Mathematical Biology

Spreading Mechanics and Differentiation of Astrocytes During Retinal Development In embryonic development, formation of the retinal vasculature is critically dependent on prior establishment of a mesh of astrocytes. Astrocytes emerge from the optic nerve head and then migrate over the retinal surface in a radially symmetric manner and mature through differentiation.  We develop aPDE model describing …

Zika Modeling The Zika virus (ZIKV) epidemic has caused an ongoing threat to global health security and spurred new investigations of the virus. Use of epidemiological models for arbovirus diseases can be a powerful tool to assist in prevention and control of the emerging disease. In this talk, we introduce six models of ZIKV, beginning with a …

An Update on the Multi-Stage Model for Carcinogenesis The multistage model for carcinogenesis was first proposed by Armitage and Doll in 1954. There were two supporting pillars that supported the proposition. The first was that changes could be observed in normal cells on the pathway to becoming cancerous. The second support for the theory was …

Soil carbon dynamics: models and questions Soil decomposition models are critical forunderstanding future climate, providing insight into a major natural source ofcarbon dioxide. Several recent models have been proposed which explicitlyrepresent microbial processes, as well as other key chemical and physicalprocesses affecting decomposition. While soil carbon models have historically beenfirst order linear ODE's these new …

Modeling HIV persistence during suppressive therapy HIV persists in infected individuals despite prolonged antiretroviral therapy. Although the latent infection of CD4+ T cells might be a major barrier to viral eradication, other factors such as cell-to-cell viral transmission and infection of macrophages can also contribute to viral persistence. In this talk, I will discuss some recent …

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 …