Nowcasting the Spread of Chikungunya Virus in the Americas

Background

In December 2013, the first locally-acquired chikungunya virus (CHIKV) infections in the Americas were reported in the Caribbean. As of May 16, 55,992 cases had been reported and the outbreak was still spreading. Identification of newly affected locations is paramount to intervention activities, but challenging due to limitations of current data on the outbreak and on CHIKV transmission. We developed models to make probabilistic predictions of spread based on current data considering these limitations.

Methods and Findings

Branching process models capturing travel patterns, local infection prevalence, climate dependent transmission factors, and associated uncertainty estimates were developed to predict probable locations for the arrival of CHIKV-infected travelers and for the initiation of local transmission. Many international cities and areas close to where transmission has already occurred were likely to have received infected travelers. Of the ten locations predicted to be the most likely locations for introduced CHIKV transmission in the first four months of the outbreak, eight had reported local cases by the end of April. Eight additional locations were likely to have had introduction leading to local transmission in April, but with substantial uncertainty.

Conclusions

Branching process models can characterize the risk of CHIKV introduction and spread during the ongoing outbreak. Local transmission of CHIKV is currently likely in several Caribbean locations and possible, though uncertain, for other locations in the continental United States, Central America, and South America. This modeling framework may also be useful for other outbreaks where the risk of pathogen spread over heterogeneous transportation networks must be rapidly assessed on the basis of limited information.     

A Mathematical Model of Chikungunya Dynamics and Control: The Major Epidemic on Réunion Island

Chikungunya is a re-emerging arboviral disease transmitted by Aedes spp. mosquitoes. Although principally endemic to Africa and Asia, recent outbreaks have occurred in Europe following introductions by returning travellers. A particularly large outbreak occurred on Réunion Island in 2006, the published data from which forms the basis of the current study. A simple, deterministic mathematical model of the transmission of the virus between humans and mosquitoes was constructed and parameterised with the up-to-date literature on infection biology. The model is fitted to the large Réunion epidemic, resulting in an estimate of 4.1 for the type reproduction number of chikungunya. Although simplistic, the model provided a close approximation of both the peak incidence of the outbreak and the final epidemic size. Sensitivity analysis using Monte Carlo simulation demonstrated the strong influence that both the latent period of infection in humans and the pre-patent period have on these two epidemiological outcomes. We show why separating these variables, which are epidemiologically distinct in chikungunya infections, is not only necessary for accurate model fitting but also important in informing control.     

Determining travel fluxes in epidemic areas

Infectious diseases attack humans from time to time and threaten the lives and survival of people all around the world. An important strategy to prevent the spatial spread of infectious diseases is to restrict population travel. With the reduction of the epidemic situation, when and where travel restrictions can be lifted, and how to organize orderly movement patterns become critical and fall within the scope of this study. We define a novel diffusion distance derived from the estimated mobility network, based on which we provide a general model to describe the spatiotemporal spread of infectious diseases with a random diffusion process and a deterministic drift process of the population. We consequently develop a multi-source data fusion method to determine the population flow in epidemic areas. In this method, we first select available subregions in epidemic areas, and then provide solutions to initiate new travel flux among these subregions. To verify our model and method, we analyze the multi-source data from mainland China and obtain a new travel flux triggering scheme in the selected 29 cities with the most active population movements in mainland China. The testable predictions in these selected cities show that reopening the borders in accordance with our proposed travel flux will not cause a second outbreak of COVID-19 in these cities. The finding provides a methodology of re-triggering travel flux during the weakening spread stage of the epidemic.     

Waning immunity and sub-clinical infection in an epidemic model: implications for pertussis in The Netherlands

In The Netherlands, an epidemic outbreak of pertussis took place in 1996-1997. Understanding of the causes of the epidemic is hampered by the fact that many cases of infection with Bordetella pertussis go by unnoticed, and by the fact that immunity against infection does not last lifelong. Motivated by these observations, we develop and analyze an age-structured epidemic model that takes these factors into account. A distinction is made between infection in immunologically naive individuals, and infection in individuals whose immune system has been primed before by infection or vaccination. While the former often lead to severe symptoms and thus are more often diagnosed and notified, the latter are largely sub-clinical. The main questions are: (1) to what extent do sub-clinical infections contribute to the circulation of B. pertussis; and (2) what might be the causes for the recent epidemic? To answer these questions, we first present a new method to estimate the force of infection from notification data. The method is applied to the 1988-1995 case notification data from The Netherlands. Estimates of the force of infection vary greatly, depending on the rate at which immunity is lost, and on the fraction of sub-clinical infections. For the 1988-1995 period, our analysis indicates that if immunity is lost at a small rate and if a majority of infections is sub-clinical, the contribution of infection in adults to the transmission process cannot be neglected. Our results furthermore indicate that a decrease in the duration of protection after vaccination due to a change in the pathogen is the most likely factor to account for the 1996-1997 epidemic.     

Disease Prevention versus Data Privacy: Using Landcover Maps to Inform Spatial Epidemic Models

The availability of epidemiological data in the early stages of an outbreak of an infectious disease is vital for modelers to make accurate predictions regarding the likely spread of disease and preferred intervention strategies. However, in some countries, the necessary demographic data are only available at an aggregate scale. We investigated the ability of models of livestock infectious diseases to predict epidemic spread and obtain optimal control policies in the event of imperfect, aggregated data. Taking a geographic information approach, we used land cover data to predict UK farm locations and investigated the influence of using these synthetic location data sets upon epidemiological predictions in the event of an outbreak of foot-and-mouth disease. When broadly classified land cover data were used to create synthetic farm locations, model predictions deviated significantly from those simulated on true data. However, when more resolved subclass land use data were used, moderate to highly accurate predictions of epidemic size, duration and optimal vaccination and ring culling strategies were obtained. This suggests that a geographic information approach may be useful where individual farm-level data are not available, to allow predictive analyses to be carried out regarding the likely spread of disease. This method can also be used for contingency planning in collaboration with policy makers to determine preferred control strategies in the event of a future outbreak of infectious disease in livestock.     

Theory versus data: how to calculate R0?

To predict the potential severity of outbreaks of infectious diseases such as SARS, HIV, TB and smallpox, a summary parameter, the basic reproduction number R(0), is generally calculated from a population-level model. R(0) specifies the average number of secondary infections caused by one infected individual during his/her entire infectious period at the start of an outbreak. R(0) is used to assess the severity of the outbreak, as well as the strength of the medical and/or behavioral interventions necessary for control. Conventionally, it is assumed that if R(0)>1 the outbreak generates an epidemic, and if R(0)<1 the outbreak becomes extinct. Here, we use computational and analytical methods to calculate the average number of secondary infections and to show that it does not necessarily represent an epidemic threshold parameter (as it has been generally assumed). Previously we have constructed a new type of individual-level model (ILM) and linked it with a population-level model. Our ILM generates the same temporal incidence and prevalence patterns as the population-level model; we use our ILM to directly calculate the average number of secondary infections (i.e., R(0)). Surprisingly, we find that this value of R(0) calculated from the ILM is very different from the epidemic threshold calculated from the population-level model. This occurs because many different individual-level processes can generate the same incidence and prevalence patterns. We show that obtaining R(0) from empirical contact tracing data collected by epidemiologists and using this R(0) as a threshold parameter for a population-level model could produce extremely misleading estimates of the infectiousness of the pathogen, the severity of an outbreak, and the strength of the medical and/or behavioral interventions necessary for control.     

A stochastic model for extinction and recurrence of epidemics: estimation and inference for measles outbreaks

Epidemic dynamics pose a great challenge to stochastic modelling because chance events are major determinants of the size and the timing of the outbreak. Reintroduction of the disease through contact with infected individuals from other areas is an important latent stochastic variable. In this study we model these stochastic processes to explain extinction and recurrence of epidemics observed in measles. We develop estimating functions for such a model and apply the methodology to temporal case counts of measles in 60 cities in England and Wales. In order to estimate the unobserved spatial contact process we suggest a method based on stochastic simulation and marginal densities. The estimation results show that it is possible to consider a unified model for the UK cities where the parameters depend on the city size. Stochastic realizations from the dynamic model realistically capture the transitions from an endemic cyclic pattern in large populations to irregular epidemic outbreaks in small human host populations.     

Analysis of a stochastic SIR epidemic on a random network incorporating household structure

This paper is concerned with a stochastic SIR (susceptible → infective → removed) model for the spread of an epidemic amongst a population of individuals, with a random network of social contacts, that is also partitioned into households. The behaviour of the model as the population size tends to infinity in an appropriate fashion is investigated. A threshold parameter which determines whether or not an epidemic with few initial infectives can become established and lead to a major outbreak is obtained, as are the probability that a major outbreak occurs and the expected proportion of the population that are ultimately infected by such an outbreak, together with methods for calculating these quantities. Monte Carlo simulations demonstrate that these asymptotic quantities accurately reflect the behaviour of finite populations, even for only moderately sized finite populations. The model is compared and contrasted with related models previously studied in the literature. The effects of the amount of clustering present in the overall population structure and the infectious period distribution on the outcomes of the model are also explored.     

The Kermack-McKendrick epidemic model revisited

The Kermack-McKendrick epidemic model of 1927 is an age of infection model, that is, a model in which the infectivity of an individual depends on the time since the individual became infective. A special case, which is formulated as a two-dimensional system of ordinary differential ordinary differential equations, has often been called the Kermack-McKendrick model. One of the products of the SARS epidemic of 2002-2003 was a variety of epidemic models including general contact rates, quarantine, and isolation. These models can be viewed as age of infection epidemic models and analyzed using the approach of the full Kermack-McKendrick model. All these models share the basic properties that there is a threshold between disappearance of the disease and an epidemic outbreak, and that an epidemic will die out without infecting the entire population.     

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.     

Learning from history, predicting the future: the UK Dutch elm disease outbreak in relation to contemporary tree disease threats

Expanding international trade and increased transportation are heavily implicated in the growing threat posed by invasive pathogens to biodiversity and landscapes. With trees and woodland in the UK now facing threats from a number of disease systems, this paper looks to historical experience with the Dutch elm disease (DED) epidemic of the 1970s to see what can be learned about an outbreak and attempts to prevent, manage and control it. The paper draws on an interdisciplinary investigation into the history, biology and policy of the epidemic. It presents a reconstruction based on a spatial modelling exercise underpinned by archival research and interviews with individuals involved in the attempted management of the epidemic at the time. The paper explores what, if anything, might have been done to contain the outbreak and discusses the wider lessons for plant protection. Reading across to present-day biosecurity concerns, the paper looks at the current outbreak of ramorum blight in the UK and presents an analysis of the unfolding epidemiology and policy of this more recent, and potentially very serious, disease outbreak. The paper concludes by reflecting on the continuing contemporary relevance of the DED experience at an important juncture in the evolution of plant protection policy.     

Design, modeling, and analysis of a feedstock logistics system

Given the location of a bio-energy plant for the conversion of biomass to bio-energy, a feedstock logistics system that relies on the use of satellite storage locations (SSLs) for temporary storage and loading of round bales is proposed. Three equipment systems are considered for handling biomass at the SSLs, and they are either placed permanently or are mobile and thereby travel from one SSL to another. A mathematical programming-based approach is utilized to determine SSLs and equipment routes in order to minimize the total cost. The use of a Side-loading Rack System results in average savings of 21.3% over a Densification System while a Rear-loading Rack System is more expensive to operate than either of the other equipment systems. The utilization of mobile equipment results in average savings of 14.8% over the equipment placed permanently. Furthermore, the Densification System is not justifiable for transportation distances less than 81 km.     

新型冠状病毒病(COVID-19)研究进展

2019年12月,湖北省武汉市暴发了一种由新型冠状病毒引起的肺炎(COVID-19)随后蔓延到中国所有省区以及多个国家和地区,WHO宣布其为全球关注的突发公共卫生事件。及时了解和表征该病毒对抗击疫情至关重要。通过收集和梳理该疫情暴发之后2个月内全球多领域研究人员关于COVID-19的论文,发现这些研究主要集中在溯源分析、检测手段、病患治疗、临床表现、药物研发、致病机理、传播途径、流行特征等方面。该冠状病毒与蝙蝠冠状病毒以及穿山甲冠状病毒相关,其利用与SARS-CoV相同的人受体ACE2,感染途径证实为呼吸系统和消化系统。该病毒具有人际传播能力,并且出现无症状传播。COVID-19确诊病例多数与武汉有关,大多数为轻症,年老者病死率较高。快速灵敏核酸检测通常作为确诊依据,目前已经筛选出有价值的候选药物如瑞德西韦进行临床试验。中国采取的旅行禁令和隔离等干预措施有效减轻了疫情蔓延。     

Nonhomogeneous birth and death models for epidemic outbreak data

In this paper, generalized nonlinear models are proposed in order to incorporate the following considerations in modeling an epidemic disease outbreak statistically. (1) The dependence of the data is handled with a nonhomogeneous death or a nonhomogeneous birth process. (2) The first stage of the outbreak is described with an epidemic susceptibles-infectives-removed (SIR) model. Soon the control measures taken will dominate the process. These measures are in addition to the natural epidemic removal process. The prevalence is related to the censored infection times in such a way that the distribution function and thus the survival function satisfy approximately the first equation of the SIR model. This leads in a natural way to the Burr family of distributions. (3) The nonhomogeneous birth process handles the fact that in practice, with some delay, infecteds are registered, but not susceptibles. (4) Finally, the ending of the epidemic caused by the measures taken is incorporated through a modification of the survival function with a final-size parameter, in the same way as is done in long-term survival models. These models are applied to three outbreaks: The Dutch classical swine fever outbreak from 1997 to 1998, the foot- and-mouth disease outbreak in Great Britain from 2001, and the Dutch avian influenza (H7N7) outbreak from 2003.     

Stochastic model of an influenza epidemic with drug resistance

A continuous-time Markov chain (CTMC) model is formulated for an influenza epidemic with drug resistance. This stochastic model is based on an influenza epidemic model, expressed in terms of a system of ordinary differential equations (ODE), developed by Stilianakis, N.I., Perelson, A.S., Hayden, F.G., [1998. Emergence of drug resistance during an influenza epidemic: insights from a mathematical model. J. Inf. Dis. 177, 863-873]. Three different treatments-chemoprophylaxis, treatment after exposure but before symptoms, and treatment after symptoms appear, are considered. The basic reproduction number, R(0), is calculated for the deterministic-model under different treatment strategies. It is shown that chemoprophylaxis always reduces the basic reproduction number. In addition, numerical simulations illustrate that the basic reproduction number is generally reduced with realistic treatment rates. Comparisons are made among the different models and the different treatment strategies with respect to the number of infected individuals during an outbreak. The final size distribution is computed for the CTMC model and, in some cases, it is shown to have a bimodal distribution corresponding to two situations: when there is no outbreak and when an outbreak occurs. Given an outbreak occurs, the total number of cases for the CTMC model is in good agreement with the ODE model. The greatest number of drug resistant cases occurs if treatment is delayed or if only symptomatic individuals are treated.     

Transition from growth to decay of an epidemic due to lockdown

We study the transition of an epidemic from growth phase to decay of the active infections in a population when lockdown health measures are introduced to reduce the probability of disease transmission. Although in the case of uniform lockdown, a simple compartmental model would indicate instantaneous transition to decay of the epidemic, this is not the case when partially isolated active clusters remain with the potential to create a series of small outbreaks. We model this using the Gillespie stochastic simulation algorithm based on a connected set of stochastic susceptible-infected-removed/recovered networks representing the locked-down majority population (in which the reproduction number is less than 1) weakly coupled to a large set of small clusters in which the infection may propagate. We find that the presence of such active clusters can lead to slower than expected decay of the epidemic and significantly delayed onset of the decay phase. We study the relative contributions of these changes, caused by the active clusters within the population, to the additional total infected population. We also demonstrate that limiting the size of the inevitable active clusters can be efficient in reducing their impact on the overall size of the epidemic outbreak. The deceleration of the decay phase becomes apparent when the active clusters form at least 5% of the population.     

人口流动性对感染性疾病扩散与传播的影响

研究人口流动性对具有斑快结构的感染性疾病传播与扩散的影响,讨论了具有斑块结构感染性疾病SIS模型的全局稳定性,得到了该模型基本再生数的倍增效应．     

A Model for a Chikungunya Outbreak in a Rural Cambodian Setting: Implications for Disease Control in Uninfected Areas

Following almost 30 years of relative silence, chikungunya fever reemerged in Kenya in 2004. It subsequently spread to the islands of the Indian Ocean, reaching Southeast Asia in 2006. The virus was first detected in Cambodia in 2011 and a large outbreak occurred in the village of Trapeang Roka Kampong Speu Province in March 2012, in which 44% of the villagers had a recent infection biologically confirmed. The epidemic curve was constructed from the number of biologically-confirmed CHIKV cases per day determined from the date of fever onset, which was self-reported during a data collection campaign conducted in the village after the outbreak. All individuals participating in the campaign had infections confirmed by laboratory analysis, allowing for the identification of asymptomatic cases and those with an unreported date of fever onset. We develop a stochastic model explicitly including such cases, all of whom do not appear on the epidemic curve. We estimate the basic reproduction number of the outbreak to be 6.46 (95% C.I. [6.24, 6.78]). We show that this estimate is particularly sensitive to changes in the biting rate and mosquito longevity. Our model also indicates that the infection was more widespread within the population on the reported epidemic start date. We show that the exclusion of asymptomatic cases and cases with undocumented onset dates can lead to an underestimation of the reproduction number which, in turn, could negatively impact control strategies implemented by public health authorities. We highlight the need for properly documenting newly emerging pathogens in immunologically naive populations and the importance of identifying the route of disease introduction.