), a seminar series on topics in mathematical biology will be hosted at NIMBioS every other Tuesday at 3:30 p.m. (unless otherwise noted) in the NIMBioS Lecture Hall on the 4th floor of 1534 White Ave., Suite 400. Seminar speakers will focus on their research initiatives at the interface of mathematics and many areas of the life sciences. Light refreshments will be served beginning 30 minutes before each talk.
Time/Date: Tuesday, November 22, 2011, 3:30 p.m.*
Location: Room 403, Blount Hall, 1534 White Ave., Suite 400
Speaker: Dr. Calistus Ngonghala, NIMBioS Postdoctoral Fellow
Topic: Backward bifurcation and periodic oscillations in model for the dymamics of malaria transmission
Abstract: A deterministic ordinary differential equation model for the dynamics of malaria transmission that explicitly integrates the demography of the malaria vector and its interaction with the human population is developed and analyzed. The model is different from standard malaria transmission models in that the vectors involved in disease transmission are those that are questing for human blood. Model results indicate the existence of nontrivial disease-free and endemic steady state solutions, which can be driven to instability via a Hopf bifurcation as a parameter is varied in parameter space. Our model therefore captures oscillations that are known to exist in the dynamics of malaria transmission without recourse to external seasonal forcing. Additionally, our model exhibits the phenomenon of backward bifurcation. Two threshold parameters that can be used for purposes of control are identified and studied. Possible reasons why it has been difficult to eradicate malaria are also advanced.
*Join us for refreshments in the NIMBioS Lobby on the 4th floor at 3 p.m.
Seminar Flyer (pdf)