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The possible control of competitive invasion by infection of the invader and multiplicative noise is studied. The basic model is the Lotka-Volterra competition system with emergent carrying capacities. Several stationary solutions of the…
Mathematical models are increasingly a part of microbiological research. Here, we share our perspective on how modeling advances the discipline by: (i) enforcing logical consistency, (ii) enabling quantitative prediction, (iii) extracting…
We introduce and analyze a spatial Lotka-Volterra competition model with local and nonlocal interactions. We study two alternative classes of nonlocal competition that differ in how each species' characteristics determine the range of the…
A general system of difference equations is presented for multispecies communities with density dependent population growth and delayed maturity. Interspecific competition, mutualism, predation, commensalism, and amensalism are…
We consider inference for a collection of partially observed, stochastic, interacting, nonlinear dynamic processes. Each process is identified with a label called its unit, and our primary motivation arises in biological metapopulation…
Firms are more likely to introduce products in markets where they anticipate stronger demand. They also possess information that is unobserved to researchers. This creates endogenous selection bias in the estimation of demand parameters.…
Deployed supervised machine learning models make predictions that interact with and influence the world. This phenomenon is called performative prediction by Perdomo et al. (ICML 2020). It is an ongoing challenge to understand the influence…
Populations interact non-linearly and are influenced by environmental fluctuations. In order to have realistic mathematical models, one needs to take into account that the environmental fluctuations are inherently stochastic. Often,…
Two non-intrusive uncertainty propagation approaches are proposed for the performance analysis of engineering systems described by expensive-to-evaluate deterministic computer models with parameters defined as interval variables. These…
We introduce a mathematical model of symbiosis between different species by taking into account the influence of each species on the carrying capacities of the others. The modeled entities can pertain to biological and ecological societies…
Complementarity among species with different traits is one of the basic processes affecting biodiversity, defined as the number of species in the ecosystem. We present here a soluble model ecosystem in which the species are characterized by…
The simultaneous growth of multiple microbial species is a problem of fundamental ecological interest. In media containing more than one growth-limiting substrate, multiple species can coexist. The question then arises: Can single-species…
Clonal interference, competition between multiple co-occurring beneficial mutations, has a major role in adaptation of asexual populations. We provide a simple individual based stochastic model of clonal interference taking into account a…
Consider the setting of constrained optimization, with some parameters unknown at solving time and requiring prediction from relevant features. Predict+Optimize is a recent framework for end-to-end training supervised learning models for…
Background: Many mathematical models have now been employed across every area of systems biology. These models increasingly involve large numbers of unknown parameters, have complex structure which can result in substantial evaluation time…
Ecologists increasingly rely on Bayesian methods to fit capture-recapture models. Capture-recapture models are used to estimate abundance while accounting for imperfect detectability in individual-level data. A variety of implementations…
In this study, we investigate the dynamics of a spatial and non spatial prey-predator interaction model that includes the following: (i) fear effect incorporated in prey birth rate; (ii) group defence of prey against predators; and (iii)…
A major challenge for community ecology is using spatio-temporal data to infer parameters of dynamical models without conducting laborious experiments. We present a novel framework from statistical physics -- Maximum Caliber -- to…
We introduce a novel approach for comparing out-of-sample multi-step forecasts obtained from a pair of nested models that is based on the forecast encompassing principle. Our proposed approach relies on an alternative way of testing the…
Clinical prediction models (CPMs) are used to predict clinically relevant outcomes or events. Typically, prognostic CPMs are derived to predict the risk of a single future outcome. However, with rising emphasis on the prediction of…