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. 2021 Aug 18;136(8):853. doi: 10.1140/epjp/s13360-021-01862-6

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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2021

This article is made available via the PMC Open Access Subset for unrestricted research re-use and secondary analysis in any form or by any means with acknowledgement of the original source. These permissions are granted for the duration of the World Health Organization (WHO) declaration of COVID-19 as a global pandemic.

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Fig. 7 — Period-doubling bifurcation and chaos in system (4) for $a = 2, b = 10, β_{1} = 0.99, d = 0.4, β_{2} = 0.01, β_{3} = 0.80, β_{4} = 0.60, c_{1} = 1, c_{2} = 2$ , $B > 0, μ > 0$ and $S_{0} = 1.35, E_{0} = 0.31, Q_{0} = 0.75$