On the principle of host evolution in host-pathogen interactions We use a two-host one pathogen immuno-epidemiological model to argue that the principle for host evolution, when the host is subjected to a fatal disease, is minimization of the case fatality proportion F. This principle is valid whether the disease is chronic or leads to recovery. In …
Carcinogenesis The multistage model for carcinogenesis was developed in the 1950’s.  The model is largely attributed to Armitage and Doll in a 1954 paper in the British Journal of Cancer.  There were some follow-up articles in the next couple of decades expanding on the mathematics of this theory.  However, after that there was a fallow …
The impact of resource abundance on consumer encounter rates (with an application to pathogen invasion risk) Territorial animals share a variety of common resources, which can be a major driver of conspecific encounter rates. We investigate how changes in resource quantity influence the rate of encounters between individuals in a population. Â A spatial resource landscape …
The Perron-Frobenius theorem and its applications The Perron-Frobenius theorem states that a positive matrix admits a positive principal eigenvalue with associated posited eigenvalue. I will discuss the applications of this result for dynamics and differential equations.
Using mathematical model to understand the impact of various preventive and control measures on the dynamics of visceral leishmaniasis in Brazil Visceral leishmaniasis (VL) is a zoonosis with global distribution. Its incidence has increased in Brazil in recent years, thus coming to represent a serious public and animal health problem. The strategies applied in Brazil, …
Calculating Human to Human Avian Influenza R0Â via Likelihood and Jacobian Approach The transmission of avian influenza between humans is extremely rare, and it mostly affects individuals who are in contact with infected poultry. Although this scenario is uncommon, there have been multiple outbreaks that occur in small infection clusters in Asia with relatively low transmissibility, …
Measuring the Electrostatic Drag of Dyaction Dynactin, an activator of dynein, connects intracellular cargo to dynein motors. Â Linear stochastic models are developed to describe the interaction of intracellular cargo, an anchor, and a functionalized motor. Â These models use known parameters and available data for dynactin to produce an estimate of electrostatic drag. Â Using available data …
Persistence and dynamics in a metapopulation model of infection We consider a metapopulation model of an Infectious Salmon Anemia virus (ISAv) infection on a network of patches connected via diffusion of the virus.  In addition  to previous results, we give analytical proof of oscillatory solutions in a system of 2 patches. We introduce a variety of network structures …
Epidemic Models Structured by Immunological Variables We develop a differential-integral equation model of epidemics in an animal population structured by immunological variables such as mean viral load and mean T-cell density. The population is subdivided into susceptible individuals whose dynamics is modeled by an ordinary differential equation, and infected/infectious individuals structured by immunological state summarized …
Quantifying the Burden of Somatic Evolution in the Context of Cancer and Aging Somatic tissue evolves over a vertebrate’s lifetime due to the accumulation of mutations in stem cell populations. Mutations may alter cellular fitness and contribute to tumorigenesis or aging. The distribution of mutational effects within somatic cells is not known. Given the unique …
