Stochastic epidemic models: A survey

This paper is a survey paper on stochastic epidemic models. A simple stochastic epidemic model is defined and exact and asymptotic (relying on a large community) properties are presented. The purpose of modelling is illustrated by studying effects of vaccination and also in terms of inference procedures for important parameters, such as the basic reproduction number and the critical vaccination coverage. Several generalizations towards realism, e.g. multitype and household epidemic models, are also presented, as is a model for endemic diseases.     

Expression of neutralizing epitope of porcine epidemic diarrhea virus in potato plants

Transgenic plants expressing recombinant proteins from pathogenic microorganisms provide an inexpensive edible vaccine for induction of local immunity. A neutralizing epitope of porcine epidemic diarrhea virus (PEDV) gene containing SEKDEL was expressed in potato using Agrobacterium-mediated transformation system. Putative transgenic plants were regenerated, and genomic PCR confirmed the presence of PEDV epitope gene in the potato plants. Based on the ELISA results, epitope of PEDV protein made up approximately 0.1% of the total soluble tuber protein.     

A sequential test for assessing the effectiveness of response strategies during an emerging epidemic

In epidemiology, the fatality rate is an important indicator of disease severity and has been used to evaluate the effects of new treatments. During an emerging epidemic with limited resources, monitoring the changes in fatality rate can also provide signals on the evaluation of government policies and healthcare quality, which helps to guide public health decision. A statistical test is developed in this paper to detect changes in fatality rate over time during the course of an emerging infectious disease. A major advantage of the proposed test is that it only requires the regularly reported numbers of deaths and recoveries, which meets the actual need as detailed surveillance data are hard to collect during the course of an emerging epidemic especially the deadly infectious diseases with large magnitude. In addition, with the sequential testing procedure, the effective measures can be detected at the earliest possible time to provide guidance to policymakers for swift action. Simulation studies showed that the proposed test performs well and is sensitive in picking up changes in the fatality rate. The test is applied to the 2014–2016 Ebola outbreak in Sierra Leone for illustration.     

The asymptotic final size distribution of reducible multitype Reed-Frost processes

The asymptotic final size distribution of a multitype Reed-Frost process, a chain-binomial model for the spread of infection in a finite, closed multitype population, is derived in the case of reducible contact pattern between types. The results are obtained using techniques developed for the irreducible case.     

On an interacting particle system modeling an epidemic

We consider an interacting particle system onZ ^dto model an epidemic. Each site ofZ ^dcan be in either one of three states: empty, healthy or infected. Healthy and infected individuals give birth at different rates to healthy individuals on empty sites. Healthy individuals get infected by infected individuals. Infected and healthy individuals die at different rates. We prove that in dimension 1 and with nearest-neighbor interactions the epidemic may persist forever if and only if the rate at which infected individuals give birth to healthy individuals is high enough. This is in sharp contrast with models analysed by Andjel and Schinazi (1994) and Sato et al. (1994) where infected individuals do not give birth. We also show that some results in the latter reference can be obtained easily and rigorously using probabilistic coupling to the contact process.     

湖南省实验动物中几种常见的人兽共患病监测

目的对2003年至2007年湖南省实验动物中沙门氏菌、汉坦病毒、仙台病毒、淋巴细胞脉络丛脑膜炎病毒、弓形虫病等几种常见的人兽共患病的流行病学进行调查。方法按《GB14922．2-2001》和《GB14922．1-2001》抽检动物。结果实验大、小鼠汉坦病毒（HV）和仙台病毒（Sendai）出现抗体阳性,实验小鼠淋巴细胞脉络丛脑膜炎病毒（LCM）出现抗体阳性,实验鼠沙门氏菌（Salmonella）检测结果阳性,实验大鼠和普通级兔弓形体（Toxoplasma）检测结果阳性。结论应加强对实验动物流行病学的监测。     

Epidemiologic interference of virus populations

Summary There are a few simulation studies for interference models in the literature but the present paper discusses an analytical model for the competition of two interfering virus populations in a community. The mathematical model consist of eight coupled differential equations which have up to four equilibrium points. Criteria for local stability are given.This paper has been read at the workshop on Nonlinear Models in Biology and Medicine, 23rd Biometric Colloquium, German Region of the Biometric Society, Nuremberg, March 1977     

Competitive exclusion and coexistence for pathogens in an epidemic model with variable population size

We study an SIR epidemic model with a variable host population size. We prove that if the model parameters satisfy certain inequalities then competition between n pathogens for a single host leads to exclusion of all pathogens except the one with the largest basic reproduction number. It is shown that a knowledge of the basic reproduction numbers is necessary but not sufficient for determining competitive exclusion. Numerical results illustrate that these inequalities are sufficient but not necessary for competitive exclusion to occur. In addition, an example is given which shows that if such inequalities are not satisfied then coexistence may occur.     

2006～2008年我院法定报告传染病疫情分析

目的了解鹰潭市人民医院法定传染病报告情况,分析其流行病学特点,为制定传染病防治对策及降低传染病的发生提供科学依据。方法对鹰潭市人民医院2006～2008年法定传染病疫情资料进行分析．结果共报告法定传染病19种,累计报告发病4170例,其中无甲类传染病报告。主要病种为感染性腹泻、肺结核、病毒性肝炎、流行性腮腺炎、菌痢,占报告总数的93．62％;死亡13例（5个病种）．结论肺结核、乙型肝炎、肠道传染病是今后传染病防治工作的重点和难点,应加大管理力度．做好传染病的预防和控制工作．     

Effect of Predators of Juvenile Rodents on the Spread of the Hantavirus Epidemic

Effects of predators of juvenile mice on the spread of the Hantavirus are analyzed in the context of a recently proposed model. Two critical values of the predation probability are identified. When the smaller of them is exceeded, the hantavirus infection vanishes without extinguishing the mice population. When the larger is exceeded, the entire mice population vanishes. These results suggest the possibility of control of the spread of the epidemic by introducing predators in areas of mice colonies in a suitable way so that such control does not kill all the mice but lowers the epidemic spread.     

A Contact-Network-Based Formulation of a Preferential Mixing Model

Heterogeneity in the number of potentially infectious contacts and connectivity correlations (“like attaches to like” i.e., assortatively mixed or “opposites attract” i.e., disassortatively mixed) have important implications for the value of the basic reproduction ratio R ₀ and final epidemic size. In this paper, we present a contact-network-based derivation of a simple differential equation model that accounts for preferential mixing based on the number of contacts. We show that results based on this model are in good qualitative agreement with results obtained from preferential mixing models used in the context of sexually transmitted diseases (STDs). This simple model can accommodate any mixing pattern ranging from completely disassortative to completely assortative and allows the derivation of a series of analytical results.     

Wildlife Trade and the Emergence of Infectious Diseases

Most recent emerging infectious diseases have been zoonotic in origin. It is our contention that one of the factors responsible for such emergence is the trade in wildlife and bushmeat in particular. This article considers the effect of increasing diversity in the species hunted on the probability of global epidemics such as SARS. In particular, we develop a mathematical model of the probability of such an outbreak in terms of the number of species hunted, the number of susceptibles, and the rate of contact. Hence, we postulate that local biodiversity loss and increasing rates of animal trafficking, and trade and transportation of animals to large cities—where there is a greater potential for person-to-person transmission—may increase the probability of such outbreaks dramatically.     

The HIV epidemic in China： history, response, and challenge

The first case of AIDS was reported in 1985 in China, but by the early 21st century, the government estimated that there were 840,000 citizens living with HIV/AIDS. The number is increasing rapidly. The major risk groups are injection drug users （IDUSs; 43%） and former plasma donors （27%）, but rates among heterosexual groups are rising rapidly. Sentinel surveillance was initiated in 1986, and now includes IDUs, men-who-have-sex-with-men, sexually transmitted disease clinic attendees, antenatal women, long-distance truck drivers, and sex workers. Although the government was slow to respond to the epidemic in the late 20th century, it has made a vigorous response in the early 21st century. Components of that response include implementation and evaluation of harm reduction programs for IDUs, education to increase knowledge and reduce stigma, treatment and social support for rural and poor HIV/AIDS patients, widespread testing, and increased funding for HIV/AIDS programs. International agencies have been generous in their support of the government initiatives. To successfully combat the epidemic, China needs to develop and train the necessary infrastructure to implement its intervention programs, particularly in the rural areas, to vigorously combat stigma and discrimination, support research especially in the universities and research institutions other than the China Centers for Disease Control, develop a system for efficient exchange of research and program information, and update legislation to reflect the current situation.     

Stochastic multitype epidemics in a community of households: estimation and form of optimal vaccination schemes

This paper treats a stochastic model for an SIR (susceptible-->infective-->removed) multitype household epidemic. The community is assumed to be closed, individuals are of different types and each individual belongs to a household. Previously obtained probabilistic and inferential results for the model are used to derive the optimal vaccination scheme. By this is meant the scheme that vaccinates the fewest among all vaccination schemes that reduce the threshold parameter below 1. This is done for the situation where all model parameters are known and also for the case where parameters are estimated from an outbreak in the community prior to vaccination. It is shown that the algorithm which chooses vaccines sequentially, at each step selecting the individual which reduces the threshold parameter the most, is not in general an optimal scheme. As a consequence, explicit characterisation of the optimal scheme is only possible in certain special cases. Two different types of vaccine responses, leaky and all-or-nothing, are considered and compared for the problems mentioned above. The methods are illustrated with some numerical examples.