The effects of strain heterology on the epidemiology of equine influenza in a vaccinated population

We assess the effects of strain heterology (strains that are immunologically similar but not identical) on equine influenza in a vaccinated population. Using data relating to individual animals, for both homologous and heterologous vaccinees, we estimate distributions for the latent and infectious periods, quantify the risk of becoming infected in terms of the quantity of cross-reactive antibodies to a key surface protein of the virus (haemagglutinin) and estimate the probability of excreting virus (i.e. becoming infectious) given that infection has occurred. The data suggest that the infectious period, the risk of becoming infected (for a given vaccine-induced level of cross-reactive antibodies) and the probability of excreting virus are increased for heterologously vaccinated animals when compared with homologously vaccinated animals. The data are used to parameterize a modified susceptible, exposed, infectious and recovered/resistant (SEIR) model, which shows that these relatively small differences combine to have a large effect at the population level, where populations of heterologous vaccinees face a significantly increased risk of an epidemic occurring.     

Containment of arthropod disease vectors

Effective containment of arthropod vectors of infectious diseases is necessary to prevent transmission of pathogens by released, infected vectors and to prevent vectors that escape from establishing populations that subsequently contribute to increased disease. Although rare, past releases illustrate what can go wrong and justify the need for guidelines that minimize risks. An overview of recommendations for insectary facilities, practices, and equipment is provided, and features of four recently published and increasingly rigorous arthropod containment levels (ACLs 1-4) are summarized. ACL-1 is appropriate for research that constitutes the lowest risk level, including uninfected arthropods or vectors that are infected with micro-organisms that do not cause disease in humans, domestic animals, or wildlife. ACL-2 is appropriate for indigenous and exotic arthropods that represent a moderate risk, including vectors infected or suspected of being infected with biosafety level (BSL)-2 infectious agents and arthropods that have been genetically modified in ways that do not significantly affect their fecundity, survival, host preference, or vector competence. ACL-3 is recommended for arthropods that are or may be infected with BSL-3 infectious agents. ACL-3 places greater emphasis on pathogen containment and more restricted access to the insectary than ACL-2. ACL-4 is intended for arthropods that are infected with the most dangerous BSL-4 infectious agents, which can cause life-threatening illness by aerosol or arthropod bite. Adherence to these guidelines will result in laboratory-based arthropod vector research that minimizes risks and results in important new contributions to applied and basic science.     

Different forms of superspreading lead to different outcomes: Heterogeneity in infectiousness and contact behavior relevant for the case of SARS-CoV-2

Superspreading events play an important role in the spread of several pathogens, such as SARS-CoV-2. While the basic reproduction number of the original Wuhan SARS-CoV-2 is estimated to be about 3 for Belgium, there is substantial inter-individual variation in the number of secondary cases each infected individual causes—with most infectious individuals generating no or only a few secondary cases, while about 20% of infectious individuals is responsible for 80% of new infections. Multiple factors contribute to the occurrence of superspreading events: heterogeneity in infectiousness, individual variations in susceptibility, differences in contact behavior, and the environment in which transmission takes place. While superspreading has been included in several infectious disease transmission models, research into the effects of different forms of superspreading on the spread of pathogens remains limited. To disentangle the effects of infectiousness-related heterogeneity on the one hand and contact-related heterogeneity on the other, we implemented both forms of superspreading in an individual-based model describing the transmission and spread of SARS-CoV-2 in a synthetic Belgian population. We considered its impact on viral spread as well as on epidemic resurgence after a period of social distancing. We found that the effects of superspreading driven by heterogeneity in infectiousness are different from the effects of superspreading driven by heterogeneity in contact behavior. On the one hand, a higher level of infectiousness-related heterogeneity results in a lower risk of an outbreak persisting following the introduction of one infected individual into the population. Outbreaks that did persist led to fewer total cases and were slower, with a lower peak which occurred at a later point in time, and a lower herd immunity threshold. Finally, the risk of resurgence of an outbreak following a period of lockdown decreased. On the other hand, when contact-related heterogeneity was high, this also led to fewer cases in total during persistent outbreaks, but caused outbreaks to be more explosive in regard to other aspects (such as higher peaks which occurred earlier, and a higher herd immunity threshold). Finally, the risk of resurgence of an outbreak following a period of lockdown increased. We found that these effects were conserved when testing combinations of infectiousness-related and contact-related heterogeneity.     

Household Epidemics: Modelling Effects of Early Stage Vaccination

A Markovian susceptible → infectious → removed (SIR) epidemic model is considered in a community partitioned into households. A vaccination strategy, which is implemented during the early stages of the disease following the detection of infected individuals is proposed. In this strategy, the detection occurs while an individual is infectious and other susceptible household members are vaccinated without further delay. Expressions are derived for the influence on the reproduction numbers of this vaccination strategy for equal and unequal household sizes. We fit previously estimated parameters from influenza and use household distributions for Sweden and Tanzania census data. The results show that the reproduction number is much higher in Tanzania (6 compared with 2) due to larger households, and that infected individuals have to be detected (and household members vaccinated) after on average 5 days in Sweden and after 3.3 days in Tanzania, a much smaller difference.     

Modelling and estimation of infectious diseases in a population with heterogeneous dynamic immunity

The paper presents a model for the evolution of an infectious disease in a population with individual-specific immunity. The immune state of an individual varies with time according to its own dynamics, depending on whether the individual is infected or not. The model involves a system of size-structured (first-order) PDEs that capture both the dynamics of the immune states and the transition between compartments consisting of infected, susceptible, etc. individuals. Due to the unavailability of precise data about the immune states of the individuals, the main focus in the paper is on developing a technique for set-membership estimations of aggregated quantities of interest. The technique involves solving specific optimization problems for the underlying PDE system and is developed up to a numerical method. Results of numerical simulations are presented for a benchmark model of SIS-type, potentially applicable to diseases like influenza and to various sexually transmitted diseases.     

一类具有垂直传播的SEIRS捕食传染病模型的全局分析

通过假设捕食系统中疾病只在食饵种群中传播,被传染的易惑者经过一段潜伏期后才具有传染性,潜伏者与染病者均具有垂直传播能力,染病者恢复后对该病不具有终身免疫力,建立了一类具有垂直传播的SEIRS捕食传染病模型,运用极限系统理论,分两种情形讨论了系统平衡点的存在性及局部稳定性,利用Lyapunov函数和二次复合矩阵等方法,得到了平衡点全局渐近稳定的条件.     

An incubating diseased-predator ecoepidemic model

We present a model for transmissible diseases spreading among predators in a predator–prey system. Upon successful contact, a susceptible individual becomes infected but is not yet able to spread the disease further. After an incubation period, the diseased individual becomes infectious. We investigate the system’s equilibria by analytical and numerical means. For a suitable set of parameter values, the system shows persistent oscillations. The model also exhibits bistability of the coexistence equilibrium with the prey-only equilibrium.     

Modelling strategies for minimizing the impact of an imported exotic infection

The global epidemic of severe acute respiratory syndrome (SARS) in 2003 demonstrated the need to determine control strategies for exotic infections. The prior determination of such strategies, and the use of mathematical models to assist this, is hampered by the obvious lack of data. We propose an integral equation model of Kermack-McKendrick type that may be used to compare strategies based on the isolation of infectious individuals. The model structures the incidence of infection according to the location of an infected individual at exposure, and requires knowledge of the infectivity kernel and the initial rate of exponential increase of cases. The model's use in the design of strategies to minimize the risk of SARS in a previously unexposed community is demonstrated.     

Genetic management of infectious diseases: a heterogeneous epidemio-genetic model illustrated with S. aureus mastitis

Given that individuals are genetically heterogeneous in their degree of resistance to infection, a model is proposed to formulate appropriate choices that will limit the spread of an infectious disease. The model is illustrated with data on S. aureus mastitis and is based on parameters characterizing the spread of the disease (contact rate, probability of infection after contact, and rate of recovery after infection), the demography (replacement and culling rates) and the genetic composition (degree of relationship and heritability of the disease trait) of the animal population. To decrease infection pressure, it is possible to apply non-genetic procedures that increase the culling (e.g., culling of chronically infected cows) and recovery (e.g., antibiotic therapy) rates of infected cows. But the contribution of the paper is to show that genetic management of infectious disease is also theoretically possible as a control measure complementary to non-genetic actions. Indeed, the probability for an uninfected individual to become infected after contact with an infected one is partially related to their degree of kinship: the more closely they are related, the more likely they are to share identical genes like those associated to the non-resistance to infection. Different prospective genetic management procedures are proposed to decrease the contact rate between infected and uninfected relatives and keep the number of secondary cases generated by one infected animal below 1.     

The effects of population structure on the spread of the HIV infection

A model for the spread of human immunodeficiency virus (HIV) in a population of male homosexuals is presented. The population is divided into five groups on the basis of degree of sexual activity. Within each group, the individuals are classified as 1) susceptible; 2) infective; or 3) removed because of a lack of sexual activity associated with advanced acquired immunodeficiency disease (AIDS). The infective individuals are further subdivided into four stages of infection. Analyses of the model address two questions with regard to the spread of HIV: (1) What is the effect of level of sexual activity on an individual's risk for infection, and (2) What is the effect that assumptions about mixing between groups have on both individual risk and transmission throughout a population? Results from analyses using a number of different parameter estimates show that increased levels of sexual activity increase the likelihood that an individual will become infected. In addition, the initial spread of the disease is markedly affected by variation in the amount of contact among individuals from different subpopulations. The steady-state incidence of the disease is not markedly affected by variation in the contact patterns, but the size of the steady-state population and therefore the proportion of infected individuals in the population does vary significantly with changes in the degree of mixing among subpopulations. These results show clearly the sensitivity of model outcomes to variation in the patterns of contact among individuals and the need for better data on such interactions to aid in understanding and predicting the spread of HIV.     

Isolation and characterization of an infectious replication-competent molecular clone of ecotropic porcine endogenous retrovirus class C

Xenotransplantation of pig organs is complicated by the existence of polytropic replication-competent porcine endogenous retroviruses (PERV) capable of infecting human cells. The potential for recombination between ecotropic PERV-C and human-tropic PERV-A and PERV-B adds another level of infectious risk. Proviral PERV-C were characterized in MAX-T cells derived from d/d haplotype miniature swine. Three proviruses were cloned from a genomic library. Clone PERV-C(1312) generated infectious particles after transfection into porcine ST-IOWA cells. Electron microscopy revealed the same morphologies of virions in MAX-T cells and in ST-IOWA cells infected with cell-free PERV-C(1312) particles, indicating that MAX-T cells harbor one functional PERV-C provirus.     

Accuracy of models for the 2001 foot-and-mouth epidemic

Since 2001 models of the spread of foot-and-mouth disease, supported by the data from the UK epidemic, have been expounded as some of the best examples of problem-driven epidemic models. These claims are generally based on a comparison between model results and epidemic data at fairly coarse spatio-temporal resolution. Here, we focus on a comparison between model and data at the individual farm level, assessing the potential of the model to predict the infectious status of farms in both the short and long terms. Although the accuracy with which the model predicts farms reporting infection is between 5 and 15%, these low levels are attributable to the expected level of variation between epidemics, and are comparable to the agreement between two independent model simulations. By contrast, while the accuracy of predicting culls is higher (20-30%), this is lower than expected from the comparison between model epidemics. These results generally support the contention that the type of the model used in 2001 was a reliable representation of the epidemic process, but highlight the difficulties of predicting the complex human response, in terms of control strategies to the perceived epidemic risk.     

Modeling breastmilk infectivity in HIV-1 infected mothers

Estimation of breastmilk infectivity in HIV-1 infected mothers is difficult because transmission can occur while the fetus is in utero, during delivery, or through breastfeeding. Since transmission can only be detected through periodic testing, however, it may be impossible to determine the actual mode of transmission in any individual child. In this article we develop a model to estimate breastmilk infectivity, along with the probabilities of in-utero and intrapartum transmission. In addition, the model allows separate estimation of early and late breastmilk infectivity, and individual variation in maternal infectivity. Methods for hypothesis testing of binary risk factors and a method for assessing goodness of fit are also described. Data from a randomized trial of breastfeeding versus formula feeding among HIV-1 infected mothers in Nairobi, Kenya, are used to illustrate the methods.     

Common source epidemics I: A stochastic model

A discrete time stochastic model is formulated for the spread of a disease which is transmitted to an uninfected but susceptible individual through an environmental source and not through contact (either direct or indirect) with infected individuals. The model incorporates both exposure and infection components. The exposure component includes consideration of the introduction of an infectious agent into the environment and the subsequent diffusion of the agent. It also includes time and location patterns for visits by individuals in the target population to the affected environment. The infection component incorporates physiological responses of exposed individuals to the infectious agent. The goal of the model is to provide a method for developing a predicted epidemic curve. Comments are given on an application of the model to the study of an outbreak of toxoplasmosis in Atlanta, Georgia, in 1977. This work was partially supported by BRSG Grant S07 RR0731 awarded by the Biomedical Research Support Grant Program, Division of Research Resources, National Institutes of Health.     

Building epidemiological models from R0: an implicit treatment of transmission in networks

Simple deterministic models are still at the core of theoretical epidemiology despite the increasing evidence for the importance of contact networks underlying transmission at the individual level. These mean-field or 'compartmental' models based on homogeneous mixing have made, and continue to make, important contributions to the epidemiology and the ecology of infectious diseases but fail to reproduce many of the features observed for disease spread in contact networks. In this work, we show that it is possible to incorporate the important effects of network structure on disease spread with a mean-field model derived from individual level considerations. We propose that the fundamental number known as the basic reproductive number of the disease, R0, which is typically derived as a threshold quantity, be used instead as a central parameter to construct the model from. We show that reliable estimates of individual level parameters can replace a detailed knowledge of network structure, which in general may be difficult to obtain. We illustrate the proposed model with small world networks and the classical example of susceptible-infected-recovered (SIR) epidemics.     

A model of the transmission of micro-organisms in a public setting and its correlation to pathogen infection risks

Aim: Gastro‐intestinal infections are widespread in the community and have considerable economic consequences. In this study, we followed chains of infection from a public toilet scenario, looking at infection risks by correlating the transmission of bacteria, fungi and viruses to our current knowledge of infectious doses. Methods and Results: Transmission of Escherichia coli, Bacillus atrophaeus spores, Candida albicans and bacteriophage MS2 from hands to surfaces was examined in a transmission model, that is toilet brush, door handle to water tap. The load of viable pathogens was significantly reduced during transfer from hands to objects. Nevertheless, it was shown that pathogens were successfully transferred to other people in contagious doses by contact with contaminated surfaces. Conclusions: Our results suggest that infection risks are mainly dependent on current infectious doses of pathogens. For enteritic viruses or bacteria, for example Norovirus or EHEC, only a few particles or cells are sufficient for infection in public lavatories, thus bearing a high risk of infection for other persons. However, there seems to be only a low probability of becoming infected with pathogens that have a high infectious dose whilst sharing the same bathroom. Significance and Impact of the Study: The transmission model for micro‐organisms enables a risk assessment of gastro‐intestinal infections on the basis of a practical approach.     

Constructing Rigorous and Broad Biosurveillance Networks for Detecting Emerging Zoonotic Outbreaks

Determining optimal surveillance networks for an emerging pathogen is difficult since it is not known beforehand what the characteristics of a pathogen will be or where it will emerge. The resources for surveillance of infectious diseases in animals and wildlife are often limited and mathematical modeling can play a supporting role in examining a wide range of scenarios of pathogen spread. We demonstrate how a hierarchy of mathematical and statistical tools can be used in surveillance planning help guide successful surveillance and mitigation policies for a wide range of zoonotic pathogens. The model forecasts can help clarify the complexities of potential scenarios, and optimize biosurveillance programs for rapidly detecting infectious diseases. Using the highly pathogenic zoonotic H5N1 avian influenza 2006-2007 epidemic in Nigeria as an example, we determined the risk for infection for localized areas in an outbreak and designed biosurveillance stations that are effective for different pathogen strains and a range of possible outbreak locations. We created a general multi-scale, multi-host stochastic SEIR epidemiological network model, with both short and long-range movement, to simulate the spread of an infectious disease through Nigerian human, poultry, backyard duck, and wild bird populations. We chose parameter ranges specific to avian influenza (but not to a particular strain) and used a Latin hypercube sample experimental design to investigate epidemic predictions in a thousand simulations. We ranked the risk of local regions by the number of times they became infected in the ensemble of simulations. These spatial statistics were then complied into a potential risk map of infection. Finally, we validated the results with a known outbreak, using spatial analysis of all the simulation runs to show the progression matched closely with the observed location of the farms infected in the 2006-2007 epidemic.