Analysis of a Multiscale Model of Ebola Virus Disease

Multiscale models are ones that link the epidemiological processes dealing with the transmission between hosts and the immunological processes dealing with the dynamics within one host. In this study, a multiscale model of Ebola Virus Disease linking epidemiological and immunological processes has been developed and analysed. The model has considered two infectious classes ; the exposed and the infected individuals. Local and global stability analyses of the Disease Free Equilibrium and the Endemic Equilibrium points of the model show that the disease dies out if the basic reproduction number Rc0 < 1 and persists in the population when Rc0 > 1 respectively. Sensitivity analysis shows that the rate of vaccination, v , is the most sensitive parameter. This indicates that effort should be directed towards implementing an effective vaccination strategy to control the spread of the disease. It has also been established that when treatment efficacy is scaled up, the viral load goes down and consequently, the transmission between hosts is also reduced. The impact of treatment on the disease spread has also been established through the coupling function (L∗) . The study indicates that a higher percentage of the exposed and the infected individuals should be treated to control the spread of the disease within the population.

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Ebola virus disease outbreak in Nigeria: transmission dynamics and rapid control

10.7287/peerj.preprints.569v3 ◽

2015 ◽

Cited By ~ 1

Author(s):

Christian L Althaus ◽

Nicola Low ◽

Emmanuel O. Musa ◽

Faisal Shuaib ◽

Sandro Gsteiger

Keyword(s):

Ebola Virus ◽

Reproduction Number ◽

Time Window ◽

Index Case ◽

Virus Disease ◽

Control Measures ◽

Ebola Virus Disease ◽

Transmission Model ◽

The Individual ◽

The Impact

International air travel has already spread Ebola virus disease (EVD) to major cities as part of the unprecedented epidemic that started in Guinea in December 2013. An infected airline passenger arrived in Nigeria on July 20, 2014 and caused an outbreak in Lagos and then Port Harcourt. After a total of 20 reported cases, including 8 deaths, Nigeria was declared EVD free on October 20, 2014. We quantified the impact of early control measures in preventing further spread of EVD in Nigeria and calculated the risk that a single undetected case will cause a new outbreak. We fitted an EVD transmission model to data from the outbreak in Nigeria and estimated the individual reproduction number of the index case at 9.0 (95% confidence interval [CI]: 5.2-15.6). We also found that the net reproduction number fell below unity 15 days (95% CI: 11-21 days) after the arrival of the index case. Hence, our study illustrates the time window for successful containment of EVD outbreaks caused by infected air travelers.

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Ebola virus disease outbreak in Nigeria: lessons to learn

10.7287/peerj.preprints.569v1 ◽

2014 ◽

Cited By ~ 1

Author(s):

Christian L Althaus ◽

Sandro Gsteiger ◽

Nicola Low

Keyword(s):

Ebola Virus ◽

Reproduction Number ◽

Virus Disease ◽

Control Measures ◽

Ebola Virus Disease ◽

Transmission Model ◽

Port Harcourt ◽

Airline Passenger ◽

Net Reproduction ◽

The Impact

International air travel has already spread Ebola virus disease (EVD) to major cities as part of the unprecedented epidemic that started in Guinea in December 2013. An infected airline passenger arrived in Nigeria on July 20, 2014 and caused an outbreak in Lagos and then Port Harcourt. After a total of 20 reported cases, including 8 deaths, Nigeria was declared EVD free on October 20, 2014. We quantified the impact of early control measures in preventing further spread of EVD in Nigeria and calculated the risk that a single undetected case will cause a new outbreak. We fitted an EVD transmission model to data from the outbreak in Nigeria and estimated the basic reproduction number R0 = 9.0 (95% confidence interval [CI]: 5.2-15.6). We also found that the net reproduction number Rt fell below unity 15 days (95% CI: 11-21 days) after the arrival of the index case. Using the estimated value of R0 in Nigeria, we calculated that the risk of an outbreak from a single undetected case was 89% (95% CI: 81-94%). Even though R0 in Nigeria was high, EVD outbreaks caused by infected air travelers can be successfully contained if control measures are rapidly implemented.

Download Full-text

Ebola virus disease outbreak in Nigeria: transmission dynamics and rapid control

10.7287/peerj.preprints.569 ◽

2015 ◽

Author(s):

Christian L Althaus ◽

Nicola Low ◽

Emmanuel O. Musa ◽

Faisal Shuaib ◽

Sandro Gsteiger

Keyword(s):

Ebola Virus ◽

Reproduction Number ◽

Time Window ◽

Index Case ◽

Virus Disease ◽

Control Measures ◽

Ebola Virus Disease ◽

Transmission Model ◽

The Individual ◽

The Impact

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Ebola virus disease outbreak in Nigeria: transmission dynamics and rapid control

10.7287/peerj.preprints.569v2 ◽

2014 ◽

Author(s):

Christian L Althaus ◽

Sandro Gsteiger ◽

Emmanuel O. Musa ◽

Faisal Shuaib ◽

Nicola Low

Keyword(s):

Ebola Virus ◽

Reproduction Number ◽

Time Window ◽

Virus Disease ◽

Control Measures ◽

Ebola Virus Disease ◽

Transmission Model ◽

Airline Passenger ◽

Net Reproduction ◽

The Impact

International air travel has already spread Ebola virus disease (EVD) to major cities as part of the unprecedented epidemic that started in Guinea in December 2013. An infected airline passenger arrived in Nigeria on July 20, 2014 and caused an outbreak in Lagos and then Port Harcourt. After a total of 20 reported cases, including 8 deaths, Nigeria was declared EVD free on October 20, 2014. We quantified the impact of early control measures in preventing further spread of EVD in Nigeria and calculated the risk that a single undetected case will cause a new outbreak. We fitted an EVD transmission model to data from the outbreak in Nigeria and estimated the basic reproduction number R0 = 9.0 (95% confidence interval [CI]: 5.2-15.6). We also found that the net reproduction number Rt fell below unity 15 days (95% CI: 11-21 days) after the arrival of the index case. Using the estimated value of R0 in Nigeria, we calculated that the risk of an outbreak from a single undetected case was 89% (95% CI: 81-94%). Even though R0 can be high, our study illustrates the time window for successful containment of EVD outbreaks caused by infected air travelers.

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Threshold Dynamics in a Model for Zika Virus Disease with Seasonality

Bulletin of Mathematical Biology ◽

10.1007/s11538-020-00844-6 ◽

2021 ◽

Vol 83 (4) ◽

Cited By ~ 1

Author(s):

Mahmoud A. Ibrahim ◽

Attila Dénes

Keyword(s):

Zika Virus ◽

Reproduction Number ◽

Virus Disease ◽

Threshold Dynamics ◽

Global Dynamics ◽

Threshold Parameter ◽

Globally Asymptotically Stable ◽

Linear Integral ◽

The Impact ◽

Disease Free

AbstractWe present a compartmental population model for the spread of Zika virus disease including sexual and vectorial transmission as well as asymptomatic carriers. We apply a non-autonomous model with time-dependent mosquito birth, death and biting rates to integrate the impact of the periodicity of weather on the spread of Zika. We define the basic reproduction number $${\mathscr {R}}_{0}$$ R 0 as the spectral radius of a linear integral operator and show that the global dynamics is determined by this threshold parameter: If $${\mathscr {R}}_0 < 1,$$ R 0 < 1 , then the disease-free periodic solution is globally asymptotically stable, while if $${\mathscr {R}}_0 > 1,$$ R 0 > 1 , then the disease persists. We show numerical examples to study what kind of parameter changes might lead to a periodic recurrence of Zika.

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