Carlos Castillo-Chavez

A deterministic model for the transmission dynamics of SIRS-type malaria in hosts and SI in mosquito populations is proposed. The host population is differentiated between naive, primary, and secondary susceptible individuals. Primary and secondary infected individuals (and also recovered) are differentiated from each other according to their degree of infectiousness. The impact of changing the relative susceptibilities of primary and secondary (with respect to naive) susceptible individuals on the dynamics is investigated. Also, the impact of changing the relative infectiousness of secondary infected, primary, and secondary recovered individuals (with respect to primary infected) on the transmission dynamics of malaria is studied.

The Mathematical and Theoretical Biology Institute (MTBI) is a national award winning Research Experience for Undergraduates (REU) that has been running every summer since 1996. Since 1997, students have developed and proposed their own research questions and derived their research projects from them as the keystone of the program. Because MTBI’s mentors have no control over what students are interested in, we need to introduce a suite of flexible techniques that can be applied to a broad variety of interests. In this paper, we walk through examples of some of the most popular techniques at MTBI: epidemiological or contagion modeling and reproductive number analysis. We include an overview of the next generation matrix method of finding the basic reproductive number, sensitivity analysis as a technique for investigating the effect of parameters on the reproductive number, and recommendations for interpreting the results. Lastly, we provide some advice to mentors who are looking to advise student-led research projects. All examples are taken from actual student projects that are generally available through the MTBI website.

Background: Recent studies have shown that Americans appear to be increasingly owning and carrying firearms for personal protection, and are increasingly storing their firearms loaded. However, the prevalence of firearm carry and/or storage with a round chambered has not hitherto been studied; in this arming configuration the weapon is loaded, with a bullet resting against the firing pin, ready to fire if the trigger is pulled. Ostensibly this decreases reaction time in a threat situation, but carries an increased risk of accidental discharge. It is unknown what fraction of firearm owners typically carry or store their firearms in this configuration, and if there have been significant temporal trends in the practice. Objective: We examine firearms detected at Transportation Security Administration (TSA) airport security checkpoints between 2012 to 2017, to examine geospatial and temporal trends in the prevalence of unsafe arming configuration in detected firearms. Results: The fraction of detected firearms found to be loaded has risen significantly since 2012 (Beta Binomial logistic regression p = 0.011). States with firearm child access prevention laws have significantly fewer firearms found by the TSA to be loaded ( p = 0.039). The fraction of loaded firearms found by the TSA to also have a round chambered has also risen significantly since 2012 (Beta Binomial logistic regression p < 0.001). By 2017, 36% of firearms found loaded were also found to have a round chambered, representing an apparent concerning trend in unsafe arming configurations during carry and storage. Conclusions: Americans appear to be increasingly using and storing firearms in unsafe arming configurations. TSA firearm detection data can potentially provide a key source of data when researching trends in firearm injury.

The role of free fatty acids (FFA) on Type 2 diabetes mellitus (T2DM) progression has been studied extensively with prior studies suggesting that individuals with shared familial genetic predisposition to metabolic-related diseases may be vulnerable to dysfunctional plasma FFA regulation. A harmful cycle arises when FFA are not properly regulated by insulin contributing to the development of insulin resistance, a key indicator for T2DM, since prolonged insulin resistance may lead to hyperglycemia. We introduce a hypothesis-driven dynamical model and use it to evaluate the role of FFA on insulin resistance progression that is mathematically constructed within the context of individuals that have genetic predisposition to dysfunctional plasma FFA. The dynamics of the nonlinear interactions that involve glucose, insulin, and FFA are modeled by incorporating a fixed-time delay with the corresponding delay-differential equations being studied numerically. The results of computational studies, that is, extensive simulations, are compared to the known minimal ordinary differential equations model. Parameter estimation and model validation are carried out using clinical data of patients who underwent bariatric surgery. These estimates provide a quantitative measure that is used to evaluate the regulation of lipolysis by insulin action measured by insulin sensitivity, within a metabolically heterogeneous population (non-diabetic to diabetic). Results show that key metabolic factors improve after surgery, such as the effect of insulin inhibition of FFA on insulin and glucose regulation, results that do match prior clinical studies. These findings indicate that the reduction in weight or body mass due to surgery improve insulin action for the regulation of glucose, FFA, and insulin levels. This reinforces what we know, namely, that insulin action is essential for regulating FFA and glucose levels and is a robust effect that can be observed not only in the long-term, but also in the short-term; thereby preventing the manifestation of T2DM.