Penalization of Singular Control Problems that Arise in Math Biology Optimal control problems applied to biological models tend to incorporate an objective function that increases quadratically with respect to the control. However, the principle of parsimony would lead one to assume linear dependence on the control instead. Problems of this form may have a solution …
Modeling social dynamics: consensus/fragmentation via repeated exchange of opinions When does an opinion formation process within an interacting group lead to consensus, polarization or fragmentation? In this talk, I will discuss several models for the dynamics of continuous opinions of individuals influenced by exchange of ideas and information within the corresponding social group. One specific …
Analysis of a model of a Zika/Dengue co-circulation We analyze a system with two vector-borne diseases (Zika and Dengue) being present. We introduce both a deterministic and a stochastic model that capture the dynamics of the system. For the deterministic model, we study the existence and the stability of different equilibrium points. For the corresponding …
Modeling the interplay between mosquito behavioral adaptation, human behavior, social economic factors and Malaria control We present a study of the interplay between mosquito behavioral adaptation, bed-nets efficacy decay and coverage, human behavior, and malaria to control strategies. The development of insecticide resistance to the common insecticides in increasing in intensity threatening the gains made …
The University of Florida will be hosting the 2019 AMS Fall Southeastern Sectional Meeting. There will be two special sessions on mathematical biology topics: Special Session on New Developments in Mathematical Biology organized by Maia Martcheva (UF), Necibe Tuncer (Florida Atlantic University), and Libin Rong (UF) Special Session on Applications of Differential Equations in Mathematical Biology organized by Nehal …
Land use change, disease, and population growth in subsistence agriculture: escaping the curse of poverty trap The extremely poor generally rely on their immediate natural environment for subsistence and suffer high rates of morbidity and mortality due to infectious diseases. We present a framework for modeling the ecology of poverty, focusing on the exemplar drivers: …
Modeling the Seasonal Transmission Dynamics of Measles Measles, a highly contagious infection caused by the measles virus, is a major public-health problem worldwide. Since the monthly data of measles cases exhibit a seasonally fluctuating pattern, based on the measles model in Earn et al. (Science 287(2000), 667-670) we propose a susceptible, exposed, infectious, and recovered (SEIR) model with periodic …
Variance functions and Taylor's law of fluctuation scaling The variance function of a family of nonnegative random variables (rvs) gives the variance of each rv as a function of its mean, assuming each rv has finite mean and finite variance. Variance functions were invented to assist statistical analyses of agricultural experiments. They have since (under …
Coinfection dynamics of heroin transmission and HIV infection in a single population We propose a coinfection model of heroin abuse and HIV infection, to describe the joint spread through a single population. The unique disease-free equilibrium always exists and it is stable only if the basic reproduction numbers of heroin abuse and HIV infection are …
The SCMB Annual Symposium is a forum to exchange ideas between the broader mathematics and biosystems communities. There will be plenary talks from mathematicians and biologists, organized in complementary pairs, as well as a a public lecture. These will be offered at a colloquium level of detail with an emphasis on engaging the full range of mathematical and biological researchers. A poster …
