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Dynamical Analysis of an SEIT Epidemic Model with Application to Ebola Virus Transmission in Guinea.

ABSTRACT: In order to investigate the transmission mechanism of the infectious individual with Ebola virus, we establish an SEIT (susceptible, exposed in the latent period, infectious, and treated/recovery) epidemic model. The basic reproduction number is defined. The mathematical analysis on the existence and stability of the disease-free equilibrium and endemic equilibrium is given. As the applications of the model, we use the recognized infectious and death cases in Guinea to estimate parameters of the model by the least square method. With suitable parameter values, we obtain the estimated value of the basic reproduction number and analyze the sensitivity and uncertainty property by partial rank correlation coefficients.

SUBMITTER: Li Z

PROVIDER: S-EPMC4504125 | biostudies-literature | 2015

REPOSITORIES: biostudies-literature

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Dynamical Analysis of an SEIT Epidemic Model with Application to Ebola Virus Transmission in Guinea.

Li Zhiming Z Teng Zhidong Z Feng Xiaomei X Li Yingke Y Zhang Huiguo H

Computational and mathematical methods in medicine 20150702

In order to investigate the transmission mechanism of the infectious individual with Ebola virus, we establish an SEIT (susceptible, exposed in the latent period, infectious, and treated/recovery) epidemic model. The basic reproduction number is defined. The mathematical analysis on the existence and stability of the disease-free equilibrium and endemic equilibrium is given. As the applications of the model, we use the recognized infectious and death cases in Guinea to estimate parameters of the ...[more]

PMID: 26246849

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Project description:Ebola virus (EBOV) transmission is currently poorly characterized and is thought to occur primarily by direct contact with infectious material; however transmission from swine to nonhuman primates via the respiratory tract has been documented. To establish an EBOV transmission model for performing studies with statistical significance, groups of six guinea pigs (gps) were challenged intranasally (i.n.) or intraperitoneally (i.p.) with 10,000 times the 50% lethal dose (LD50) of gp-adapted EBOV, and naive gps were then introduced as cage mates for contact exposure at 1 day postinfection (p.i.). The animals were monitored for survival and clinical signs of disease and quantitated for virus shedding postexposure. Changes in the duration of contact of naive gps with infected animals were evaluated for their impact on transmission efficiency. Transmission was more efficient from i.n.- than from i.p.-challenged gps, with 17% versus 83% of naive gps surviving exposure, respectively. Virus shedding was detected beginning at 3 days p.i. from both i.n.- and i.p.-challenged animals. Contact duration positively correlated with transmission efficiency, and the abrogation of direct contact between infected and naive animals through the erection of a steel mesh was effective at stopping virus spread, provided that infectious animal bedding was absent from the cages. Histopathological and immunohistochemical findings show that i.n.-infected gps display enhanced lung pathology and EBOV antigen in the trachea, which supports increased virus transmission from these animals. The results suggest that i.n.-challenged gps are more infectious to naive animals than their systemically infected counterparts and that transmission occurs through direct contact with infectious materials, including those transported through air movement over short distances.Ebola is generally thought to be spread between humans though infectious bodily fluids. However, a study has shown that Ebola can be spread from pigs to monkeys without direct contact. Further studies have been hampered, because an economical animal model for Ebola transmission is not available. To address this, we established a transmission model in guinea pigs and determined the mechanisms behind virus spread. The survival data, in addition to microscopic examination of lung and trachea sections, show that mucosal infection of guinea pigs is an efficient model for Ebola transmission. Virus spread is increased with longer contact times with an infected animal and is possible without direct contact between an infected and a naive host but can be stopped if infectious materials are absent. These results warrant consideration for the development of future strategies against Ebola transmission and for a better understanding of the parameters involved in virus spread.

Project description:BackgroundAn epidemic of Ebola virus disease of unprecedented size continues in parts of west Africa. For the first time, large urban centres such as Conakry, the capital of Guinea, are affected. We did an observational study of patients with Ebola virus disease in three regions of Guinea, including Conakry, aiming to map the routes of transmission and assess the effect of interventions.MethodsBetween Feb 10, 2014, and Aug 25, 2014, we obtained data from the linelist of all confirmed and probable cases in Guinea (as of Sept 16, 2014), a laboratory database of information about patients, and interviews with patients and their families and neighbours. With this information, we mapped chains of transmission, identified which setting infections most probably originated from (community, hospitals, or funerals), and computed the context-specific and overall reproduction numbers.FindingsOf 193 confirmed and probable cases of Ebola virus disease reported in Conakry, Boffa, and Télimélé, 152 (79%) were positioned in chains of transmission. Health-care workers contributed little to transmission. In March, 2014, individuals with Ebola virus disease who were not health-care workers infected a mean of 2·3 people (95% CI 1·6-3·2): 1·4 (0·9-2·2) in the community, 0·4 (0·1-0·9) in hospitals, and 0·5 (0·2-1·0) at funerals. After the implementation of infection control in April, the reproduction number in hospitals and at funerals reduced to lower than 0·1. In the community, the reproduction number dropped by 50% for patients that were admitted to hospital, but remained unchanged for those that were not. In March, hospital transmissions constituted 35% (seven of 20) of all transmissions and funeral transmissions constituted 15% (three); but from April to the end of the study period, they constituted only 9% (11 of 128) and 4% (five), respectively. 82% (119 of 145) of transmission occurred in the community and 72% (105) between family members. Our simulations show that a 10% increase in hospital admissions could have reduced the length of chains by 26% (95% CI 4-45).InterpretationIn Conakry, interventions had the potential to stop the epidemic, but reintroductions of the disease and poor cooperation of a few families led to prolonged low-level spread, showing the challenges of Ebola virus disease control in large urban centres. Monitoring of chains of transmission is crucial to assess and optimise local control strategies for Ebola virus disease.FundingLabex IBEID, Reacting, PREDEMICS, NIGMS MIDAS initiative, Institut Pasteur de Dakar.

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Dynamical Analysis of an SEIT Epidemic Model with Application to Ebola Virus Transmission in Guinea.

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Dynamical Analysis of an SEIT Epidemic Model with Application to Ebola Virus Transmission in Guinea.

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