• Title/Summary/Keyword: Susceptible-infectious-recovered Model

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Optimal Control Scheme for SEIR Model in Viral Communications (Viral 통신에서의 SEIR모델을 위한 최적제어 기법)

  • Radwan, Amr
    • Journal of the Korea Institute of Information and Communication Engineering
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    • v.20 no.8
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    • pp.1487-1493
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    • 2016
  • The susceptible, exposed, infectious, and recovered model (SEIR) is used extensively in the field of epidemiology. On the other hand, dissemination information among users through internet grows exponentially. This information spreading can be modeled as an epidemic. In this paper, we derive the mathematical model of SEIR in viral communication from the view of optimal control theory. Overall the methods based on classical calculus, In order to solve the optimal control problem, proved to be more efficient and accurate. According to Pontryagin's minimum principle (PMP) the Hamiltonian function must be optimized by the control variables at all points along the solution trajectory. We present our method based on the PMP and forward backward algorithm. In this algorithm, one should integrate forward in time for the state equations then integrate backward in time for the adjoint equations resulting from the optimality conditions. The problem is mathematically analyzed and numerically solved as well.

ANALYSIS OF AN SEIQRVS EPIDEMIC DYNAMICS FOR INFECTIOUS VIRAL DISEASE: QUARANTINE AS A CONTROL STRATEGY

  • RAKESH SINGH TOMAR;JOYDIP DHAR;AJAY KUMAR
    • Journal of applied mathematics & informatics
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    • v.41 no.1
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    • pp.107-121
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    • 2023
  • An epidemic infectious disease model consists of six compartments viz. Susceptible, Exposed, Infected, Quarantine, Recovered, and Virus with nonlinear saturation incidence rate is proposed to know the viral disease dynamics. There exist two biological equilibrium points for the model system. The system's local and global stability is done through Lyapunov's direct method about equilibrium points. The sensitivity analysis has been performed for the basic reproduction number and equilibrium points through the normalized forward sensitivity index. Sensitivity analysis shows that virus growth and quarantine rates are more sensitive parameters. In support of mathematical conclusions, numerical experimentation has been shown.

An Integrated Epidemiological and Economic Analysis of Vaccination against Highly Pathogenic Porcine Reproductive and Respiratory Syndrome (PRRS) in Thua Thien Hue Province, Vietnam

  • Zhang, Haifeng;Kono, Hiroichi;Kubota, Satoko
    • Asian-Australasian Journal of Animal Sciences
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    • v.27 no.10
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    • pp.1499-1512
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    • 2014
  • The purposes of this study are to assess pig farmers' preference for highly pathogenic porcine reproductive and respiratory syndrome (PRRS) vaccine, and estimate the cost and benefit of PRRS vaccination in Vietnam. This study employed an integrated epidemiological and economic analysis which combined susceptible-infectious-recovered (SIR) model, choice experiment (CE) and cost-benefit analysis (CBA) together. The result of SIR model showed the basic reproduction number ($R_0$) of PRRS transmission in this study is 1.3, consequently, the optimal vaccination percentage is 26%. The results of CE in this study indicate that Vietnam pig farmers are showing a high preference for the PRRS vaccine. However, their mean willingness to pay is lower than the potential cost of PRRS vaccine. It can be considered to be one of the reasons that the PRRS vaccination ratio is still low in Vietnam. The results of CBA specified from the whole society's point of view (Social perspective), the benefits of PRRS vaccination are 2.3 to 4.5 times larger than the costs. To support policy making for increasing the PRRS vaccination proportion, this study indicates two ways to increase the vaccination proportion: i) decrease vaccine price by providing a subsidy, ii) provide compensation of culling only for PRRS vaccinated pigs.

Modeling of transmission pathways on canine heartworm dynamics

  • Seo, Sat Byul
    • Korean Journal of Veterinary Research
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    • v.60 no.1
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    • pp.15-18
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    • 2020
  • Canine heartworm disease is a vector-borne disease that is transmitted from dog to dog by mosquitoes. It causes epidemics that disrupt the health environments of dogs and are burdensome for many dog owners. Recent trends of changing temperatures and weather conditions in South Korea may have an impact on the population of mosquitoes, and it affects the population of dogs at risk of heartworm infection. Mathematical modeling has become an important measure for analyzing the epidemiological characteristics of infectious diseases. However, canine heartworm infection transmission has not been reported yet through mathematical modeling. We develop a mathematical model of canine heartworm infection to predict the population of infected dogs depending on the vector (mosquito) population using a susceptible, exposed, infected, and recovered model. Simulation results show that after 1 year, 3,289 dogs out of 73,602 (about 4.5%) are exposed and 134 (about 0.2%) are infected. Only 0.2% of susceptible dogs become infected after 1 year. However, if all exposed dogs are maintained in the same circumstances without any treatment, then the number of infected subjects will increase over time. This may increase the possibility of other dogs, especially dogs that live outside, being infected.

THE DOMAIN OF ATTRACTION FOR A SEIR EPIDEMIC MODEL BASED ON SUM OF SQUARE OPTIMIZATION

  • Chen, Xiangyong;Li, Chunji;Lu, Jufang;Jing, Yuanwei
    • Bulletin of the Korean Mathematical Society
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    • v.49 no.3
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    • pp.517-528
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    • 2012
  • This paper is estimating the domain of attraction for a class of susceptible-exposed-infectious-recovered (SEIR) epidemic dynamic models by using sum of squares optimization. First, the stability is analyzed for the equilibriums of SEIR model, and the domain of attraction in the endemic equilibrium is estimated by using sum of squares optimization. Finally, a numerical example is examined.

A study of epidemic model using SEIR model (SEIR 모형을 이용한 전염병 모형 예측 연구)

  • Do, Mijin;Kim, Jongtae;Choi, Boseung
    • Journal of the Korean Data and Information Science Society
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    • v.28 no.2
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    • pp.297-307
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    • 2017
  • The epidemic model is used to model the spread of disease and to control the disease. In this research, we utilize SEIR model which is one of applications the SIR model that incorporates Exposed step to the model. The SEIR model assumes that a people in the susceptible contacted infected moves to the exposed period. After staying in the period, the infectee tends to sequentially proceed to the status of infected, recovered, and removed. This type of infection can be used for research in cases where there is a latency period after infectious disease. In this research, we collected respiratory infectious disease data for the Middle East Respiratory Syndrome Coronavirus (MERSCoV). Assuming that the spread of disease follows a stochastic process rather than a deterministic one, we utilized the Poisson process for the variation of infection and applied epidemic model to the stochastic chemical reaction model. Using observed pandemic data, we estimated three parameters in the SIER model; exposed rate, transmission rate, and recovery rate. After estimating the model, we applied the fitted model to the explanation of spread disease. Additionally, we include a process for generating the Exposed trajectory during the model estimation process due to the lack of the information of exact trajectory of Exposed.

Implementation of integrated monitoring system for trace and path prediction of infectious disease (전염병의 경로 추적 및 예측을 위한 통합 정보 시스템 구현)

  • Kim, Eungyeong;Lee, Seok;Byun, Young Tae;Lee, Hyuk-Jae;Lee, Taikjin
    • Journal of Internet Computing and Services
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    • v.14 no.5
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    • pp.69-76
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    • 2013
  • The incidence of globally infectious and pathogenic diseases such as H1N1 (swine flu) and Avian Influenza (AI) has recently increased. An infectious disease is a pathogen-caused disease, which can be passed from the infected person to the susceptible host. Pathogens of infectious diseases, which are bacillus, spirochaeta, rickettsia, virus, fungus, and parasite, etc., cause various symptoms such as respiratory disease, gastrointestinal disease, liver disease, and acute febrile illness. They can be spread through various means such as food, water, insect, breathing and contact with other persons. Recently, most countries around the world use a mathematical model to predict and prepare for the spread of infectious diseases. In a modern society, however, infectious diseases are spread in a fast and complicated manner because of rapid development of transportation (both ground and underground). Therefore, we do not have enough time to predict the fast spreading and complicated infectious diseases. Therefore, new system, which can prevent the spread of infectious diseases by predicting its pathway, needs to be developed. In this study, to solve this kind of problem, an integrated monitoring system, which can track and predict the pathway of infectious diseases for its realtime monitoring and control, is developed. This system is implemented based on the conventional mathematical model called by 'Susceptible-Infectious-Recovered (SIR) Model.' The proposed model has characteristics that both inter- and intra-city modes of transportation to express interpersonal contact (i.e., migration flow) are considered. They include the means of transportation such as bus, train, car and airplane. Also, modified real data according to the geographical characteristics of Korea are employed to reflect realistic circumstances of possible disease spreading in Korea. We can predict where and when vaccination needs to be performed by parameters control in this model. The simulation includes several assumptions and scenarios. Using the data of Statistics Korea, five major cities, which are assumed to have the most population migration have been chosen; Seoul, Incheon (Incheon International Airport), Gangneung, Pyeongchang and Wonju. It was assumed that the cities were connected in one network, and infectious disease was spread through denoted transportation methods only. In terms of traffic volume, daily traffic volume was obtained from Korean Statistical Information Service (KOSIS). In addition, the population of each city was acquired from Statistics Korea. Moreover, data on H1N1 (swine flu) were provided by Korea Centers for Disease Control and Prevention, and air transport statistics were obtained from Aeronautical Information Portal System. As mentioned above, daily traffic volume, population statistics, H1N1 (swine flu) and air transport statistics data have been adjusted in consideration of the current conditions in Korea and several realistic assumptions and scenarios. Three scenarios (occurrence of H1N1 in Incheon International Airport, not-vaccinated in all cities and vaccinated in Seoul and Pyeongchang respectively) were simulated, and the number of days taken for the number of the infected to reach its peak and proportion of Infectious (I) were compared. According to the simulation, the number of days was the fastest in Seoul with 37 days and the slowest in Pyeongchang with 43 days when vaccination was not considered. In terms of the proportion of I, Seoul was the highest while Pyeongchang was the lowest. When they were vaccinated in Seoul, the number of days taken for the number of the infected to reach at its peak was the fastest in Seoul with 37 days and the slowest in Pyeongchang with 43 days. In terms of the proportion of I, Gangneung was the highest while Pyeongchang was the lowest. When they were vaccinated in Pyeongchang, the number of days was the fastest in Seoul with 37 days and the slowest in Pyeongchang with 43 days. In terms of the proportion of I, Gangneung was the highest while Pyeongchang was the lowest. Based on the results above, it has been confirmed that H1N1, upon the first occurrence, is proportionally spread by the traffic volume in each city. Because the infection pathway is different by the traffic volume in each city, therefore, it is possible to come up with a preventive measurement against infectious disease by tracking and predicting its pathway through the analysis of traffic volume.

An estimation method of probability of infection using Reed - Frost model (Reed - Frost 모형을 이용한 전염병 감염 확률 추정)

  • Eom, Eunjin;Hwang, Jinseub;Choi, Boseung
    • Journal of the Korean Data and Information Science Society
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    • v.28 no.1
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    • pp.57-66
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    • 2017
  • SIR model (Kermack and McKendrik, 1927) is one of the most popular method to explain the spread of disease, In order to construct SIR model, we need to estimate transition rate parameter and recovery rate parameter. If we don't have any information of the two rate parameters, we should estimate using observed whole trajectory of pandemic of disease. Thus, with restricted observed data, we can't estimate rate parameters. In this research, we introduced Reed-Frost model (Andersson and Britton, 2000) to calculate the probability of infection in the early stage of pandemic with the restriction of data. When we have an initial number of susceptible and infected, and a final number of infected, we can apply Reed - Frost model and we can get the probability of infection. We applied the Reed - Frost model to the Vibrio cholerae pandemic data from Republic of the Cameroon and calculated the probability of infection at the early stage. We also construct SIR model using the result of Reed - Frost model.