Stochastic two-group models with transmission dependent on host infectivity or susceptibility

ABSTRACT

Stochastic epidemic models with two groups are formulated and applied to emerging and re-emerging infectious diseases. In recent emerging diseases, disease spread has been attributed to superspreaders, highly infectious individuals that infect a large number of susceptible individuals. In some re-emerging infectious diseases, disease spread is attributed to waning immunity in susceptible hosts. We apply a continuous-time Markov chain (CTMC) model to study disease emergence or re-emergence from different groups, where the transmission rates depend on either the infectious host or the susceptible host. Multitype branching processes approximate the dynamics of the CTMC model near the disease-free equilibrium and are used to estimate the probability of a minor or a major epidemic. It is shown that the probability of a major epidemic is greater if initiated by an individual from the superspreader group or by an individual from the highly susceptible group. The models are applied to Severe Acute Respiratory Syndrome and measles.     

A useful relationship between epidemiology and queueing theory: The distribution of the number of infectives at the moment of the first detection

In this paper we establish a relation between the spread of infectious diseases and the dynamics of so called M/G/1 queues with processor sharing. The relation between the spread of epidemics and branching processes, which is well known in epidemiology, and the relation between M/G/1 queues and birth death processes, which is well known in queueing theory, will be combined to provide a framework in which results from queueing theory can be used in epidemiology and vice versa.In particular, we consider the number of infectious individuals in a standard SIR epidemic model at the moment of the first detection of the epidemic, where infectious individuals are detected at a constant per capita rate. We use a result from the literature on queueing processes to show that this number of infectious individuals is geometrically distributed.     

中国埃博拉诊疗中心布局流程的设计与思考

为了应对西非埃博拉病毒病疫情,中国人民解放军援利医疗队在利比里亚建立并独立运营了埃博拉诊疗中心。中心严格按照传染病医院的防护要求和标准,设计科学合理的布局流程,实现有效的感染防控。详细说明了中国埃博拉诊疗中心的布局与流程设计,归纳阐述其特点,并对做好布局流程应把握的几个重点问题进行了探讨。     

Community-Centered Responses to Ebola in Urban Liberia: The View from Below

BackgroundThe West African Ebola epidemic has demonstrated that the existing range of medical and epidemiological responses to emerging disease outbreaks is insufficient, especially in post-conflict contexts with exceedingly poor healthcare infrastructures. In this context, community-based responses have proven vital for containing Ebola virus disease (EVD) and shifting the epidemic curve. Despite a surge in interest in local innovations that effectively contained the epidemic, the mechanisms for community-based response remain unclear. This study provides baseline information on community-based epidemic control priorities and identifies innovative local strategies for containing EVD in Liberia.Conclusions/SignificanceLocal communities’ strategies and recommendations give insight into how urban Liberian communities contained the EVD outbreak while navigating the systemic failures of the initial state and international response. Communities in urban Liberia adapted to the epidemic using multiple coping strategies. In the absence of health, infrastructural and material supports, local people engaged in self-reliance in order to contain the epidemic at the micro-social level. These innovations were regarded as necessary, but as less desirable than a well-supported health-systems based response; and were seen as involving considerable individual, social, and public health costs, including heightened vulnerability to infection.     

Human activities link fruit bat presence to Ebola virus disease outbreaks

1. A significant link between forest loss and fragmentation and outbreaks of Ebola virus disease (EVD) in humans has been documented. Deforestation may alter the natural circulation of viruses and change the composition, abundance, behaviour and possibly viral exposure of reservoir species. This in turn might increase contact between infected animals and humans.
2. Fruit bats of the family Pteropodidae have been suspected as reservoirs of the Ebola virus. At present, the only evidence associating fruit bats with EVD is the presence of seropositive individuals in eight species and polymerase chain reaction-positive individuals in three of these.
3. Our study investigates whether human activities can increase African fruit bat geographical ranges and whether this influence overlaps geographically with EVD outbreaks that, in turn, are favoured by deforestation.
4. We use species observation records for the 20 fruit bat species found in favourable areas for the Ebola virus to determine factors affecting the bats' range inside the predicted Ebola virus area. We do this by employing a hypothetico-deductive approach based on favourability modelling.
5. We show that the range of some fruit bat species is linked to human activities within the favourable areas for the Ebola virus. More specifically, the areas where human activities favour the presence of five fruit bat species overlap with the areas where EVD outbreaks in humans were themselves favoured by deforestation. These five species are as follows: Eidolon helvum, Epomops franqueti, Megaloglossus woermanni, Micropteropus pusillus and Rousettus aegyptiacus. Of these five, all but Megaloglossus woermanni have recorded seropositive individuals. For the remaining 15 bat species, we found no biogeographical support for the hypothesis that positive human influence on fruit bats could be associated with EVD outbreaks in deforested areas within the tropical forest biome in West and Central Africa.
6. Our work is a useful first step allowing further investigation of the networks and pathways that may lead to an EVD outbreak. The modelling framework we employ here can be used for other emerging infectious diseases.

     

A general model for stochastic SIR epidemics with two levels of mixing

This paper is concerned with a general stochastic model for susceptible→infective→removed epidemics, among a closed finite population, in which during its infectious period a typical infective makes both local and global contacts. Each local contact of a given infective is with an individual chosen independently according to a contact distribution ‘centred’ on that infective, and each global contact is with an individual chosen independently and uniformly from the whole population. The asymptotic situation in which the local contact distribution remains fixed as the population becomes large is considered. The concepts of local infectious clump and local susceptibility set are used to develop a unified approach to the threshold behaviour of this class of epidemic models. In particular, a threshold parameter R_* governing whether or not global epidemics can occur, the probability that a global epidemic occurs and the mean proportion of initial susceptibles ultimately infected by a global epidemic are all determined. The theory is specialised to (i) the households model, in which the population is partitioned into households and local contacts are chosen uniformly within an infective’s household; (ii) the overlapping groups model, in which the population is partitioned in several ways, with local uniform mixing within the elements of the partitions; and (iii) the great circle model, in which individuals are equally spaced on a circle and local contacts are nearest-neighbour.     

Evaluating Subcriticality during the Ebola Epidemic in West Africa

The 2014–2015 Ebola outbreak is the largest and most widespread to date. In order to estimate ongoing transmission in the affected countries, we estimated the weekly average number of secondary cases caused by one individual infected with Ebola throughout the infectious period for each affected West African country using a stochastic hidden Markov model fitted to case data from the World Health Organization. If the average number of infections caused by one Ebola infection is less than 1.0, the epidemic is subcritical and cannot sustain itself. The epidemics in Liberia and Sierra Leone have approached subcriticality at some point during the epidemic; the epidemic in Guinea is ongoing with no evidence that it is subcritical. Response efforts to control the epidemic should continue in order to eliminate Ebola cases in West Africa.     

Predicting and Evaluating the Epidemic Trend of Ebola Virus Disease in the 2014-2015 Outbreak and the Effects of Intervention Measures

We constructed dynamic Ebola virus disease (EVD) transmission models to predict epidemic trends and evaluate intervention measure efficacy following the 2014 EVD epidemic in West Africa. We estimated the effective vaccination rate for the population, with basic reproduction number (R₀) as the intermediate variable. Periodic EVD fluctuation was analyzed by solving a Jacobian matrix of differential equations based on a SIR (susceptible, infective, and removed) model. A comprehensive compartment model was constructed to fit and predict EVD transmission patterns, and to evaluate the effects of control and prevention measures. Effective EVD vaccination rates were estimated to be 42% (31–50%), 45% (42–48%), and 51% (44–56%) among susceptible individuals in Guinea, Liberia and Sierra Leone, respectively. In the absence of control measures, there would be rapid mortality in these three countries, and an EVD epidemic would be likely recur in 2035, and then again 8~9 years later. Oscillation intervals would shorten and outbreak severity would decrease until the periodicity reached ~5.3 years. Measures that reduced the spread of EVD included: early diagnosis, treatment in isolation, isolating/monitoring close contacts, timely corpse removal, post-recovery condom use, and preventing or quarantining imported cases. EVD may re-emerge within two decades without control and prevention measures. Mass vaccination campaigns and control and prevention measures should be instituted to prevent future EVD epidemics.     

External Quality Assessment of Molecular Detection of Ebola Virus in China

In 2014, Ebola hemorrhagic fever broke out in West Africa. As contact between China and West Africa is frequent, the possibility that Ebola virus would enter China was high. Thus, an external assessment of the quality of Ebola virus detection was organized by the National Center for Clinical Laboratories in China. Virus-like particles encapsulating known sequences of epidemic strains of Ebola virus from 2014 were prepared as positive quality controls. The sample panel, which was composed of seven positive and three negative samples, was dispatched to 19 laboratories participating in this assessment of Ebola virus detection. Accurate detection was reported at 14 of the 19 participating laboratories, with a sensitivity of 91.43% and a specificity of 100%. Four participants (21.05%) reported false-negative results and were classified as “acceptable.” One participant (5.26%) did not detect any positive samples and was thus classified as “improvable.” Based on the results returned, the ability to detect weakly positive Ebola specimens should be improved. Furthermore, commercial assays and the standard primers offered by the Chinese Centers for Disease Control and Prevention were found to be most accurate and dependable for Ebola detection. A two-target detection approach is recommended for Ebola screening; this approach could reduce the probability of false-negative results. Additionally, standardization of operations and punctual adjustment of instruments are necessary for the control and prevention of Ebola virus.     

An SIR epidemic model with partial temporary immunity modeled with delay

The SIR epidemic model for disease dynamics considers recovered individuals to be permanently immune, while the SIS epidemic model considers recovered individuals to be immediately resusceptible. We study the case of temporary immunity in an SIR-based model with delayed coupling between the susceptible and removed classes, which results in a coupled set of delay differential equations. We find conditions for which the endemic steady state becomes unstable to periodic outbreaks. We then use analytical and numerical bifurcation analysis to describe how the severity and period of the outbreaks depend on the model parameters.      

Estimation of the Exposure of the UK Population to the Bovine Spongiform Encephalopathy Agent through Dietary Intake During the Period 1980 to 1996

Although the incidence of variant Creutzfeldt-Jakob disease (vCJD) has declined to 1 since 2012 in the UK, uncertainty remains regarding possible future cases and the size of the subclinical population that may cause secondary transmission of the disease through blood transfusion. Estimating the number of individuals who were exposed to the bovine spongiform encephalopathy (BSE) infectious agent and may be susceptible to vCJD will help to clarify related public health concerns and plan strategies. In this paper, we explore this estimate by describing the probability of potential exposure due to dietary intake throughout the BSE epidemic period from 1980 to 1996 as a stochastic Poisson process. We estimate the age- and gender-specific exposure intensities in food categories of beef and beef-containing dishes, burgers and kebabs, pies, and sausages, separating the two periods of 1980–1989 and 1990–1996 due to the specified bovine offal legislation of 1989. The estimated total number of (living) exposed individuals during each period is 5,089,027 (95% confidence interval [CI] 4,514,963–6,410,317), which was obtained by multiplying the population size of different birth cohorts by the probability of exposure via dietary intake and the probability of survival until the end of 2013. The estimated number is approximately doubled, assuming a contamination rate of . Among those individuals estimated, 31,855 (95% CI 26,849–42,541) are susceptible to infection. We also examined the threshold hypothesis by fitting an extreme-value distribution to the estimated infectious dose of the exposed individuals and obtained a threshold estimate of 13.7 bID₅₀ (95% CI 6.6–26.2 bID₅₀) (Weibull). The results provide useful information on potential carriers of prion disease who may pose a threat of infection via blood transfusion and thus provide insight into the likelihood of new incidents of vCJD occurring in the future.     

Heterogeneity of Rift Valley fever virus transmission potential across livestock hosts,quantified through a model-based analysis of host viral load and vector infection

Quantifying the variation of pathogens’ life history traits in multiple host systems is crucial to understand their transmission dynamics. It is particularly important for arthropod-borne viruses (arboviruses), which are prone to infecting several species of vertebrate hosts. Here, we focus on how host-pathogen interactions determine the ability of host species to transmit a virus to susceptible vectors upon a potentially infectious contact. Rift Valley fever (RVF) is a viral, vector-borne, zoonotic disease, chosen as a case study. The relative contributions of livestock species to RVFV transmission has not been previously quantified. To estimate their potential to transmit the virus over the course of their infection, we 1) fitted a within-host model to viral RNA and infectious virus measures, obtained daily from infected lambs, calves, and young goats, 2) estimated the relationship between vertebrate host infectious titers and probability to infect mosquitoes, and 3) estimated the net infectiousness of each host species over the duration of their infectious periods, taking into account different survival outcomes for lambs. Our results indicate that the efficiency of viral replication, along with the lifespan of infectious particles, could be sources of heterogeneity between hosts. Given available data on RVFV competent vectors, we found that, for similar infectious titers, infection rates in the Aedes genus were on average higher than in the Culex genus. Consequently, for Aedes-mediated infections, we estimated the net infectiousness of lambs to be 2.93 (median) and 3.65 times higher than that of calves and goats, respectively. In lambs, we estimated the overall infectiousness to be 1.93 times higher in individuals which eventually died from the infection than in those recovering. Beyond infectiousness, the relative contributions of host species to transmission depend on local ecological factors, including relative abundances and vector host-feeding preferences. Quantifying these contributions will ultimately help design efficient, targeted, surveillance and vaccination strategies.     

Variational data assimilation with epidemic models

Mathematical modelling is playing an increasing role in developing an understanding of the dynamics of communicable disease and assisting the construction and implementation of intervention strategies. The threat of novel emergent pathogens in human and animal hosts implies the requirement for methods that can robustly estimate epidemiological parameters and provide forecasts. Here, a technique called variational data assimilation is introduced as a means of optimally melding dynamic epidemic models with epidemiological observations and data to provide forecasts and parameter estimates. Using data from a simulated epidemic process the method is used to estimate the start time of an epidemic, to provide a forecast of future epidemic behaviour and estimate the basic reproductive ratio. A feature of the method is that it uses a basic continuous-time SIR model, which is often the first point of departure for epidemiological modelling during the early stages of an outbreak. The method is illustrated by application to data gathered during an outbreak of influenza in a school environment.     

Evaluating the influence of epidemiological parameters and host ecology on the spread of phocine distemper virus through populations of harbour seals

Background

Outbreaks of phocine distemper virus (PDV) in Europe during 1988 and 2002 were responsible for the death of around 23,000 and 30,000 harbour seals, respectively. These epidemics, particularly the one in 2002, provided an unusual opportunity to estimate epidemic parameters for a wildlife disease. There were marked regional differences in the values of some parameters both within and between epidemics.

Methodology and Principal Findings

We used an individual-based model of seal movement that allowed us to incorporate realistic representations of space, time and animal behaviour into a traditional epidemiological modelling framework. We explored the potential influence of a range of ecological (foraging trip duration, time of epidemic onset, population size) and epidemiological (length of infectious period, contact rate between infectious and susceptible individuals, case mortality) parameters on four readily-measurable epidemic characteristics (number of dead individuals, duration of epidemic, peak mortality date and prevalence) and on the probability that an epidemic would occur in a particular region. We analysed the outputs as if they were the results of a series of virtual experiments, using Generalised Linear Modelling. All six variables had a significant effect on the probability that an epidemic would be recognised as an unusual mortality event by human observers.

Conclusions

Regional and temporal variation in contact rate was the most likely cause of the observed differences between the two epidemics. This variation could be a consequence of differences in the way individuals divide their time between land and sea at different times of the year.     

Optimizing Real-Time Vaccine Allocation in a Stochastic SIR Model

Real-time vaccination following an outbreak can effectively mitigate the damage caused by an infectious disease. However, in many cases, available resources are insufficient to vaccinate the entire at-risk population, logistics result in delayed vaccine deployment, and the interaction between members of different cities facilitates a wide spatial spread of infection. Limited vaccine, time delays, and interaction (or coupling) of cities lead to tradeoffs that impact the overall magnitude of the epidemic. These tradeoffs mandate investigation of optimal strategies that minimize the severity of the epidemic by prioritizing allocation of vaccine to specific subpopulations. We use an SIR model to describe the disease dynamics of an epidemic which breaks out in one city and spreads to another. We solve a master equation to determine the resulting probability distribution of the final epidemic size. We then identify tradeoffs between vaccine, time delay, and coupling, and we determine the optimal vaccination protocols resulting from these tradeoffs.     

Ebola in great apes – current knowledge,possibilities for vaccination,and implications for conservation and human health

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Dynamical behaviour of epidemiological models with sub-optimal immunity and nonlinear incidence

In this paper we analyze the dynamics of two families of epidemiological models which correspond to transitions from the SIR (susceptible-infectious-resistant) to the SIS (susceptible-infectious-susceptible) frameworks. In these models we assume that the force of infection is a nonlinear function of density of infectious individuals, I. Conditions for the existence of backwards bifurcations, oscillations and Bogdanov-Takens points are given.