Modelling preventive measures and their effect on generation times in emerging epidemics

We present a stochastic epidemic model to study the effect of various preventive measures, such as uniform reduction of contacts and transmission, vaccination, isolation, screening and contact tracing, on a disease outbreak in a homogeneously mixing community. The model is based on an infectivity process, which we define through stochastic contact and infectiousness processes, so that each individual has an independent infectivity profile. In particular, we monitor variations of the reproduction number and of the distribution of generation times. We show that some interventions, i.e. uniform reduction and vaccination, affect the former while leaving the latter unchanged, whereas other interventions, i.e. isolation, screening and contact tracing, affect both quantities. We provide a theoretical analysis of the variation of these quantities, and we show that, in practice, the variation of the generation time distribution can be significant and that it can cause biases in the estimation of reproduction numbers. The framework, because of its general nature, captures the properties of many infectious diseases, but particular emphasis is on COVID-19, for which numerical results are provided.     

Social encounter networks: collective properties and disease transmission

A fundamental challenge of modern infectious disease epidemiology is to quantify the networks of social and physical contacts through which transmission can occur. Understanding the collective properties of these interactions is critical for both accurate prediction of the spread of infection and determining optimal control measures. However, even the basic properties of such networks are poorly quantified, forcing predictions to be made based on strong assumptions concerning network structure. Here, we report on the results of a large-scale survey of social encounters mainly conducted in Great Britain. First, we characterize the distribution of contacts, which possesses a lognormal body and a power-law tail with an exponent of −2.45; we provide a plausible mechanistic model that captures this form. Analysis of the high level of local clustering of contacts reveals additional structure within the network, implying that social contacts are degree assortative. Finally, we describe the epidemiological implications of this local network structure: these contradict the usual predictions from networks with heavy-tailed degree distributions and contain public-health messages about control. Our findings help us to determine the types of realistic network structure that should be assumed in future population level studies of infection transmission, leading to better interpretations of epidemiological data and more appropriate policy decisions.     

Heterogeneous influence of individuals’ behavior on mask efficacy in gathering environments

Wearing masks is an easy way to operate and popular measure for preventing epidemics. Although masks can slow down the spread of viruses, their efficacy in gathering environments involving heterogeneous person-to-person contacts remains unknown. Therefore, we aim to investigate the epidemic prevention effect of masks in different real-life gathering environments. This study uses four real interpersonal contact datasets to construct four empirical networks to represent four gathering environments. The transmission of COVID-19 is simulated using the Monte Carlo simulation method. The heterogeneity of individuals can cause mask efficacy in a specific gathering environment to be different from the baseline efficacy in general society. Furthermore, the heterogeneity of gathering environments causes the epidemic prevention effect of masks to differ. Wearing masks can greatly reduce the probability of clustered epidemics and the infection scale in primary schools, high schools, and hospitals. However, the use of masks alone in primary schools and hospitals cannot control outbreaks. In high schools with social distancing between classes and in workplaces where the interpersonal contact is relatively sparse, masks can meet the need for prevention. Given the heterogeneity of individual behavior, if individuals who are more active in terms of interpersonal contact are prioritized for mask-wearing, the epidemic prevention effect of masks can be improved. Finally, asymptomatic infection has varying effects on the prevention effect of masks in different environments. The effect can be weakened or eliminated by increasing the usage rate of masks in high schools and workplaces. However, the effect on primary schools and hospitals cannot be weakened. This study contributes to the accurate evaluation of mask efficacy in various gathering environments to provide scientific guidance for epidemic prevention.     

Effect of data quality on estimates of farm infectiousness trends in the UK 2001 foot-and-mouth disease epidemic

Most of the mathematical models that were developed to study the UK 2001 foot-and-mouth disease epidemic assumed that the infectiousness of infected premises was constant over their infectious periods. However, there is some controversy over whether this assumption is appropriate. Uncertainty about which farm infected which in 2001 means that the only method to determine if there were trends in farm infectiousness is the fitting of mechanistic mathematical models to the epidemic data. The parameter values that are estimated using this technique, however, may be influenced by missing and inaccurate data. In particular to the UK 2001 epidemic, this includes unreported infectives, inaccurate farm infection dates and unknown farm latent periods. Here, we show that such data degradation prevents successful determination of trends in farm infectiousness.     

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.     

Multi-scale modelling reveals that early super-spreader events are a likely contributor to novel variant predominance

The emergence of new SARS-CoV-2 variants of concern (VOC) has hampered international efforts to contain the COVID-19 pandemic. VOCs have been characterized to varying degrees by higher transmissibility, worse infection outcomes and evasion of vaccine and infection-induced immunologic memory. VOCs are hypothesized to have originated from animal reservoirs, communities in regions with low surveillance and/or single individuals with poor immunologic control of the virus. Yet, the factors dictating which variants ultimately predominate remain incompletely characterized. Here we present a multi-scale model of SARS-CoV-2 dynamics that describes population spread through individuals whose viral loads and numbers of contacts (drawn from an over-dispersed distribution) are both time-varying. This framework allows us to explore how super-spreader events (SSE) (defined as greater than five secondary infections per day) contribute to variant emergence. We find stochasticity remains a powerful determinant of predominance. Variants that predominate are more likely to be associated with higher infectiousness, an SSE early after variant emergence and ongoing decline of the current dominant variant. Additionally, our simulations reveal that most new highly infectious variants that infect one or a few individuals do not achieve permanence in the population. Consequently, interventions that reduce super-spreading may delay or mitigate emergence of VOCs.     

Will an outbreak exceed available resources for control? Estimating the risk from invading pathogens using practical definitions of a severe epidemic

Forecasting whether or not initial reports of disease will be followed by a severe epidemic is an important component of disease management. Standard epidemic risk estimates involve assuming that infections occur according to a branching process and correspond to the probability that the outbreak persists beyond the initial stochastic phase. However, an alternative assessment is to predict whether or not initial cases will lead to a severe epidemic in which available control resources are exceeded. We show how this risk can be estimated by considering three practically relevant potential definitions of a severe epidemic; namely, an outbreak in which: (i) a large number of hosts are infected simultaneously; (ii) a large total number of infections occur; and (iii) the pathogen remains in the population for a long period. We show that the probability of a severe epidemic under these definitions often coincides with the standard branching process estimate for the major epidemic probability. However, these practically relevant risk assessments can also be different from the major epidemic probability, as well as from each other. This holds in different epidemiological systems, highlighting that careful consideration of how to classify a severe epidemic is vital for accurate epidemic risk quantification.     

COVID-19 hospitalization rates rise exponentially with age,inversely proportional to thymic T-cell production

Here, we report that COVID-19 hospitalization rates follow an exponential relationship with age, doubling for every 16 years of age or equivalently increasing by 4.5% per year of life (R² = 0.98). This mirrors the well-studied exponential decline of both thymus volume and T-cell production, which halve every 16 years. COVID-19 can therefore be added to the list of other diseases with this property, including those caused by methicillin-resistant Staphylococcus aureus, MERS-CoV, West Nile virus, Streptococcus pneumoniae and certain cancers, such as chronic myeloid leukaemia and brain cancers. In addition, the incidence of severe disease and mortality due to COVID-19 are both higher in men, consistent with the degree to which thymic involution (and the decrease in T-cell production with age) is more severe in men compared to women. Since these properties are shared with some non-contagious diseases, we hypothesized that the age dependence does not come from social-mixing patterns, i.e. that the probability of hospitalization given infection rises exponentially, doubling every 16 years. A Bayesian analysis of daily hospitalizations, incorporating contact matrices, found that this relationship holds for every age group except for the under 20s. While older adults have fewer contacts than young adults, our analysis suggests that there is an approximate cancellation between the effects of fewer contacts for the elderly and higher infectiousness due to a higher probability of developing severe disease. Our model fitting suggests under 20s have 49–75% additional immune protection beyond that predicted by strong thymus function alone, consistent with increased juvenile cross-immunity from other viruses. We found no evidence for differences between age groups in susceptibility to infection or infectiousness to others (given disease state), i.e. the only important factor in the age dependence of hospitalization rates is the probability of hospitalization given infection. These findings suggest the existence of a T-cell exhaustion threshold, proportional to thymic output and that clonal expansion of peripheral T-cells does not affect disease risk. The strikingly simple inverse relationship between risk and thymic T-cell output adds to the evidence that thymic involution is an important factor in the decline of the immune system with age and may also be an important clue in understanding disease progression, not just for COVID-19 but other diseases as well.     

Epidemic cycles driven by host behaviour

Host immunity and demographics (the recruitment of susceptibles via birthrate) have been demonstrated to be a key determinant of the periodicity of measles, pertussis and dengue epidemics. However, not all epidemic cycles are from pathogens inducing sterilizing immunity or are driven by demographics. Many sexually transmitted infections are driven by sexual behaviour. We present a mathematical model of disease transmission where individuals can disconnect and reconnect depending on the infectious status of their contacts. We fit the model to historic syphilis (Treponema pallidum) and gonorrhea (Neisseria gonorrhoeae) incidence in the USA and explore potential intervention strategies against syphilis. We find that cycles in syphilis incidence can be driven solely by changing sexual behaviour in structured populations. Our model also explains the lack of similar cycles in gonorrhea incidence even if the two infections share the same propagation pathways. Our model similarly illustrates how sudden epidemic outbreaks can occur on time scales smaller than the characteristic demographic time scale of the population and that weaker infections can lead to more violent outbreaks. Behaviour also appears to be critical for control strategies as we found a bigger sensitivity to behavioural interventions than antibiotic treatment. Thus, behavioural interventions may play a larger role than previously thought, especially in the face of antibiotic resistance and low intervention efficacies.     

Accounting for biological variability and sampling scale: a multi-scale approach to building epidemic models.

When one considers the fine-scale spread of an epidemic, one usually knows the sources of biological variability and their qualitative effect on the epidemic process. The force of infection on a susceptible unit depends on the locations and the strengths of the infectious units, and on the environmental and intrinsic factors affecting infectivity and/or susceptibility. The infection probability for the susceptible unit can then be modelled as a function of these factors. Thus, one can build a conceptual model at the fine scale. However, the epidemic is generally observed at a larger scale and one has to build a model adapted to this larger scale. But how can the sources of variation identified at the fine scale be integrated into the model at the larger scale? To answer this question, we present, in the context of plant epidemiology, a multi-scale approach which consists of defining a base model built at the fine scale and upscaling it to match the scale of the sampling and the data. This approach will enable comparing experiments involving different observational processes.     

Transmission and control of an emerging influenza pandemic in a small-world airline network

The avian influenza virus H5N1 and the 2009 swine flu H1N1 are potentially serious pandemic threats to human health, and air travel readily facilitates the spread of infectious diseases. However, past studies have not yet incorporated the effects of air travel on the transmission of influenza in the construction of mathematical epidemic models. Therefore, this paper focused on the human-to-human transmission of influenza, and investigated the effects of air travel activities on an influenza pandemic in a small-world network. These activities of air travel include passengers’ consolidation, conveyance and distribution in airports and flights. Dynamic transmission models were developed to assess the expected burdens of the pandemic, with and without control measures. This study also investigated how the small-world properties of an air transportation network facilitate the spread of influenza around the globe. The results show that, as soon as the influenza is spread to the top 50 global airports, the transmission is greatly accelerated. Under the constraint of limited resources, a strategy that first applies control measures to the top 50 airports after day 13 and then soon afterwards to all other airports may result in remarkable containment effectiveness. As the infectiousness of the disease increases, it will expand the scale of the pandemic, and move the start time of the pandemic ahead.     

Modelling the performance of isoniazid preventive therapy for reducing tuberculosis in HIV endemic settings: the effects of network structure

Individuals living with HIV experience a much higher risk of progression from latent M. tuberculosis infection to active tuberculosis (TB) disease relative to individuals with intact immune systems. A several-month daily course of a single drug during latent infection (i.e. isoniazid preventive therapy (IPT)) has proved in clinical trials to substantially reduce an HIV-infected individual''s risk of TB disease. As a result of these findings and ongoing studies, the World Health Organization has produced strong guidelines for implementing IPT on a community-wide scale for individuals with HIV at risk of TB disease. To date, there has been limited use of IPT at a community-wide level. In this paper, we present a new co-network model for HIV and TB co-epidemics to address questions about how the population-level impact of community-wide IPT may differ from the individual-level impact of IPT offered to selected individuals. In particular, we examine how the effect of clustering of contacts within high-TB incidence communities may affect the rates of re-infection with TB and how this clustering modifies the expected population-level effects of IPT. We find that populations with clustering of respiratory contacts experience aggregation of TB cases and high numbers of re-infection events. While, encouragingly, the overall population-level effects of community-wide IPT appear to be sustained regardless of network structure, we find that in populations where these contacts are highly clustered, there is dramatic heterogeneity in the impact of IPT: in some sub-regions of these populations, TB is nearly eliminated, while in others, repeated re-infection almost completely undermines the effect of IPT. Our findings imply that as IPT programmes are brought to scale, we should expect local heterogeneity of effectiveness as a result of the complex patterns of disease transmission within communities.     

Epidemic Spreading–Information Dissemination Coupling Mechanism in Heterogeneous Areas

With COVID-19 continuing to rage around the world, there is a spread of epidemic-related information on social networking platforms. This phenomenon may inhibit or promote the scale of epidemic transmission. This study constructed a double-layer epidemic spreading–information dissemination network based on the movements of individuals across regions to analyze the dynamic evolution and coupling mechanism of information dissemination and epidemic transmission. We also proposed measures to control the spread of the epidemic by analyzing the factors affecting dynamic transmission. We constructed a state probability equation based on Markov chain theory and performed Monte Carlo simulations to demonstrate the interaction between information dissemination and epidemic transmission. The simulation results showed that the higher the information dissemination rate, the larger the scale of information dissemination and the smaller the scale of epidemic transmission. In addition, the higher the recovery rate of the epidemic or the lower the infection rate of the epidemic, the smaller the scale of information dissemination and the smaller the scale of epidemic transmission. Moreover, the greater the probability of individuals moving across regions, the larger the spread of the epidemic and information. Finally, the higher the probability of an individual taking preventive behavior, the smaller the spread of the epidemic and information. Therefore, it is possible to suppress epidemic spread by increasing the information dissemination rate, epidemic recovery rate, and probability of individuals taking preventive behavior, while also reducing the infection rate of the epidemic and appropriately implementing regional blockades.     

Dynamics of infectious disease transmission by inhalable respiratory droplets

Transmission of respiratory infectious diseases in humans, for instance influenza, occurs by several modes. Respiratory droplets provide a vector of transmission of an infectious pathogen that may contribute to different transmission modes. An epidemiological model incorporating the dynamics of inhalable respiratory droplets is developed to assess their relevance in the infectious process. Inhalable respiratory droplets are divided into respirable droplets, with droplet diameter less than 10 µm, and inspirable droplets, with diameter in the range 10–100 µm: both droplet classes may be inhaled or settle. Droplet dynamics is determined by their physical properties (size), whereas population dynamics is determined by, among other parameters, the pathogen infectivity and the host contact rates. Three model influenza epidemic scenarios, mediated by different airborne or settled droplet classes, are analysed. The scenarios are distinguished by the characteristic times associated with breathing at contact and with hand-to-face contact. The scenarios suggest that airborne transmission, mediated by respirable droplets, provides the dominant transmission mode in middle and long-term epidemics, whereas inspirable droplets, be they airborne or settled, characterize short-term epidemics with high attack rates. The model neglects close-contact transmission by droplet sprays (direct projection onto facial mucous membranes), retaining close-contact transmission by inspirable droplets.     

SARS传播的数学原理及预测与控制

众所周知,SARS对中国社会带来了重大的影响。我们以北京地区4月到6月有关SARS的数据为参考资料,就病毒的实际传播特征引入了电子线路中的负反馈的概念,建立了SARS传播的负反馈系统,并在分析该系统参数实际意义的情况下,建立时间序列的模型。该模型将传染率定义为时间的函数,以拟合数据和实际数据之间的总残差最小为目标,利用matlab中的fminsearch函数模拟得到最优的模型参数。该模型可以较好的预测SARS的发展趋势,且可以就此趋势提出如何控制SARS传播的措施。继而,本文通过模拟出在不同日期提前或滞后5天实施隔离政策所引起SARS发展趋势变化的曲线,分析了卫生部门实施隔离政策的日期对SARS发展趋势的影响。 在SARS对经济影响的这个问题上,本文适当选取医疗业具有代表性的17支股票,构造了医疗板块指数,以此测度医疗业的经济表现。在传统的CAPM模型中,我们引入了虚拟变量,利用OLS技术进行估计分析,检验出SARS这一事件对医药业的经济影响是正影响。该影响反映在医疗版指数的日收益上,但这个影响是由SARS引起的,会随着SARS的结束而结束。     

Sub-spreading events limit the reliable elimination of heterogeneous epidemics

We show that sub-spreading events, i.e. transmission events in which an infection propagates to few or no individuals, can be surprisingly important for defining the lifetime of an infectious disease epidemic and hence its waiting time to elimination or fade-out, measured from the time-point of its last observed case. While limiting super-spreading promotes more effective control when cases are growing, we find that when incidence is waning, curbing sub-spreading is more important for achieving reliable elimination of the epidemic. Controlling super-spreading in this low-transmissibility phase offers diminishing returns over non-selective, population-wide measures. By restricting sub-spreading, we efficiently dampen remaining variations among the reproduction numbers of infectious events, which minimizes the risk of premature and late end-of-epidemic declarations. Because case-ascertainment or reporting rates can be modelled in exactly the same way as control policies, we concurrently show that the under-reporting of sub-spreading events during waning phases will engender overconfident assessments of epidemic elimination. While controlling sub-spreading may not be easily realized, the likely neglecting of these events by surveillance systems could result in unexpectedly risky end-of-epidemic declarations. Super-spreading controls the size of the epidemic peak but sub-spreading mediates the variability of its tail.     

A stochastic model for infectious salmon anemia (ISA) in Atlantic salmon farming.

Infectious salmon anemia (ISA) is one of the main infectious diseases in Atlantic salmon farming with major economical implications. Despite the strong regulatory interventions, the ISA epidemic is not under control, worldwide. We study the data covering salmon farming in Norway from 2002 to 2005 and propose a stochastic space-time model for the transmission of the virus. We model seaway transmission between farm sites, transmission through shared management and infrastructure, biomass effects and other potential pathways within the farming industry. We find that biomass has an effect on infectiousness, the local contact network and seaway distance of 5 km represent similar risks, but a large component of risk originates from other sources, among which are possibly infected salmon smolt and boat traffic.     

Buying Time for an Effective Epidemic Response: The Impact of a Public Holiday for Outbreak Control on COVID-19 Epidemic Spread

Rapid responses in the early stage of a new epidemic are crucial in outbreak control. Public holidays for outbreak control could provide a critical time window for a rapid rollout of social distancing and other control measures at a large population scale. The objective of our study was to explore the impact of the timing and duration of outbreak-control holidays on the coronavirus disease 2019 (COVID-19) epidemic spread during the early stage in China. We developed a compartment model to simulate the dynamic transmission of COVID-19 in China starting from January 2020. We projected and compared epidemic trajectories with and without an outbreak-control holiday that started during the Chinese Lunar New Year. We considered multiple scenarios of the outbreak-control holiday with different durations and starting times, and under different assumptions about viral transmission rates. We estimated the delays in days to reach certain thresholds of infections under different scenarios. Our results show that the outbreak-control holiday in China likely stalled the spread of COVID-19 for several days. The base case outbreak-control holiday (21 d for Hubei Province and 10 d for all other provinces) delayed the time to reach 100 000 confirmed infections by 7.54 d. A longer outbreak-control holiday would have had stronger effects. A nationwide outbreak-control holiday of 21 d would have delayed the time to 100 000 confirmed infections by nearly 10 d. Furthermore, we find that outbreak-control holidays that start earlier in the course of a new epidemic are more effective in stalling epidemic spread than later holidays and that additional control measures during the holidays can boost the holiday effect. In conclusion, an outbreak-control holiday can likely effectively delay the transmission of epidemics that spread through social contacts. The temporary delay in the epidemic trajectory buys time, which scientists can use to discover transmission routes and identify effective public health interventions and which governments can use to build physical infrastructure, organize medical supplies, and deploy human resources for long-term epidemic mitigation and control efforts.