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.     

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.     

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.     

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.     

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.     

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.     

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．     

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.     

20世纪以来流感在人群中的流行特征

自1918年西班牙流感爆发以来,流感病毒已经导致了五次人群中的大规模流行,除西班牙流感外,还有1957年由H2N2病毒引发的亚洲流感、1968年由H3N2病毒引发的香港流感、以及1977年的俄罗斯流感和2009年的墨西哥流感。而西班牙流感、俄罗斯流感和墨西哥流感三次流感的大流行均是由H1N1病毒毒株引起。此外,许多局部人群中的小规模流行与感染也被证实是流感病毒直接经人与人之间传播所导致。本文将主要对五次人流感的大规模爆发以及具有代表性的局部流行事件的流行病学特点以及病毒序列特征作一个小结。     

A multi-structured epidemic problem with direct and indirect transmission in heterogeneous environments

In this work, we analyse a deterministic epidemic mathematical model motivated by the propagation of a hantavirus (Puumala hantavirus) within a bank vole population (Clethrionomys glareolus). The host population is split into juvenile and adult individuals. A heterogeneous spatial chronological age and infection age structure is considered, and also indirect transmission via the environment. Maturation rates for juvenile individuals are adult density-dependent. For the reaction–diffusion systems with age structures derived, we give global existence, uniqueness and global boundedness results. A model with transmission to humans is also studied here.     

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     

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。     

Simple Epidemic Models with Positive Latent Period

This paper deals with two types of simple epidemic models, namely, deterministic and stochastic wherein the latent period is assumed to be positive. In the deterministic epidemic model, the distributions of susceptibles, inactive infectives, active infectives and that of epidemic curve which gives the rate at which new infections take place have been obtained. The expression for the expected time of the entire epidemic has been derived. Also the partial differential equation for the moment generating function of the proportion of susceptibles in the population is established. In the end, we have studied a stochastic approach of the system.     

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.