A historical perspective of demographic models will be presented, from the simplest, unstructured, exponential growth models, to state-of-the-art, age- and sex-structured ones with logistic growth. The marriage problem will be described and examples using real-life data will be used to apply models to population forecasting. Finally, some examples of application of these models to epidemic forecasting will be shown, to childhood and to sexually transmitted diseases.
Having grown up in East Los Angeles, California, Dr. Erika Camacho understands many of the struggles that students and women of color must endure in striving to attain their academic and professional goals. Dr. Camacho will be sharing her life experiences and the challenges she had to overcome to help her achieve her personal and professional goals. She will share stories about the key individuals and decisions that contributed to her success and transformation. Dr. Camacho will also share her passion for social activism and continual drive to transform the world of academia and strengthen our communities. Her life story is full of insights and lessons of empowerment for all.
Retinitis pigmentosa (RP) is a group of inherited degenerative eye diseases characterized by mutations in the genetic structure of the photoreceptors that leads to the premature death of both rod and cone photoreceptors. Defects in particular genes encoding proteins that are involved in either the photoreceptor structure, phototransduction cascades, or visual cycle are expressed in the rods but ultimately affect both types of cells. RP is ``typically'' manifested by a steady death of rods followed by a period of stability in which cones survive initially and then inevitably die too. In some RP cases, rods and cones die off simultaneously or even cone death precedes rod death (reverse RP). The mechanisms and factors involved in the development of the different types of RP are not well understood nor have researchers been able to provide more than a limited number of short-term therapies. In this talk I will give an introduction of the relevant physiology of the eye as it pertains to RP and highlight some of the leading work in this area as well as existing mathematical models, including some of our work. In this research, we trace the progression of RP to complete blindness through each subtype via bifurcation theory. We show that the evolution of RP from one stage to another often requires the failure of multiple components. Our results indicate that a delicate balance between the availability of nutrients and the rates of shedding and renewal of photoreceptors is needed at every stage of RP to halt its progression. This work provides a framework for future physiological investigations potentially leading to long-term targeted multi-facet interventions and therapies dependent on the particular stage and subtype of RP under consideration. The results of this mathematical model may also give insight into the progression of many other degenerative eye diseases involving genetic mutations or secondary photoreceptor death and potential ways to circumvent these diseases.
As a group of genetic diseases, cancer presents some of the most challenging problems for basic scientists, clinical investigators, and practitioners. In order to design treatments that are capable of abating malignant tumor growth, it is necessary to make use of cross-disciplinary, systems science approaches, in which innovative theoretical and computational cancer models play a central role. The goal of this talk is to demonstrate how combining mathematical modeling, numerical simulation, and carefully designed experiments can provide a predictive framework for better understanding tumor development and for improving cancer treatment.
Mathematics has played an important role in helping understand the mechanisms responsible for the spread of diseases in populations. In this presentation, I will highlight the work of physicians like Sir Ronald Ross who pioneered the use of mathematics in epidemiology and discuss some recent applications. The lecture will be accessible to undergraduates including students interested in ecology and population biology as well as in the applications of mathematics in the life and social sciences.