Space and contact networks: capturing the locality of disease transmission.

While an arbitrary level of complexity may be included in simulations of spatial epidemics, computational intensity and analytical intractability mean that such models often lack transparency into the determinants of epidemiological dynamics. Although numerous approaches attempt to resolve this complexity-tractability trade-off, moment closure methods arguably offer the most promising and robust frameworks for capturing the role of the locality of contact processes on global disease dynamics. While a close analogy may be made between full stochastic spatial transmission models and dynamic network models, we consider here the special case where the dynamics of the network topology change on time-scales much longer than the epidemiological processes imposed on them; in such cases, the use of static network models are justified. We show that in such cases, static network models may provide excellent approximations to the underlying spatial contact process through an appropriate choice of the effective neighbourhood size. We also demonstrate the robustness of this mapping by examining the equivalence of deterministic approximations to the full spatial and network models derived under third-order moment closure assumptions. For systems where deviation from homogeneous mixing is limited, we show that pair equations developed for network models are at least as good an approximation to the underlying stochastic spatial model as more complex spatial moment equations, with both classes of approximation becoming less accurate only for highly localized kernels.     

Influence of network dynamics on the spread of sexually transmitted diseases

Network epidemiology often assumes that the relationships defining the social network of a population are static. The dynamics of relationships is only taken indirectly into account by assuming that the relevant information to study epidemic spread is encoded in the network obtained, by considering numbers of partners accumulated over periods of time roughly proportional to the infectious period of the disease. On the other hand, models explicitly including social dynamics are often too schematic to provide a reasonable representation of a real population, or so detailed that no general conclusions can be drawn from them. Here, we present a model of social dynamics that is general enough so its parameters can be obtained by fitting data from surveys about sexual behaviour, but that can still be studied analytically, using mean-field techniques. This allows us to obtain some general results about epidemic spreading. We show that using accumulated network data to estimate the static epidemic threshold lead to a significant underestimation of that threshold. We also show that, for a dynamic network, the relative epidemic threshold is an increasing function of the infectious period of the disease, implying that the static value is a lower bound to the real threshold. A practical example is given of how to apply the model to the study of a real population.     

Impact of the implementation of rest days in live bird markets on the dynamics of H5N1 highly pathogenic avian influenza

Live bird markets (LBMs) act as a network ‘hub’ and potential reservoir of infection for domestic poultry. They may therefore be responsible for sustaining H5N1 highly pathogenic avian influenza (HPAI) virus circulation within the poultry sector, and thus a suitable target for implementing control strategies. We developed a stochastic transmission model to understand how market functioning impacts on the transmission dynamics. We then investigated the potential for rest days—periods during which markets are emptied and disinfected—to modulate the dynamics of H5N1 HPAI within the poultry sector using a stochastic meta-population model. Our results suggest that under plausible parameter scenarios, HPAI H5N1 could be sustained silently within LBMs with the time spent by poultry in markets and the frequency of introduction of new susceptible birds'' dominant factors determining sustained silent spread. Compared with interventions applied in farms (i.e. stamping out, vaccination), our model shows that frequent rest days are an effective means to reduce HPAI transmission. Furthermore, our model predicts that full market closure would be only slightly more effective than rest days to reduce transmission. Strategies applied within markets could thus help to control transmission of the disease.     

Epidemiological mechanisms of genetic resistance to kuru

Transmissible spongiform encephalopathies (TSEs), such as kuru, are invariably fatal neurodegenerative conditions caused by a malformation of the prion protein. Heterozygosity of codon 129 of the prion protein gene has been associated with increased host resistance to TSEs, although the mechanism by which this resistance is achieved has not been determined. To evaluate the epidemiological mechanism of human resistance to kuru, we developed a model that combines the dynamics of kuru transmission and the population genetics of human resistance. We fitted our model to kuru data from the epidemic that occurred in Papua New Guinea over the last hundred years. To elucidate the epidemiological mechanism of human resistance, we estimated the incubation period and transmission rate of kuru for codon 129 heterozygotes and homozygotes using kuru incidence data and human genotype frequency data from 1957 to 2004. Our results indicate that human resistance arises from a combination of both a longer incubation period and reduced susceptibility to infection. This work provides evidence for balancing selection acting on a human population and the mechanistic basis for the heterozygote resistance to kuru.     

Noise, nonlinearity and seasonality: the epidemics of whooping cough revisited

Understanding the mechanisms that generate oscillations in the incidence of childhood infectious diseases has preoccupied epidemiologists and population ecologists for nearly two centuries. This body of work has generated simple yet powerful explanations for the epidemics of measles and chickenpox, while the dynamics of other infectious diseases, such as whooping cough, have proved more challenging to decipher. A number of authors have, in recent years, proposed that the noisy and somewhat irregular epidemics of whooping cough may arise due to stochasticity and its interaction with nonlinearity in transmission and seasonal variation in contact rates. The reason underlying the susceptibility of whooping cough dynamics to noise and the precise nature of its transient dynamics remain poorly understood. Here we use household data on the incubation period in order to parametrize more realistic distributions of the latent and infectious periods. We demonstrate that previously reported phenomena result from transients following the interaction between the stable annual attractor and unstable multiennial solutions.     

Unidirectional AGV guidepath network design: A heuristic algorithm

In an AGV system, the design of the guidepath network is one of the most important factors that determine the system effectiveness. Many alternative guidepath design schema have been introduced in the literature. However, the methods generally address the static production environment where the product mix or machine routings are assumed to be stable over time. In today's dynamic production systems with small lot sizes and short product cycles, the assumption of an unchanging product mix over an extended period is unrealistic in some situations. Considerable system inefficiency can be introduced when a network designed under the assumption of a stable product mix is used when indeed the product mix has changed. To avoid this kind of hidden source of inefficiency, what is needed is a tool that can recognize when a previously designed network is inappropriate for a new product mix and then uses the new product routing information to reconfigure a new network appropriate for the new production condition. A heuristic algorithm for the design of AGV guidepath in an environment with changing product mix is proposed here. The algorithm not only makes it possible to adapt the system network as the product mix changes, but also produces new designs at reasonably short computational time.     

The role of modelling in identifying drug targets for diseases of the cell cycle.

The cell cycle is implicated in diseases that are the leading cause of mortality and morbidity in the developed world. Until recently, the search for drug targets has focused on relatively small parts of the regulatory network under the assumption that key events can be controlled by targeting single pathways. This is valid provided the impact of couplings to the wider scale context of the network can be ignored. The resulting depth of study has revealed many new insights; however, these have been won at the expense of breadth and a proper understanding of the consequences of links between the different parts of the network. Since it is now becoming clear that these early assumptions may not hold and successful treatments are likely to employ drugs that simultaneously target a number of different sites in the regulatory network, it is timely to redress this imbalance. However, the substantial increase in complexity presents new challenges and necessitates parallel theoretical and experimental approaches. We review the current status of theoretical models for the cell cycle in light of these new challenges. Many of the existing approaches are not sufficiently comprehensive to simultaneously incorporate the required extent of couplings. Where more appropriate levels of complexity are incorporated, the models are difficult to link directly to currently available data. Further progress requires a better integration of experiment and theory. New kinds of data are required that are quantitative, have a higher temporal resolution and that allow simultaneous quantitative comparison of the concentration of larger numbers of different proteins. More comprehensive models are required and must accommodate not only substantial uncertainties in the structure and kinetic parameters of the networks, but also high levels of ignorance. The most recent results relating network complexity to robustness of the dynamics provide clues that suggest progress is possible.     

Modelling the spread of infectious salmon anaemia among salmon farms based on seaway distances between farms and genetic relationships between infectious salmon anaemia virus isolates

Infectious salmon anaemia (ISA) is an important infectious disease in Atlantic salmon farming causing recurrent epidemic outbreaks worldwide. The focus of this paper is on tracing the spread of ISA among Norwegian salmon farms. To trace transmission pathways for the ISA virus (ISAV), we use phylogenetic relationships between virus isolates in combination with space–time data on disease occurrences. The rate of ISA infection of salmon farms is modelled stochastically, where seaway distances between farms and genetic distances between ISAV isolates from infected farms play prominent roles. The model was fitted to data covering all cohorts of farmed salmon and the history of all farms with ISA between 2003 and summer 2009. Both seaway and genetic distances were significantly associated with the rate of ISA infection. The fitted model predicts that the risk of infection from a neighbourhood infectious farm decreases with increasing seaway distance between the two farms. Furthermore, for a given infected farm with a given ISAV genotype, the source of infection is significantly more likely to be ISAV of a small genetic distance than of moderate or large genetic distances. Nearly half of the farms with ISA in the investigated period are predicted to have been infected by an infectious farm in their neighbourhood, whereas the remaining half of the infected farms had unknown sources. For many of the neighbourhood infected farms, it was possible to point out one or a few infectious farms as the most probable sources of infection. This makes it possible to map probable infection pathways.     

Mixed-mode oscillations in a three time-scale system of ODEs motivated by a neuronal model

We present a mathematical study of some aspects of mixed-mode oscillation (MMO) dynamics in a three time-scale system of ODEs as well as analyse related features of a biophysical model of a neuron from the entorhinal cortex that serves as a motivation for our study. The neuronal model includes standard spiking currents (sodium and potassium) that play a critical role in the analysis of the interspike interval as well as persistent sodium and slow potassium (M) currents. We reduce the dimensionality of the neuronal model from six to three dimensions in order to investigate a regime in which MMOs are generated and to motivate the three time-scale model system upon which we focus our study. We further analyse in detail the mechanism of the transition from MMOs to spiking in our model system. In particular, we prove the existence of a special solution, a singular primary canard, that serves as a transition between MMOs and spiking in the singular limit by employing appropriate rescalings and centre manifold reductions. Additionally, we conjecture that the singular canard solution is the limit of a family of canards and provides numerical evidence for the conjecture.     

Effect of the initial dose of foot-and-mouth disease virus on the early viral dynamics within pigs

This paper investigates the early viral dynamics of foot-and-mouth disease (FMD) within infected pigs. Using an existing within-host model, we investigate whether individual variation can be explained by the effect of the initial dose of FMD virus. To do this, we consider the experimental data on the concentration of FMD virus genomes in the blood (viral load). In this experiment, 12 pigs were inoculated with one of three different doses of FMD virus: low; medium; or high. Measurements of the viral load were recorded over a time course of approximately 11 days for every 8 hours. The model is a set of deterministic differential equations with the following variables: viral load; virus in the interstitial space; and the proportion of epithelial cells available for infection, infected and uninfected. The model was fitted to the data for each animal individually and also simultaneously over all animals varying only the initial dose. We show that the general trend in the data can be explained by varying only the initial dose. The higher the initial dose the earlier the development of a detectable viral load.     

Face masking and COVID-19: potential effects of variolation on transmission dynamics

Face masks do not completely prevent transmission of respiratory infections, but masked individuals are likely to inhale fewer infectious particles. If smaller infectious doses tend to yield milder infections, yet ultimately induce similar levels of immunity, then masking could reduce the prevalence of severe disease even if the total number of infections is unaffected. It has been suggested that this effect of masking is analogous to the pre-vaccination practice of variolation for smallpox, whereby susceptible individuals were intentionally infected with small doses of live virus (and often acquired immunity without severe disease). We present a simple epidemiological model in which mask-induced variolation causes milder infections, potentially with lower transmission rate and/or different duration. We derive relationships between the effectiveness of mask-induced variolation and important epidemiological metrics (the basic reproduction number and initial epidemic growth rate, and the peak prevalence, attack rate and equilibrium prevalence of severe infections). We illustrate our results using parameter estimates for the original SARS-CoV-2 wild-type virus, as well as the Alpha, Delta and Omicron variants. Our results suggest that if variolation is a genuine side-effect of masking, then the importance of face masks as a tool for reducing healthcare burdens from COVID-19 may be under-appreciated.     

Acoustic wave propagation in disordered microscale granular media under compression

We investigate the effect of dynamic and uniaxial static loading on the wave speeds and rise times of laser generated acoustic waves traveling through a disordered, multilayer aggregate of 2 \(\mu {\mathrm {m}}\) diameter silica microspheres, where the excited dynamic amplitudes are estimated to approach the level of the static overlap between the particles caused by adhesion and externally applied loads. Two cases are studied: a case where the as-fabricated particle network is retained, and a case where the static load has been increased to the point where the aggregate collapses and a rearrangement of the particle network occurs. We observe increases in wave speeds with static loading significantly lower than, and in approximate agreement with, predictions from models based on Hertzian contact mechanics for the pre- and post-collapse states, respectively. The measured rise time of the leading pulse is found to decrease with increasing static load in both cases, which we attribute to decreased scattering and stiffening of the contact network. Finally, we observe an increase in wave speed with increased excitation amplitude that depends on static loading, and whether the system is in the pre- or post-collapse state. The wave speed dependence on amplitude and static load is found to be in qualitative agreement with a one-dimensional discrete model of adhesive spheres, although the observed difference between pre- and post-collapse states is not captured. This investigation, and the approach presented herein, may find use in future studies of the contact mechanics and dynamics of adhesive microgranular systems.     

A dynamic dose–response model to account for exposure patterns in risk assessment: a case study in inhalation anthrax

The most commonly used dose–response models implicitly assume that accumulation of dose is a time-independent process where each pathogen has a fixed risk of initiating infection. Immune particle neutralization of pathogens, however, may create strong time dependence; i.e. temporally clustered pathogens have a better chance of overwhelming the immune particles than pathogen exposures that occur at lower levels for longer periods of time. In environmental transmission systems, we expect different routes of transmission to elicit different dose–timing patterns and thus potentially different realizations of risk. We present a dose–response model that captures time dependence in a manner that incorporates the dynamics of initial immune response. We then demonstrate the parameter estimation of our model in a dose–response survival analysis using empirical time-series data of inhalational anthrax in monkeys in which we find slight dose–timing effects. Future dose–response experiments should include varying the time pattern of exposure in addition to varying the total doses delivered. Ultimately, the dynamic dose–response paradigm presented here will improve modelling of environmental transmission systems where different systems have different time patterns of exposure.     

Escherichia coli O157 infection on Scottish cattle farms: dynamics and control

In this study, we parametrize a stochastic individual-based model of the transmission dynamics of Escherichia coli O157 infection among Scottish cattle farms and use the model to predict the impacts of both targeted and non-targeted interventions. We first generate distributions of model parameter estimates using Markov chain Monte Carlo methods. Despite considerable uncertainty in parameter values, each set of parameter values within the 95th percentile range implies a fairly similar impact of interventions. Interventions that reduce the transmission coefficient and/or increase the recovery rate of infected farms (e.g. via vaccination and biosecurity) are much more effective in reducing the level of infection than reducing cattle movement rates, which improves effectiveness only when the overall control effort is small. Targeted interventions based on farm-level risk factors are more efficient than non-targeted interventions. Herd size is a major determinant of risk of infection, and our simulations confirmed that targeting interventions at farms with the largest herds is almost as effective as targeting based on overall risk. However, because of the striking characteristic that the infection force depends weakly on the number of infected farms, no interventions that are less than 100 per cent effective can eradicate E. coli O157 infection from Scottish cattle farms, implying that eliminating the disease is impractical.     

Predicting undetected infections during the 2007 foot-and-mouth disease outbreak

Active disease surveillance during epidemics is of utmost importance in detecting and eliminating new cases quickly, and targeting such surveillance to high-risk individuals is considered more efficient than applying a random strategy. Contact tracing has been used as a form of at-risk targeting, and a variety of mathematical models have indicated that it is likely to be highly efficient. However, for fast-moving epidemics, resource constraints limit the ability of the authorities to perform, and follow up, contact tracing effectively. As an alternative, we present a novel real-time Bayesian statistical methodology to determine currently undetected (occult) infections. For the UK foot-and-mouth disease (FMD) epidemic of 2007, we use real-time epidemic data synthesized with previous knowledge of FMD outbreaks in the UK to predict which premises might have been infected, but remained undetected, at any point during the outbreak. This provides both a framework for targeting surveillance in the face of limited resources and an indicator of the current severity and spatial extent of the epidemic. We anticipate that this methodology will be of substantial benefit in future outbreaks, providing a compromise between targeted manual surveillance and random or spatially targeted strategies.     

Spatial connectivity in mosquito-borne disease models: a systematic review of methods and assumptions

Spatial connectivity plays an important role in mosquito-borne disease transmission. Connectivity can arise for many reasons, including shared environments, vector ecology and human movement. This systematic review synthesizes the spatial methods used to model mosquito-borne diseases, their spatial connectivity assumptions and the data used to inform spatial model components. We identified 248 papers eligible for inclusion. Most used statistical models (84.2%), although mechanistic are increasingly used. We identified 17 spatial models which used one of four methods (spatial covariates, local regression, random effects/fields and movement matrices). Over 80% of studies assumed that connectivity was distance-based despite this approach ignoring distant connections and potentially oversimplifying the process of transmission. Studies were more likely to assume connectivity was driven by human movement if the disease was transmitted by an Aedes mosquito. Connectivity arising from human movement was more commonly assumed in studies using a mechanistic model, likely influenced by a lack of statistical models able to account for these connections. Although models have been increasing in complexity, it is important to select the most appropriate, parsimonious model available based on the research question, disease transmission process, the spatial scale and availability of data, and the way spatial connectivity is assumed to occur.     

A combined within-host and between-hosts modelling framework for the evolution of resistance to antimalarial drugs

The spread of drug resistance represents a significant challenge to many disease control efforts. The evolution of resistance is a complex process influenced by transmission dynamics between hosts as well as infection dynamics within these hosts. This study aims to investigate how these two processes combine to impact the evolution of resistance in malaria parasites. We introduce a stochastic modelling framework combining an epidemiological model of Plasmodium transmission and an explicit within-human infection model for two competing strains. Immunity, treatment and resistance costs are included in the within-host model. We show that the spread of resistance is generally less likely in areas of intense transmission, and therefore of increased competition between strains, an effect exacerbated when costs of resistance are higher. We also illustrate how treatment influences the spread of resistance, with a trade-off between slowing resistance and curbing disease incidence. We show that treatment coverage has a stronger impact on disease prevalence, whereas treatment efficacy primarily affects resistance spread, suggesting that coverage should constitute the primary focus of control efforts. Finally, we illustrate the importance of feedbacks between modelling scales. Overall, our results underline the importance of concomitantly modelling the evolution of resistance within and between hosts.     

Modelling the effectiveness and risks of vaccination strategies to control classical swine fever epidemics

In a recent update of the Dutch contingency plan for controlling outbreaks of classical swine fever (CSF), emergency vaccination is preferred to large-scale pre-emptive culling. This policy change raised two questions: can emergency vaccination be as effective as pre-emptive culling, and what are the implications for showing freedom of infection? Here, we integrate quantitative information available on CSF virus transmission and vaccination effects into a stochastic mathematical model that describes the transmission dynamics at the level of animals, farms and livestock areas. This multilevel approach connects individual-level interventions to large-scale effects. Using this model, we compare the performance of five different control strategies applied to hypothetical CSF epidemics in The Netherlands and, for each of these strategies, we study the properties of three different screening scenarios to show freedom of infection. We find that vaccination in a ring of 2 km radius around a detected infection source is as effective as ring culling in a 1 km radius. Feasible screening scenarios, adapted to the use of emergency vaccination, can reduce the enhanced risks of (initially) undetected farm outbreaks by targeting vaccinated farms. Altogether, our results suggest that emergency vaccination against CSF can be equally effective and safe as pre-emptive culling.     

Study on sub-cycling algorithm for flexible multi-body system—integral theory and implementation flow chart

A sub-cycling integration algorithm (or named multi-time-steps integration algorithm), which has been successfully applied to FEM dynamical analysis, was firstly presented by Belytschko et al. (Comput Methods Appl Mech Eng 17/18:259–275, 1979). However, the problem of how to apply this type of algorithm to flexible multi-body dynamics (FMD) problems still lacks investigation up to now. Similar to the region-partitioning method used in FEM, this paper presents a central-difference-based sub-cycling integral method by decomposing the variables of an FMD equation into several groups and adopting different integral step sizes to each group of the variables. Based on the condensed form of an FMD equation, a group of common update formulae and a sub-step update formula, which constitute the sub-cycling together, are established in the paper. Furthermore, an implementation flowchart of the sub-cycling is presented. Stability of the sub-cycling will be analyzed and numerical examples will be performed to verify availability and precision of the sub-cycling in part II of the paper.