rescomp: An R package for defining, simulating and visualizing ODE models of consumer-resource interactions

Mechanistic models of resource competition underpin numerous foundational concepts and theories in ecology, and continue to be employed widely to address diverse research questions. Nevertheless, current software tools present a comparatively steep barrier to entry. I introduce the R package rescomp to support the specification, simulation and visualisaton of a broad spectrum of consumer-resource interactions. rescomp is compatible with diverse model specifications, including an unlimited number of consumers and resources, different consumer functional responses (type I, II and III), different resource types (essential or substitutable) and supply dynamics (chemostats, logistic and/or pulsed), delayed consumer introductions, time dependent growth and consumption parameters, and instantaneous changes to consumer and/or resource densities. Several examples on implementing rescomp are provided. In addition, a wide variety of additional examples can be found in the package vignettes, including using rescomp to reproduce the results of several well known studies from the literature. rescomp provides users with an accessible tool to reproduce classic models in ecology, to specify models resembling a wide range of experimental designs, and to explore diverse novel model formulations.

Mini-batch optimization enables training of ODE models on large-scale datasets

Quantitative dynamic models are widely used to study cellular signal processing. A critical step in modelling is the estimation of unknown model parameters from experimental data. As model sizes and datasets are steadily growing, established parameter optimization approaches for mechanistic models become computationally extremely challenging. Mini-batch optimization methods, as employed in deep learning, have better scaling properties. In this work, we adapt, apply, and benchmark mini-batch optimization for ordinary differential equation (ODE) models, thereby establishing a direct link between dynamic modelling and machine learning. On our main application example, a large-scale model of cancer signaling, we benchmark mini-batch optimization against established methods, achieving better optimization results and reducing computation by more than an order of magnitude. We expect that our work will serve as a first step towards mini-batch optimization tailored to ODE models and enable modelling of even larger and more complex systems than what is currently possible.

A Concise Review of State Estimation Techniques for Partial Differential Equation Systems

While state estimation techniques are routinely applied to systems represented by ordinary differential equation (ODE) models, it remains a challenging task to design an observer for a distributed parameter system described by partial differential equations (PDEs). Indeed, PDE systems present a number of unique challenges related to the space-time dependence of the states, and well-established methods for ODE systems do not translate directly. However, the steady progresses in computational power allows executing increasingly sophisticated algorithms, and the field of state estimation for PDE systems has received revived interest in the last decades, also from a theoretical point of view. This paper provides a concise overview of some of the available methods for the design of state observers, or software sensors, for linear and semilinear PDE systems based on both early and late lumping approaches.

Effect of Human Mobility On The Spatial Spread of Airborne Diseases: An Epidemic Model With Indirect Transmission

We extended a class of coupled PDE-ODE models for studying the spatial spread of airborne diseases by incorporating human mobility. Human populations are modeled with patches, and a Lagrangian perspective is used to keep track of individuals’ places of residence. The movement of pathogens in the air is modeled with linear diffusion and coupled to the SIR dynamics of each human population through an integral of the density of pathogen around the population patch. In the limit of fast diffusion pathogens, the method of matched asymptotic analysis is used to reduce the coupled PDE-ODE model to a nonlinear system of ODEs for the average density of pathogens in the air. The reduced system of ODEs is used to derive the basic reproduction number and the final size relation for the model. Numerical simulations of the full PDE-ODE model and the reduced system of ODEs are used to assess the impact of human mobility, together with the diffusion of pathogens on the dynamics of the disease. Results from the two models are consistent and show that human mobility significantly affects disease dynamics. In addition, we show that an increase in the diffusion rate of pathogen leads to a smaller epidemic.

Impulsive Fire Disturbance in a Savanna Model: Tree–Grass Coexistence States, Multiple Stable System States, and Resilience

Savanna ecosystems are shaped by the frequency and intensity of regular fires. We model savannas via an ordinary differential equation (ODE) encoding a one-sided inhibitory Lotka–Volterra interaction between trees and grass. By applying fire as a discrete disturbance, we create an impulsive dynamical system that allows us to identify the impact of variation in fire frequency and intensity. The model exhibits three different bistability regimes: between savanna and grassland; two savanna states; and savanna and woodland. The impulsive model reveals rich bifurcation structures in response to changes in fire intensity and frequency—structures that are largely invisible to analogous ODE models with continuous fire. In addition, by using the amount of grass as an example of a socially valued function of the system state, we examine the resilience of the social value to different disturbance regimes. We find that large transitions (“tipping”) in the valued quantity can be triggered by small changes in disturbance regime.

Fitting deterministic population models to stochastic data: from trajectory matching to state-space models

Population and community ecology traditionally has a very strong theoretical foundation with well-known models, such as the logistic and its many variations, and many modification of the classical Lotka-Volterra predator-prey and interspecific competition models. More and more, these classical models are confronted to data via fitting to empirical time-series, from the field or from the laboratory, for purposes of projections or for estimating model parameters of interest. However, the interface between mathematical population or community models and data, provided by a statistical model, is far from trivial. In order to help empiricists make informed decisions, we here ask which error structure one should use when fitting classical deterministic ODE models to empirical data, from single species to community dynamics and trophic interactions. We use both realistically simulated data and empirical data from microcosms to answer this question in a Bayesian framework. We find that pure observation error models mostly perform adequately overall. However, state-space models clearly outperform simpler approaches when observation errors are sufficiently large or biological models sufficiently complex. Finally, we provide a comprehensive tutorial for fitting these models in R.

Modeling the propagation of the Dengue, Zika and Chikungunya virus in the city of Bello using Agent-Based Modeling and Simulation

Agent-Based Models (ABM) have become a very useful tool to simulate the propagation of infectious diseases. To enhance the scope of these simulation models, some authors have combined ABMs with ODE models which are called Hybrid ABMs, and allows the simulation of models that demand a very high computational cost. In the present project, the main approach is to develop hybrid ABMs to understand the transmission dynamics of vector-borne diseases such as Dengue, Zika, and Chikungunya considering some geospatial characteristics of the city of Bello, Colombia. Some assumptions were considered to develop the computational model to understand and verify if the transmission dynamics were happening according to their theoretical behavior. The results obtained were satisfactory, and for future work, the idea is to integrate more components and make the model more realistic.

Generation of multicellular spatiotemporal models of population dynamics from ordinary differential equations, with applications in viral infection

Background The biophysics of an organism span multiple scales from subcellular to organismal and include processes characterized by spatial properties, such as the diffusion of molecules, cell migration, and flow of intravenous fluids. Mathematical biology seeks to explain biophysical processes in mathematical terms at, and across, all relevant spatial and temporal scales, through the generation of representative models. While non-spatial, ordinary differential equation (ODE) models are often used and readily calibrated to experimental data, they do not explicitly represent the spatial and stochastic features of a biological system, limiting their insights and applications. However, spatial models describing biological systems with spatial information are mathematically complex and computationally expensive, which limits the ability to calibrate and deploy them and highlights the need for simpler methods able to model the spatial features of biological systems. Results In this work, we develop a formal method for deriving cell-based, spatial, multicellular models from ODE models of population dynamics in biological systems, and vice versa. We provide examples of generating spatiotemporal, multicellular models from ODE models of viral infection and immune response. In these models, the determinants of agreement of spatial and non-spatial models are the degree of spatial heterogeneity in viral production and rates of extracellular viral diffusion and decay. We show how ODE model parameters can implicitly represent spatial parameters, and cell-based spatial models can generate uncertain predictions through sensitivity to stochastic cellular events, which is not a feature of ODE models. Using our method, we can test ODE models in a multicellular, spatial context and translate information to and from non-spatial and spatial models, which help to employ spatiotemporal multicellular models using calibrated ODE model parameters. We additionally investigate objects and processes implicitly represented by ODE model terms and parameters and improve the reproducibility of spatial, stochastic models. Conclusion We developed and demonstrate a method for generating spatiotemporal, multicellular models from non-spatial population dynamics models of multicellular systems. We envision employing our method to generate new ODE model terms from spatiotemporal and multicellular models, recast popular ODE models on a cellular basis, and generate better models for critical applications where spatial and stochastic features affect outcomes.