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Discrete-time exploited fish epidemic models

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Abstract

We extend classic discrete-time susceptible-infective-susceptible (SIS) and susceptible-exposed-infectious-susceptible epidemic models to include disease transmission dynamics in exploited fish populations that exhibit compensatory (contest competition) and overcompensatory (scramble competition) stock dynamics with and without the strong Allee effect. We compute the basic reproductive number, \({\mathfrak{R}_{0}}\), and use it to predict the (uniform) persistence or extinction of the infective exploited fish population, where the fish stock dynamics are compensatory and the strong Allee mechanism is either present or absent. We use the SIS epidemic model to explore the relationship between the stock demographic equation and the epidemic process, where the total stock population dynamics are overcompensatory. As in “higher” human and animal populations, we show that the demographic exploited fish population dynamics drive both the susceptible and infective stock dynamics.

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Authors and Affiliations

  1. Department of Mathematics, Howard University, Washington, DC, 20059, USA

    Abdul-Aziz Yakubu

  2. Department of Mathematics, Morgan State University, Baltimore, MD, 21251, USA

    Najat Ziyadi

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  1. Abdul-Aziz Yakubu
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  2. Najat Ziyadi
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Correspondence to Abdul-Aziz Yakubu.

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Yakubu, AA., Ziyadi, N. Discrete-time exploited fish epidemic models. Afr. Mat. 22, 177–199 (2011). https://doi.org/10.1007/s13370-011-0016-z

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