A robust study of the transmission dynamics of zoonotic infection through non-integer derivative

• Autorzy: Jan Rashid , Alharbi Asma , Boulaaras Salah , Alyobi Sultan , Khan Zaryab

Identyfikatory

DOI

10.1515/dema-2022-0179

• Języki publikacji: EN

Abstrakty

EN

In Sub-Saharan Africa, zoonotic diseases are the leading cause of sickness and mortality, yet preventing their spread has long been difficult. Vaccination initiatives have significantly reduced the frequency of zoonotic diseases mostly in African regions. Nonetheless, zoonotic illnesses continue to be a hazard to underdeveloped countries. Zoonotic infections are spread by direct contact, food, and water. We construct an epidemic model to understand zoonotic disease transmission phenomena. The model is examined using the fundamental results of fractional theory. The reproduction parameter R0 was obtained by inspecting the model’s steady states. The stability of the system’s steady states has been demonstrated. The system’s reproduction parameter is quantitatively explored by varying various input parameters. Furthermore, the presence and uniqueness of the solution of the proposed dynamics of zoonotic diseases have been demonstrated. Different simulations of the recommended zoonotic disease model with different input factors are performed to inspect the complex dynamics of zoonotic disease with the influence of various model factors. To establish effective prevention and control measures for the infection, we analyse dynamical behaviour of the system. Decreasing the fractional order θ can decrease the infection level significantly. Different factors for reducing zoonotic diseases were recommended to regional policymakers.

Słowa kluczowe

EN

zoonotic disease; Caputo-Fabrizio operator; mathematical model; qualitative analysis; fixed point theory; numerical findings

PL

operator Caputo-Fabrizio; model matematyczny; analiza jakościowa; teoria punktu stałego

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2022
• Tom: Vol. 55, nr 1
• Strony: 922--938
• Opis fizyczny: Bibliogr. 26 poz., tab., wykr.

Twórcy

autor

Jan Rashid

• Department of Mathematics, University of Swabi, Swabi 23561, KPK, Pakistan

autor

Alharbi Asma

• Department of Mathematics, College of Sciences and Arts, Qassim University, ArRass, Saudi Arabia

autor

Boulaaras Salah

• Department of Mathematics, College of Sciences and Arts, Qassim University, ArRass, Saudi Arabia

autor

Alyobi Sultan

• Department of Mathematics, King Abdulaziz University, College of Science & Arts, Rabigh, Saudi Arabia

autor

Khan Zaryab

• Department of Mathematics, University of Swabi, Swabi 23561, KPK, Pakistan

Bibliografia

• [1] S. Osman, O. D. Makinde, and D. M. Theuri, Stability analysis and modelling of listeriosis dynamics in human and animal populations, Glob. J. Pure Appl. Math. 14 (2018), no. 1, 115–137.
• [2] G. D. Inglis, V. F. Boras, A. L. Webb, V. V. Suttorp, P. Hodgkinson, and E. N. Taboada, Enhanced microbiological surveillance reveals that temporal case clusters contribute to the high rates of campylobacteriosis in a model agroecosystem, Int. J. Med. Microbiol. 309 (2019), no. 3–4, 232–244.
• [3] W. Cha, T. Henderson, J. Collins, and S. D. Manning, Factors associated with increasing campylobacteriosis incidence in Michigan, 2004–2013, Epidemiol. Infect. 144 (2016), no. 15, 3316–3325.
• [4] A. H. Havelaar, W. van Pelt, C. W. Ang, J. A. Wagenaar, J. P. van Putten, U. Gross, et al., Immunity to Campylobacter: its role in risk assessment and epidemiology, Crit. Rev. Microbiol. 35 (2009), no. 1, 1–22.
• [5] S. Boulaaras, R. Jan, A. Khan, and M. Ahsan, Dynamical analysis of the transmission of dengue fever via Caputo-Fabrizio fractional derivative, Chaos Soliton. Fractals X 8 (2022), 100072.
• [6] R. Jan, A. Khan, S. Boulaaras, and S. A. Zubair, Dynamical behaviour and chaotic phenomena of HIV infection through fractional calculus, Discrete Dyn. Nat. Soc. 2022 (2022), 1–19.
• [7] R. Jan, W. Shah, W. Deebani, and E. Alzahrani, Analysis and dynamical behaviour of a novel dengue model via fractional calculus, Int. J. Biomath. 15 (2022), no. 6, 2250036.
• [8] R. Jan and S. Boulaaras, Analysis of fractional-order dynamics of dengue infection with non-linear incidence functions, Trans. Inst. Meas. 44 (2022), no. 13, 01423312221085049.
• [9] A. Mhlanga, Assessing the impact of optimal health education programs on the control of zoonotic diseases, Comput. Math. Methods Med. 2020 (2020), 1–15.
• [10] R. Jan, M. A. Khan, and J. F. Gómez-Aguilar, Asymptomatic carriers in transmission dynamics of dengue with control interventions, Optim. Control Appl. Methods 41 (2020), no. 2, 430–447.
• [11] R. Jan and Y. Xiao, Effect of partial immunity on transmission dynamics of dengue disease with optimal control, Math. Methods Appl. Sci. 42 (2019), no. 6, 1967–1983.
• [12] R. Jan and Y. Xiao, Effect of pulse vaccination on dynamics of dengue with periodic transmission functions, Adv. Difference Equations 2019 (2019), no. 1, 1–17.
• [13] S. Osman, D. Otoo, and O. D. Makinde, Modeling anthrax with optimal control and cost effectiveness analysis, Appl. Math. 11 (2020), no. 3, 255.
• [14] R. Gorenflo and F. Mainardi, Fractional calculus, In: Fractals and Fractional Calculus in Continuum Mechanics, Springer, Vienna, 1997, pp. 223–276.
• [15] S. G. Samko, A. A. Kilbas, and O. I. Marichev, Fractional Integrals and Derivatives, vol. 1, Gordon and Breach Science Publishers, Yverdon-les-Bains, Switzerland, 1993.
• [16] R. Jan, M. A. Khan, P. Kumam, and P. Thounthong, Modeling the transmission of dengue infection through fractional derivatives, Chaos Solit. Fractals. 127 (2019), 189–216.
• [17] M. Abdulhameed, D. Vieru, and R. Roslan, Magnetohydrodynamic electroosmotic flow of Maxwell fluids with Caputo? Fabrizio derivatives through circular tubes, Comput. Math. 74 (2017), no. 10, 2503–2519.
• [18] E. Hanert, Front dynamics in a two-species competition model driven by Lévy flights, J. Theor. Biol. 300 (2012), 134–142.
• [19] M. Caputo and M. Fabrizio, On the singular kernels for fractional derivatives. Some applications to partial differential equations, Progr. Fract. Differ. Appl. 7 (2021), no. 2, 1–4.
• [20] J. Losada and J. J. Nieto, Fractional integral associated to fractional derivatives with nonsingular kernels, Progr. Fract. Differ. Appl. 7 (2021), no. 3, 1–7.
• [21] M. AliDokuyucu, E. Celik, H. Bulut, and H. Mehmet Baskonus, Cancer treatment model with the Caputo-Fabrizio fractional derivative, Eur. Phys. J. Plus. 133 (2018), no. 3, 1–6.
• [22] M. M. El-Dessoky and M. A. Khan, Application of Caputo-Fabrizio derivative to a cancer model with unknown parameters, Discrete Contin. Dyn. Syst. Ser-S. 14 (2021), no. 10, 3557.
• [23] Z. Shah, R. Jan, P. Kumam, W. Deebani, and M. Shutaywi, Fractional dynamics of HIV with source term for the supply of new CD4. T-cells depending on the viral load via Caputo-Fabrizio derivative, Molecules 26 (2021), no. 6, 1806.
• [24] Z. Shah, E. Bonyah, E. Alzahrani, R. Jan, and N. Aedh Alreshidi, Chaotic phenomena and oscillations in dynamical behaviour of financial system via fractional calculus, Complexity 2022 (2022), no. 3, 1–14.
• [25] H. M. Srivastava, R. Jan, A. Jan, W. Deebani, and M. Shutaywi, Fractional-calculus analysis of the transmission dynamics of the dengue infection, Chaos Interdisc. J. Nonlinear Sci. 31 (2021), no. 5, 053130.
• [26] A. Atangana and K. M. Owolabi, New numerical approach for fractional differential equations, Math. Model Nat. Phenom. 13 (2018), no. 1, 3.

Uwagi

PL

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).