### Fractional-order dynamics of Rift Valley fever in ruminant host with vaccination

Asif Jan, Rashid Jan, Hassan Khan, M. S. Zobaer, Rasool Shah

#### Abstract

Rift Valley fever is the most terrifying animal disease around the globe, which transfers through mosquitoes and caused by a virus. This infection is life-threatening and heavily affects the economic sectors. Therefore, it is valuable to conceptualize the dynamics of Rift Valley fever to understand its transmission pathway to provide better control policies. Here, we construct an epidemic model for Rift Valley fever with vaccination through fractional derivatives. Firstly, we present the proposed Rift Valley fever dynamics in the Caputo framework. The basic knowledge of fractional calculus is used to determine the rudimentary properties of the proposed fractional model, which include positivity, uniqueness, and boundedness of the solutions. We investigate our constructed model of Rift Valley fever for equilibria and determined the basic reproduction number of the system through next-generation technique, indicated by R0. The stability results are established for the infection-fee steady-state of the system. Numerical simulations are conducted and sensitivity analysis of R0 through partial rank correlation coefficient (PRCC) method is carried out to show the importance of different parameters in R0. Then the Rift Valley fever model is analyzed in the Atangana-Baleanu framework, furthermore, we present a numerical scheme for the proposed fractional model to illustrate the solution pathway of the model. We notice that the fractional-order dynamics can explain the complex system of Rift Valley fever infection more precisely and accurately rather than the integer-order dynamics. It is also observed that the Atangana-Baleanu operator provides more accurate results than the Caputo fractional derivative.

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Published: 2020-11-03

Asif Jan, Rashid Jan, Hassan Khan, M. S. Zobaer, Rasool Shah, Fractional-order dynamics of Rift Valley fever in ruminant host with vaccination, Commun. Math. Biol. Neurosci., 2020 (2020), Article ID 79

Copyright © 2020 Asif Jan, Rashid Jan, Hassan Khan, M. S. Zobaer, Rasool Shah. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Commun. Math. Biol. Neurosci.

ISSN 2052-2541

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