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Transmission dynamics of epidemic spread and outbreak of Ebola in West Africa: fuzzy modeling and simulation

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Abstract

In this paper, an attempt is made to understand the transmission dynamics of Ebola virus disease (EVD) incorporating fuzziness in all biological parameters due to its natural variability. To characterize the transmission trajectories of Ebola outbreak, we propose and analyze two SEIR and SEIRHD type transmission models. Using triangular fuzzy numbers for the imprecise parameters, we first study the existence of the equilibria and their stability. Both of the model have two equilibria, namely the disease-free and endemic. Stability of the disease-free and endemic equilibria is related with basic reproduction number that has been calculated from next generation matrix. Stability analysis of the system shows that the disease free equilibrium is locally as well as globally asymptotically stable when the basic reproduction number is less than unity. Under some additional conditions, the model system becomes locally asymptotically stable at unique endemic equilibrium when basic reproduction number is greater than unity. Finally, we perform some numerical experiments to justify the theoretical estimate.

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Notes

  1. Similar type of concepts have already been used in [31].

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Acknowledgements

The first author acknowledge with thanks the support received through a research grant, provided by the Council of Scientific and Industrial Research (CSIR) (Grant No. 09/085(0113)/2015-EMR-1), New Delhi, under which this work has been carried out.

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  1. Department of Applied Mathematics, Indian Institute of Technology (ISM), Dhanbad, 826004, India

    Renu Verma, S. P. Tiwari & Ranjit Kumar Upadhyay

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Verma, R., Tiwari, S.P. & Upadhyay, R.K. Transmission dynamics of epidemic spread and outbreak of Ebola in West Africa: fuzzy modeling and simulation. J. Appl. Math. Comput. 60, 637–671 (2019). https://doi.org/10.1007/s12190-018-01231-0

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