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Quarantine Model on the Transmission of Ebola Virus Disease in the Human Population with Infectious Dead Class

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Abstract

The deadly Ebola virus which spreads through human-to-human transmission via direct contact is a serious threat to the human population where the rate of death due to the Ebola virus infection is very high, with an average of approximately fifty percent, which has been seen to go as high as ninety percent in some outbreaks. In this paper, we attempt to understand the spreading behavior of Ebola virus disease (EVD) in the human population by developing a novel epidemic model with five classes susceptible-exposed-infectious-quarantine- infectious dead. We have used the very close real parametric values as per the data released by the World Health Organization (WHO). To minimize the spread of EVD, critical analysis is performed both in the presence and absence of control measures. The effect of quarantine on the infectious population is critically analyzed, and it is observed that quarantining the infectious population may play a vital role in controlling the spread of EVD. The reproduction number is obtained and the asymptotic stability is established both analytically and numerically. Extensive numerical simulations with examples and time series analysis are carried out under different control measures using MATLAB. Numerical simulations of our model and time series analysis reveal that the dead bodies are a major source of the spread of infection and thus our assumption that the deaths occurring among patients in the infectious or quarantined classes, lead to a transition into the dead (D) class, which contributes to the process of infection of susceptible members of the population is established. Once the dead bodies are buried, only they are assumed to be finally removed from the population. Introducing infectious dead class in our model is a novel idea that helped us to understand how we can minimize the transmission rate of EVD in the population.

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Data Availability

Enquiries about data availability should be directed to the authors.

Abbreviations

S:

Susceptible population

E:

Exposed population

I:

Infectious population

Q:

Quarantine population

D:

Death population due to the Ebola virus before dead bodies are buried

\(\mu\) :

Natural death rate i.e. death other than Ebola virus and the influx rate as well

\(\delta_{1}\) :

Disease induced death rate for non-quarantined infectious individuals

\(\delta_{2}\) :

Disease induced death rate for quarantined individuals

\(\delta\) :

The rate at which dead bodies are buried

\(\alpha\) :

The rate at which suspected cases (E) are quarantined

\(\xi\) :

The rate at which confirmed cases (I) are quarantined

\(\gamma\) :

The rate at which suspected cases (E) are confirmed

\(\eta p\) :

The probability and rate of quarantine population to recovered and again joined the susceptible population

\(\beta\) :

Per infectivity contact rate (from infectious patients to susceptible population)

\(\beta_{D}\) :

Per infectivity contact rate (from dead bodies to susceptible population)

\(\beta_{Q}\) :

Per infectivity contact rate (from quarantined patients to susceptible population mainly health workers)

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Authors and Affiliations

  1. Department of Zoology, Vinoba Bhave University, Hazaribag, India

    Archana Mishra

  2. Adarsh College, Rajdhanwar, Giridih, Vinoba Bhave University, Hazaribag, India

    Bimal Kumar Mishra

  3. Department of Computer Science and Engineering, Birla Institute of Technlogy, Patna Campus, Patna, India

    Ajit Kumar Keshri

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Contributions

AM wrote the Introduction part, developed the Mathematical Model. BKM established the stability and performed the simulation. AKK provided the examples and performed the analysis.

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Correspondence to Bimal Kumar Mishra.

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Mishra, A., Mishra, B.K. & Keshri, A.K. Quarantine Model on the Transmission of Ebola Virus Disease in the Human Population with Infectious Dead Class. Int. J. Appl. Comput. Math 9, 133 (2023). https://doi.org/10.1007/s40819-023-01608-1

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Keywords

Mathematics Subject Classfication

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