ABSTRACT

Animal movement paths are represented by point-location time series called relocation data. How well such paths can be simulated, when the rules governing movement depend on the internal state of individuals and environmental factors (both local and, when memory is involved, global) remains an open question. To answer this, we formulate and test models able to capture the essential statistics of multiphase versions of such paths (viz., movement-phase-specific step-length and turning-angle means, variances, auto-correlation, and cross correlation values), as well as broad scale movement patterns. The latter may include patchy coverage of the landscape, as well as the existence of home-range boundaries and gravitational centers-of-movement (e.g., centered around nests). Here we present a Numerus Model Builder implementation of two kinds of models: a high-frequency, multi-mode, biased, correlated random walk designed to simulate real movement data at a scale that permits simulation and identification of path segments that range from minutes to days; and a model that uses statistics extracted from relocation data—either empirical or simulated—to construct movement modes and phases at subhourly to daily scales. We evaluate how well our derived statistical movement model captures patterns produced by our more detailed simulation model as a way to evaluate how well derived statistical movement models may capture patterns occurring in empirical data.

We formulate a refined SEIR epidemic model that explicitly includes a contact class C that either thwarts pathogen invasion and returns to the susceptible class S or progresses successively through latent, asymptomatic, and symptomatic classes L, A, and I. Individuals in both A and I may go directly to an immune class V, and in I to a dead class D. We extend this SCLAIV formulation by including a set of drivers that can be used to develop policy to manage current Covid-19 and similar type disease outbreaks. These drivers include surveillance, social distancing (rate and efficacy), social relaxation, quarantining (linked to contact tracing), patient treatment/isolation and vaccination processes, each of which can be represented by a non-negative constant or an s-shaped switching flow. The latter are defined in terms of onset and switching times, initial and final values, and abruptness of switching. We built a Covid-19NMB-DASA web app to generate both deterministic and stochastic solutions to our SCLAIV and drivers model and use incidence and mortality data to provide both maximum-likelihood estimation (MLE) and Bayesian MCMC fitting of parameters. In the context of South African and English Covid-19 incidence data we demonstrate how to both identify and evaluate the role of drivers in ongoing outbreaks. In particular, we show that early social distancing in South Africa likely averted around 80,000 observed cases (actual number is double if only half the cases are observed) during the months of June and July. We also demonstrated that incidence rates in South Africa will increase to between a conservative estimate of 15 and 30 thousand observed cases per day (at a 50% surveillance level) by the end of August if stronger social distancing measures are not effected during July and August, 2020. On different a note, we show that comparably good local MLE fits of the English data using surveillance, social distancing and social relaxation drivers can represent very different kinds of outbreaks—one with close to 90% and another with under 8% immune individuals. This latter result provides a cautionary tale of why fitting SEIR-like models to incidence or prevalence data can be extremely problematic when not anchored by other critical measures, such as levels of immunity in the population. Our presentation illustrates how our SCLAIV formulation can be used to carry out forensic and scenario analyses of disease outbreaks such as Covid-19 in well defined regions.

Background

An understanding of epidemiological dynamics, once confined to mathematical epidemiologists and applied mathematicians, can be disseminated to a non-mathematical community of health care professionals and applied biologists through simple-to-use simulation applications. We used Numerus Model Builder RAMP ^Ⓡ (Runtime Alterable Model Platform) technology, to construct deterministic and stochastic versions of compartmental SIR (Susceptible, Infectious, Recovered with immunity) models as simple-to-use, freely available, epidemic simulation application programs.

Results

We take the reader through simulations used to demonstrate the following concepts: 1) disease prevalence curves of unmitigated outbreaks have a single peak and result in epidemics that 'burn' through the population to become extinguished when the proportion of the susceptible population drops below a critical level; 2) if immunity in recovered individuals wanes sufficiently fast then the disease persists indefinitely as an endemic state, with possible dampening oscillations following the initial outbreak phase; 3) the steepness and initial peak of the prevalence curve are influenced by the basic reproductive value R₀, which must exceed 1 for an epidemic to occur; 4) the probability that a single infectious individual in a closed population (i.e. no migration) gives rise to an epidemic increases with the value of R₀>1; 5) behavior that adaptively decreases the contact rate among individuals with increasing prevalence has major effects on the prevalence curve including dramatic flattening of the prevalence curve along with the generation of multiple prevalence peaks; 6) the impacts of treatment are complicated to model because they effect multiple processes including transmission, recovery and mortality; 7) the impacts of vaccination policies, constrained by a fixed number of vaccination regimens and by the rate and timing of delivery, are crucially important to maximizing the ability of vaccination programs to reduce mortality.

Conclusion

Our presentation makes transparent the key assumptions underlying SIR epidemic models. Our RAMP simulators are meant to augment rather than replace classroom material when teaching epidemiological dynamics. They are sufficiently versatile to be used by students to address a range of research questions for term papers and even dissertations.

In this paper, we present methods for building a Java Runtime-Alterable-Model Platform (RAMP) of complex dynamical systems. We illustrate our methods by building a multivariant SEIR (epidemic) RAMP. Underlying our RAMP is an individual-based model that includes adaptive contact rates, pathogen genetic drift, waning and cross immunity. Besides allowing parameter values, process descriptions, and scriptable runtime drivers to be easily modified during simulations, our RAMP is easily integrated into other computational platforms, such as our illustrated example with R-Studio. Processes descriptions that can be runtime altered within our SEIR RAMP include pathogen variant-dependent host shedding, environmental persistence, host transmission, and within-host pathogen mutation and replication. They also include adaptive social distancing and adaptive application of vaccination rates and variant-valency of vaccines. We present simulation results using parameter values and process descriptions relevant to the current COVID-19 pandemic. Our results suggest that if waning immunity outpaces vaccination rates, then vaccination rollouts may fail to contain the most transmissible variants, particularly if vaccine valencies do not adapt to escape mutations. Our SEIR RAMP is designed for easy-use by individuals and groups involved in formulating social-distancing and adaptive vaccination rollout policies. More generally, our RAMP concept facilitates construction of highly flexible complex systems models of all types, which can then be easily shared among researchers and policymakers as stand alone applications programs.

We present methods for building a Java Runtime-Alterable-Model Platform (RAMP) of complex dynamical systems. We illustrate our methods by building a multivariant SEIR (epidemic) RAMP. Underlying our RAMP is an individual-based model that includes adaptive contact rates, pathogen genetic drift, waning and cross-immunity. Besides allowing parameter values, process descriptions and scriptable runtime drivers to be easily modified during simulations, our RAMP can used within R-Studio and other computational platforms. Process descriptions that can be runtime altered within our SEIR RAMP include pathogen variant-dependent host shedding, environmental persistence, host transmission and within-host pathogen mutation and replication. They also include adaptive social distancing and adaptive application of vaccination rates and variant-valency of vaccines. We present simulation results using parameter values and process descriptions relevant to the current COVID-19 pandemic. Our results suggest that if waning immunity outpaces vaccination rates, then vaccination rollouts may fail to contain the most transmissible variants, particularly if vaccine valencies are not adapted to deal with escape mutations. Our SEIR RAMP is designed for easy use by others. More generally, our RAMP concept facilitates construction of highly flexible complex systems models of all types, which can then be easily shared as stand-alone application programs.