with H Gulbudak

DOI

Nutrient-Phytoplankton-Zooplankton-Detritus (NPZD) models, describing the interactions between phytoplankton, zooplankton systems, and their ecosystem, are used to predict their ecological and evolutionary population dynamics.  These organisms form the base two trophic levels of aquatic ecosystems. Hence understanding their population dynamics and how disturbances can affect these systems is crucial. Here, starting from a base NPZ modeling framework, we incorporate the harmful effects of phytoplankton overpopulation on zooplankton - representing a crucial next step in harmful algal bloom (HAB) modeling - and split the nutrient compartment to formulate an NPZD model.  We then mathematically analyze the NPZ system upon which this new model is based, including local and global stability of equilibria, Hopf bifurcation condition, and forward hysteresis, where the bi-stability occurs with multiple attractors.  Finally, we extend the threshold analysis to the NPZD model, which displays both forward hysteresis with bi-stability and Hopf bifurcation under different parameter regimes, and examine ecological implications after incorporating seasonality and ecological disturbances. Ultimately, we quantify ecosystem health in terms of the relative values of the robust persistence thresholds for phytoplankton and zooplankton and find (i) ecosystems sufficiently favoring phytoplankton, as quantified by the relative values of the plankton persistence numbers, are vulnerable to both HABs and (local) zooplankton extinction (ii) even healthy ecosystems are extremely sensitive to nutrient depletion over relatively short time scales.

with Y Ram, M W Feldman, K Laland, L Fortunado, J Blanco-Portillo et al

The field of cultural evolution studies how culture changes over time. Some questions of immediate interest in this discipline are: What are the patterns of genetic and cultural co-evolution? How do these patterns vary across populations, species, and subsets of cultural traits? How do ecological, geographical, and climatic factors interact with and impact these patterns? Both human cultural and genetic traits can exhibit complex patterns of transmission and evolution. A chief aim of both the cultural and life sciences is explaining and exploring these patterns. A number of models, both mathematical, and verbal have long existed to assist in the task, and several studies have sought to quantify these patterns within and across differing geographic and temporal scales both within and across these disciplines. Human ecology seeks to use principles from multiple related natural sciences in order to understand human behavior. Such efforts can and should be informed by many disciplines, as ecological, geographical, genetic, and cultural factors are all deeply intertwined.

The long-term goal of this project is to help bring human cultural traits to equal standing with genetic data while studying co-evolution of culture and genetics. The overall objective is to quantitatively underpin patterns of gene-culture co-variation to test both new and previously suggested hypotheses. Our central hypothesis is that there are significant patterns of co-variation between spread of cultural subsistence technologies and related genetic traits, as well as other cultural and genetic traits. This encompasses agro-pastoralism, such as wheat cultivation and distribution of gluten allergies, and dairy practices and lactose tolerance; gathering strategies, such as geographic distribution of peanuts and peanut allergies, distance from the coast and shellfish allergies [43], distribution of strawberries and strawberry allergies; as well culturally significant non-subsistence plants (e.g. kava), animals (chickens, lizards), phonemes, words, religion, maritime technology and more.

with H Gulbudak, B. Beechler, E. Gorsich, S. Gubbins, E. Perez, A. Jolles et al

Foot-and mouth disease viruses are highly contagious, globally distributed pathogens that can infect a broad range of cloven-hoofed ungulates, including livestock and wild species. Infectious disease dynamics necessarily operate across biological scales: pathogens replicate within hosts; they transmit among hosts, and across host populations. As such, functional changes in the pathogen-host interaction, affecting pathogen vital rates and host immune dynamics can generate cascading effects at molecular to landscape scales. Linking pathogen dynamics across biological scales is thus critical to understanding evolutionary trajectories of host-pathogen systems, and represents a central challenge in disease ecology.

with H. Gulbudak and C. Browne

Dengue, a neglected tropical disease, is a globally distributed arboviral (genus Flavivirus) pathogen primarily spread by Aedes mosquitoes and infecting circa 390 million individuals per annum.  Subsequent to primary infection immune memory is cross-protective for two to three months after which protection is serotype specific, and secondarily infected patients have elevated risk of severe dengue. A hypothesis for this increased risk, known as antibody-dependent enhancement (ADE), is that antibodies increase dengue severity and boost virus replication.  One hypothesized mechanistic explanation for this effect is, hypothesis 1: that ADE occurs during an intermediate risk window with respect to decay of cross-reactive antibody titre.

In addition to increased risk of severe dengue for secondarily infected DENV patients, there are a number of empirically observed differences in the time-course of events between primary and secondary infection.  A proposed explanation for this is hypothesis 2: differences in initial cross-reactive antibody level mechanistically explain observed differences between primary and secondary infection in timing  of within-host events

Here we test these hypotheses using viral kinetics data collected from the Hospital for Tropical Diseases (Ho Chi Minh City, Vietnam) between May 2007 and July 2008 and a viral-immune kinetics model developed in prior work, which we fit to the data.  Our results provide further support for the tested hypotheses, including explicit data-backed dependence of infection severity on pre-existent cross-reactive antibody concentration not produced by other mechanistic models, and recapitulate the data well.

DOI 

with C Browne, H Gulbudak

Each state in the United States exhibited a unique response to the COVID-19 outbreak, along with variable levels of testing, leading to different actual case burdens in the country.   In this study, via per-capita testing dependent ascertainment rates, along with case and death data, we fit a minimal epidemic model for each state. We estimate infection-level responsive lockdown entry and exit rates (representing government and behavioral reaction), along with the true number of cases as of May 31, 2020.  Ultimately we provide error corrected estimates for commonly used metrics such as infection fatality ratio and overall case ascertainment for all 55 states and territories considered, along with the United States in aggregate, in order to correlate outbreak severity with first wave intervention attributes and suggest potential management strategies for future outbreaks.  We observe a theoretically predicted inverse proportionality relation between outbreak size and lockdown rate, with scale dependent on the underlying reproduction number and simulations suggesting a critical population quarantine ``half-life'' of  30 days independent of other model parameters.

DOI 

with C Browne, H Gulbudak

Abstract: Rapid growth of the COVID-19 epidemic in China induced extensive efforts of contact tracing and social-distancing/lockdowns, which quickly contained the outbreak and has been replicated to varying degrees around the world. We construct a novel infectious disease model incorporating these distinct quarantine measures (contact tracing and self-quarantine) as reactionary interventions dependent on current infection levels. Derivation of the final outbreak size leads to a simple inverse proportionality relationship with self-quarantine, revealing a fundamental principle of exponentially increasing cumulative cases when delaying mass quarantine or lockdown measures beyond a critical time period. In contrast, contact tracing results in a proportional reduction in reproduction number, flattening the epidemic curve but only having sizable impact on final size when a large proportion of contacts are traced. We fit the mathematical model to data from China on reported cases and quarantined contacts, finding that lockdowns had an overwhelming influence on out-break size and duration, whereas contact tracing played a role in reducing peak number of infected. Sensitivity analysis and simulations under different re-opening scenarios illustrate the differential effects that responsive contact tracing and lockdowns can have on current and second wave outbreaks.