Fractional Dynamics of Vector-Borne Infection with Sexual Transmission Rate and Vaccination

Shah Hussain, Elissa Nadia Madi, Naveed Iqbal, Thongchai Botmart, Yeliz Karaca and Wael W. Mohammed
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Shah Hussain: Faculty of Informatics and Computing, Universiti Sultan Zainal Abidin (UniSZA), Besut Campus, Terengganu 22200, Malaysia
Elissa Nadia Madi: Faculty of Informatics and Computing, Universiti Sultan Zainal Abidin (UniSZA), Besut Campus, Terengganu 22200, Malaysia
Naveed Iqbal: Department of Mathematics, College of Science, University of Ha’il, Ha’il 81481, Saudi Arabia
Thongchai Botmart: Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand
Yeliz Karaca: UMass Medical School, University of Massachusetts, 55 Lake Avenue North, Worcester, MA 01655, USA
Wael W. Mohammed: Department of Mathematics, College of Science, University of Ha’il, Ha’il 81481, Saudi Arabia

Mathematics, 2021, vol. 9, issue 23, 1-22

Abstract: New fractional operators have the aim of attracting nonlocal problems that display fractal behaviour; and thus fractional derivatives have applications in long-term relation description along with micro-scaled and macro-scaled phenomena. Formulated by fractional operators, the formulation of a dynamical system is used in applications for the description of systems with long-range interactions. Vector-borne illnesses are one of the world’s most serious public health issues with a large economic impact on the nations that are impacted. Population increase, urbanization, globalization, and a lack of public health infrastructure have all had a role in the introduction and reemergence of vector-borne illnesses during the last four decades. The control of these infections are important to lessen the economic burden of vector-borne diseases in infected regions. In this research work, we formulate the transmission process of Zika virus with the impact of sexual incidence rate and vaccination in terms of mathematics. We presented the fundamental theory of fractional operators Caputo–Fabrizio (CF) and Atangana–Baleanu (AB) for the analysis of the proposed system. We examine our system of Zika infection and determined the endemic indicator through a next-generation matrix technique. The uniqueness and existence of the solution has been investigated through fixed point theory. Accordingly, a numerical method has been introduced to investigate the dynamical nature of the system and make a comparison of the outcomes of the operators. The impact of different input factors has been conceptualized through dynamical behaviour of the system. We observed that lowering the index of memory, the fractional system provides accurate results about the recommended Zika dynamics and dramatically reduces infected people. It has been proved that high efficacy of a vaccine can lower the level of infection. Moreover, the impact of other parameters on the system of Zika virus infection are highlighted through numerical results.

Keywords: zika virus; fractional derivative; mathematical model; sexual incidence rate; existence and uniqueness; fixed point theory; dynamical behaviour (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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