Modeling fractional-order dynamics of Syphilis via Mittag-Leffler law

E. Bonyah; C. W. Chukwu; M. L. Juga; Fatmawati; E. Bonyah; C. W. Chukwu; M. L. Juga; Fatmawati

doi:10.3934/math.2021485

AIMS Mathematics

2021, Volume 6, Issue 8: 8367-8389. doi: 10.3934/math.2021485

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Modeling fractional-order dynamics of Syphilis via Mittag-Leffler law

1.
Department of Mathematics Education, Akenten Appiah-Menka University of Skills Training and Entrepreneurial Development, Kumasi, Ghana
2.
Department of Mathematics and Applied Mathematics, University of Johannesburg, Auckland Park, 2006, South Africa
3.
Department of Mathematics, Faculty of Science and Technology, Universitas Airlangga, Surabaya 60115, Indonesia

Received: 17 February 2021 Accepted: 13 May 2021 Published: 31 May 2021
MSC : 34A08, 92B05

Syphilis is one the most dangerous sexually transmitted disease which is common in the world. In this work, we formulate and analyze a mathematical model of Syphilis with an emphasis on treatment in the sense of Caputo-Fabrizio (CF) and Atangana-Baleanu (Mittag-Leffler law) derivatives. The basic reproduction number of the CF model which presents information on the spread of the disease is determined. The model's steady states were found, and the disease-free state's local and global stability are established based on the basic reproduction number. The existence and uniqueness of solutions for both Caputo-Fabrizio and Atangana-Baleanu derivative in the Caputo sense are established. Numerical simulations were carried out to support the analytical solution, which indicates that the fractional-order derivatives influence the dynamics of the spread of Syphilis in any community induced with the disease.
- sexually transmitted disease,
- syphilis model,
- Mittag-Leffler,
- Caputo-Fabrizio,
- Atangana-Baleanu
Citation: E. Bonyah, C. W. Chukwu, M. L. Juga, Fatmawati. Modeling fractional-order dynamics of Syphilis via Mittag-Leffler law[J]. AIMS Mathematics, 2021, 6(8): 8367-8389. doi: 10.3934/math.2021485

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Abstract

Syphilis is one the most dangerous sexually transmitted disease which is common in the world. In this work, we formulate and analyze a mathematical model of Syphilis with an emphasis on treatment in the sense of Caputo-Fabrizio (CF) and Atangana-Baleanu (Mittag-Leffler law) derivatives. The basic reproduction number of the CF model which presents information on the spread of the disease is determined. The model's steady states were found, and the disease-free state's local and global stability are established based on the basic reproduction number. The existence and uniqueness of solutions for both Caputo-Fabrizio and Atangana-Baleanu derivative in the Caputo sense are established. Numerical simulations were carried out to support the analytical solution, which indicates that the fractional-order derivatives influence the dynamics of the spread of Syphilis in any community induced with the disease.

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