A comparison of COVID-19 outbreaks across US Combined Statistical Areas using new methods for estimating R0 and social distancing behaviour.

We investigated the initial outbreak rates and subsequent social distancing behaviour over the initial phase of the COVID-19 pandemic across 29 Combined Statistical Areas (CSAs) of the United States. We used the Numerus Model Builder Data and Simulation Analysis (NMB-DASA) web application to fit the exponential phase of a SCLAIV+D (Susceptible, Contact, Latent, Asymptomatic infectious, symptomatic Infectious, Vaccinated, Dead) disease classes model to outbreaks, thereby allowing us to obtain an estimate of the basic reproductive number R0 for each CSA. Values of R0 ranged from 1.9 to 9.4, with a mean and standard deviation of 4.5±1.8. Fixing the parameters from the exponential fit, we again used NMB-DASA to estimate a set of social distancing behaviour parameters to compute an epidemic flattening index cflatten. Finally, we applied hierarchical clustering methods using this index to divide CSA outbreaks into two clusters: those presenting a social distancing response that was either weaker or stronger. We found cflatten to be more influential in the clustering process than R0. Thus, our results suggest that the behavioural response after a short initial exponential growth phase is likely to be more determinative of the rise of an epidemic than R0 itself.

Simulation applications to support teaching and research in epidemiological dynamics.

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.

A runtime alterable epidemic model with genetic drift, waning immunity and vaccinations.

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.

Modeling the population effects of escape mutations in SARS-CoV-2 to guide vaccination strategies.

SARS-Cov-2 escape mutations (EM) have been detected and are spreading. Vaccines may need adjustment to respond to these or future mutations. We designed a population level model integrating both waning immunity and EM. We also designed a set of criteria for elaborating and fitting this model to cross-neutralization and other data with a goal of minimizing vaccine decision errors. We formulated four related models. These differ regarding which strains can drift to escape immunity in the host when that immunity was elicited by different strains. Across changing waning and escape mutation parameter values, these model variations led to patterns where: 1) EM are rare in the first epidemic, 2) rebound outbreaks after the first outbreak are accelerated by increasing waning and by increasing drifting, 3) the long term endemic level of infection is determined mostly by waning rates with small effects of the drifting parameter, 4) EM caused loss of vaccine effectiveness, and under some conditions: vaccines induced EM that caused higher levels of infection with vaccines than without them. The differences and similarities across the four models suggest paths for developing models specifying the epitopes where EM act. This model provides a base on which to construct epitope specific evolutionary models using new high-throughput assay data from population samples to guide vaccine decisions.

A versatile web app for identifying the drivers of COVID-19 epidemics.

BACKGROUND: No versatile web app exists that allows epidemiologists and managers around the world to comprehensively analyze the impacts of COVID-19 mitigation. The http://covid-webapp.numerusinc.com/ web app presented here fills this gap. METHODS: Our web app uses a model that explicitly identifies susceptible, contact, latent, asymptomatic, symptomatic and recovered classes of individuals, and a parallel set of response classes, subject to lower pathogen-contact rates. The user inputs a CSV file of incidence and, if of interest, mortality rate data. A default set of parameters is available that can be overwritten through input or online entry, and a user-selected subset of these can be fitted to the model using maximum-likelihood estimation (MLE). Model fitting and forecasting intervals are specifiable and changes to parameters allow counterfactual and forecasting scenarios. Confidence or credible intervals can be generated using stochastic simulations, based on MLE values, or on an inputted CSV file containing Markov chain Monte Carlo (MCMC) estimates of one or more parameters. RESULTS: We illustrate the use of our web app in extracting social distancing, social relaxation, surveillance or virulence switching functions (i.e., time varying drivers) from the incidence and mortality rates of COVID-19 epidemics in Israel, South Africa, and England. The Israeli outbreak exhibits four distinct phases: initial outbreak, social distancing, social relaxation, and a second wave mitigation phase. An MCMC projection of this latter phase suggests the Israeli epidemic will continue to produce into late November an average of around 1500 new case per day, unless the population practices social-relaxation measures at least 5-fold below the level in August, which itself is 4-fold below the level at the start of July. Our analysis of the relatively late South African outbreak that became the world's fifth largest COVID-19 epidemic in July revealed that the decline through late July and early August was characterised by a social distancing driver operating at more than twice the per-capita applicable-disease-class (pc-adc) rate of the social relaxation driver. Our analysis of the relatively early English outbreak, identified a more than 2-fold improvement in surveillance over the course of the epidemic. It also identified a pc-adc social distancing rate in early August that, though nearly four times the pc-adc social relaxation rate, appeared to barely contain a second wave that would break out if social distancing was further relaxed. CONCLUSION: Our web app provides policy makers and health officers who have no epidemiological modelling or computer coding expertise with an invaluable tool for assessing the impacts of different outbreak mitigation policies and measures. This includes an ability to generate an epidemic-suppression or curve-flattening index that measures the intensity with which behavioural responses suppress or flatten the epidemic curve in the region under consideration.

Adequacy of SEIR models when epidemics have spatial structure: Ebola in Sierra Leone.

Dynamic SEIR (Susceptible, Exposed, Infectious, Removed) compartmental models provide a tool for predicting the size and duration of both unfettered and managed outbreaks-the latter in the context of interventions such as case detection, patient isolation, vaccination and treatment. The reliability of this tool depends on the validity of key assumptions that include homogeneity of individuals and spatio-temporal homogeneity. Although the SEIR compartmental framework can easily be extended to include demographic (e.g. age) and additional disease (e.g. healthcare workers) classes, dependence of transmission rates on time, and metapopulation structure, fitting such extended models is hampered by both a proliferation of free parameters and insufficient or inappropriate data. This raises the question of how effective a tool the basic SEIR framework may actually be. We go some way here to answering this question in the context of the 2014-2015 outbreak of Ebola in West Africa by comparing fits of an SEIR time-dependent transmission model to both country- and district-level weekly incidence data. Our novel approach in estimating the effective-size-of-the-populations-at-risk ( Neff) and initial number of exposed individuals ( E0) at both district and country levels, as well as the transmission function parameters, including a time-to-halving-the-force-of-infection ( tf/2) parameter, provides new insights into this Ebola outbreak. It reveals that the estimate R0 ≈ 1.7 from country-level data appears to seriously underestimate R0 ≈ 3.3 - 4.3 obtained from more spatially homogeneous district-level data. Country-level data also overestimate tf/2 ≈ 22 weeks, compared with 8-10 weeks from district-level data. Additionally, estimates for the duration of individual infectiousness is around two weeks from spatially inhomogeneous country-level data compared with 2.4-4.5 weeks from spatially more homogeneous district-level data, which estimates are rather high compared with most values reported in the literature. This article is part of the theme issue 'Modelling infectious disease outbreaks in humans, animals and plants: approaches and important themes'. This issue is linked with the subsequent theme issue 'Modelling infectious disease outbreaks in humans, animals and plants: epidemic forecasting and control'.

Modeling epidemics: A primer and Numerus Model Builder implementation.

Epidemiological models are dominated by compartmental models, of which SIR formulations are the most commonly used. These formulations can be continuous or discrete (in either the state-variable values or time), deterministic or stochastic, or spatially homogeneous or heterogeneous, the latter often embracing a network formulation. Here we review the continuous and discrete deterministic and discrete stochastic formulations of the SIR dynamical systems models, and we outline how they can be easily and rapidly constructed using Numerus Model Builder, a graphically-driven coding platform. We also demonstrate how to extend these models to a metapopulation setting using NMB network and mapping tools.

An Agent-Based Model of School Closing in Under-Vacccinated Communities During Measles Outbreaks.

The winter 2014-15 measles outbreak in the US represents a significant crisis in the emergence of a functionally extirpated pathogen. Conclusively linking this outbreak to decreases in the measles/mumps/rubella (MMR) vaccination rate (driven by anti-vaccine sentiment) is critical to motivating MMR vaccination. We used the NOVA modeling platform to build a stochastic, spatially-structured, individual-based SEIR model of outbreaks, under the assumption that R0 ≈ 7 for measles. We show this implies that herd immunity requires vaccination coverage of greater than approximately 85%. We used a network structured version of our NOVA model that involved two communities, one at the relatively low coverage of 85% coverage and one at the higher coverage of 95%, both of which had 400-student schools embedded, as well as students occasionally visiting superspreading sites (e.g. high-density theme parks, cinemas, etc.). These two vaccination coverage levels are within the range of values occurring across California counties. Transmission rates at schools and superspreading sites were arbitrarily set to respectively 5 and 15 times background community rates. Simulations of our model demonstrate that a 'send unvaccinated students home' policy in low coverage counties is extremely effective at shutting down outbreaks of measles.

Sympatric speciation in structureless environments.

BACKGROUND: Darwin and the architects of the Modern Synthesis found sympatric speciation difficult to explain and suggested it is unlikely to occur. Increasingly, evidence over the past few decades suggest that sympatric speciation can occur under ecological conditions that require at most intraspecific competition for a structured resource. Here we used an individual-based population model with variable foraging strategies to study the evolution of mating behavior among foraging strategy types. Initially, individuals were placed at random on a structureless resource landscape, with subsequent spatial variation induced through foraging activity itself. The fitness of individuals was determined by their biomass at the end of each generational cycle. The model incorporates three diallelic, codominant foraging strategy genes, and one mate-choice or m-trait (i.e. incipient magic trait) gene, where the latter is inactive when random mating is assumed. RESULTS: Under non-random mating, the m-trait gene promotes increasing levels of either disassortative or assortative mating when the frequency of m respectively increases or decreases from 0.5. Our evolutionary simulations demonstrate that, under initial random mating conditions, an activated m-trait gene evolves to promote assortative mating because the system, in trying to fit a multipeak adaptive landscape, causes heterozygous individuals to be less fit than homozygous individuals. CONCLUSION: Our results extend our theoretical understanding that sympatric speciation can evolve under nicheless or gradientless resource conditions: i.e. the underlying resource is monomorphic and initially spatially homogeneous. Further the simplicity and generality of our model suggests that sympatric speciation may be more likely than previously thought to occur in mobile, sexually-reproducing organisms.

Panmictic and Clonal Evolution on a Single Patchy Resource Produces Polymorphic Foraging Guilds.

We develop a stochastic, agent-based model to study how genetic traits and experiential changes in the state of agents and available resources influence individuals' foraging and movement behaviors. These behaviors are manifest as decisions on when to stay and exploit a current resource patch or move to a particular neighboring patch, based on information of the resource qualities of the patches and the anticipated level of intraspecific competition within patches. We use a genetic algorithm approach and an individual's biomass as a fitness surrogate to explore the foraging strategy diversity of evolving guilds under clonal versus hermaphroditic sexual reproduction. We first present the resource exploitation processes, movement on cellular arrays, and genetic algorithm components of the model. We then discuss their implementation on the Nova software platform. This platform seamlessly combines the dynamical systems modeling of consumer-resource interactions with agent-based modeling of individuals moving over a landscapes, using an architecture that lays transparent the following four hierarchical simulation levels: 1.) within-patch consumer-resource dynamics, 2.) within-generation movement and competition mitigation processes, 3.) across-generation evolutionary processes, and 4.) multiple runs to generate the statistics needed for comparative analyses. The focus of our analysis is on the question of how the biomass production efficiency and the diversity of guilds of foraging strategy types, exploiting resources over a patchy landscape, evolve under clonal versus random hermaphroditic sexual reproduction. Our results indicate greater biomass production efficiency under clonal reproduction only at higher population densities, and demonstrate that polymorphisms evolve and are maintained under random mating systems. The latter result questions the notion that some type of associative mating structure is needed to maintain genetic polymorphisms among individuals exploiting a common patchy resource on an otherwise spatially homogeneous landscape.

Tactics and strategies for managing Ebola outbreaks and the salience of immunization.

We present a stochastic transmission chain simulation model for Ebola viral disease (EVD) in West Africa, with the salutary result that the virus may be more controllable than previously suspected. The ongoing tactics to detect cases as rapidly as possible and isolate individuals as safely as practicable is essential to saving lives in the current outbreaks in Guinea, Liberia, and Sierra Leone. Equally important are educational campaigns that reduce contact rates between susceptible and infectious individuals in the community once an outbreak occurs. However, due to the relatively low R 0 of Ebola (around 1.5 to 2.5 next generation cases are produced per current generation case in naïve populations), rapid isolation of infectious individuals proves to be highly efficacious in containing outbreaks in new areas, while vaccination programs, even with low efficacy vaccines, can be decisive in curbing future outbreaks in areas where the Ebola virus is maintained in reservoir populations.

Stent-graft limb deployment in the external iliac artery increases the risk of limb occlusion following endovascular AAA repair.

PURPOSE: To assess whether deployment of an endograft limb in the external iliac artery (EIA) increases the rate of limb occlusion following endovascular aneurysm repair (EVAR). METHODS: Interrogation of a prospectively maintained database identified 661 patients (596 men; median age 73 years, range 37-93) with infrarenal abdominal aortic aneurysm who underwent EVAR between 1996 and 2010 using Zenith stent-grafts predominately. Of these, 567 patients [56 (9.9%) women] had both endograft limbs deployed in the CIA (1203 limbs at risk), while 94 patients [9 (9.6%) women] had at least 1 limb in the EIA (22 bilateral; 116 limbs at risk). An adjunctive bare metal stent was used in 8 (9%) limbs deployed in the EIA. RESULTS: There were 31 limb occlusions, all unilateral: 17 (3%) patients in the CIA group had an occluded limb (1% of limbs at risk) vs. 14 (15%) patients in the EIA group (12% of limbs at risk; p<0.0001). The median time to occlusion was 3 months (0-60) in the CIA group and 1 month (0-36) in the EIA group. The majority of occlusions were treated by extra-anatomical revascularization, most often a femorofemoral crossover bypass. No legs were amputated following occlusion of a limb placed in the CIA, but there were 3 amputations in the EIA group (p=0.003). CONCLUSION: Deployment of endograft limbs into the EIA led to a higher rate of occlusion and leg amputation. Increased tortuosity of the EIA and a smaller caliber vessel are likely to account for the increased risk.

Use of a remotely steerable "robotic" catheter in a branched endovascular aortic graft.

We report the use of a remotely steerable catheter to treat kinked renal bridging stents 8 months after branched endovascular repair of a type III thoracoabdominal aortic aneurysm. Conventional techniques using single, coaxial, and manually steerable sheaths proved too unstable to provide the support required to pass a wire against resistance through the kinked stent. A remotely steerable "robotic" catheter provided sufficient precision and stability to cross the kink and reline it with an additional stent, restoring renal perfusion. This technology can help achieve precise and stable introducer sheath position. Further evaluation is necessary to understand the wider applications.

Percutaneous closure and "push-pull" technique to repair arterial lead and sheath placement complicating cardiac resynchronization therapy.

We present a case of inadvertent subclavian arterial puncture and lead placement to the left ventricle in a patient undergoing cardiac resynchronization therapy. We describe the use of a "push-pull" technique within an arterial setting to allow removal of the lead, while maintaining access through the same puncture to allow an arterial-closure device to then seal the artery at this site. As a result of this percutaneous approach, the patient avoided the need for a vascular surgical procedure.

Endovascular repair of the aorta and aortic arch arteries damaged during mediastinoscopy.

Despite advances in imaging techniques, mediastinoscopy remains an important tool for the staging of the mediastinum in non-small cell lung cancer and diagnosing lymphoma with mediastinal adenopathy. Injury to the arterial system during mediastinoscopy is infrequent but a potentially fatal complication. We report three cases of injury to the aorta and supra-aortic arteries sustained during mediastinoscopy. These were effectively managed by endovascular techniques. Patient recovery was uncomplicated and median length of stay was 3 days. This technique avoids major open surgery in a high-risk group of patients and may offer a mortality benefit and more rapid resumption of oncological treatment.

Acute rupture of a fibromuscular dysplasia related renal artery aneurysm: emergency treatment with a covered stent.

We report the successful exclusion of a ruptured left renal artery aneurysm as a first presentation of fibromuscular dysplasia in a haemodynamically unstable 57-year-old man. The aneurysm was repaired in an emergency setting by deployment of a covered stent with a satisfactory result. Follow-up computed tomography confirmed successful exclusion of the aneurysm. A renal artery branch originating from the aneurismal sac was sacrificed with subsequent regional infarction. Our experience shows that the use of a covered stent is an effective, quick and life saving procedure in a ruptured renal artery aneurysm.

Image-guided therapies in orthopedic oncology.

The treatment of patients who have malignancies of bone often require multidisciplinary care. The aim of this review is to outline percutaneous techniques that may be useful for the diagnosis and treatment of these patients. In particular, the existing procedures of percutaneous biopsy, alcoholization (ethanol ablation), vertebroplasty, kyphoplasty, osteoplasty, radiofrequency ablation, laser photocoagulation, and vascular embolization are reviewed. Aspects of each technique, including mechanism of action, patient selection, treatment technique, and recent patient outcome are presented.