A Caputo-Fabrizio fractional-order cholera model and its sensitivity analysis

Idris Ahmed; Ali Akgül; Fahd Jarad; Poom Kumam; Kamsing Nonlaopon

doi:10.53391/mmnsa.1293162

Araştırma Makalesi

Yıl 2023, Cilt: 3 Sayı: 2, 170 - 187, 30.06.2023

Idris Ahmed Ali Akgül Fahd Jarad Poom Kumam Kamsing Nonlaopon

https://doi.org/10.53391/mmnsa.1293162

Cited By: 5

Öz

Kaynakça

Acosta, C.J., Galindo, C.M., Kimario, J., Senkoro, K., Urassa, H., Casals, C. et al. Cholera outbreak in southern Tanzania: risk factors and patterns of transmission. Emerging Infectious Diseases, 7, 583-587, (2001).
Luquero, F.J., Rondy, M., Boncy, J., Munger, A., Mekaoui, H., Rymshaw, E. et al. Mortality rates during cholera epidemic, Haiti, 2010–2011. Emerging Infectious Diseases, 22(3), 410-416, (2016).
Mgonja, D.S., Massawe, E.S. and Makinde, O.D. Computational modelling of Cholera Bacteriophage with treatment. Open Journal of Epidemiology, 5(3), 172-186, (2015).
Moore, M., Gould, P. and Keary, B.S. Global urbanization and impact on health. International Journal of Hygiene and Environmental Health, 206(4-5), 269-278, (2003).
Biswas, D. and Pal, S. Role of awareness to control transmission of HIV/AIDS epidemic with treatment and sensitivity analysis. Journal of Statistics and Management Systems, 25(3), 617-644, (2022).
Abimbade, S.F., Olaniyi, S., Ajala, O.A. and Ibrahim, M.O. Optimal control analysis of a tuberculosis model with exogenous re-infection and incomplete treatment. Optimal Control Applications and Methods, 41(6), 2349-2368, (2020).
Mukandavire, Z., Garira, W. and Tchuenche, J.M. Modelling effects of public health educational campaigns on HIV/AIDS transmission dynamics. Applied Mathematical Modelling, 33(4), 2084-2095, (2009).
Ahmed, I., Yusuf, A., Ibrahim, A., Kumam, P., and Ibrahim, M. J. A mathematical model of the ongoing coronavirus disease (COVID-19) pandemic: a case study in Turkey. Science and Technology Asia, 27(4), 248-258, (2022).
Peter, O.J., Qureshi, S., Yusuf, A., Al-Shomrani, M. and Idowu, A.A. A new mathematical model of COVID-19 using real data from Pakistan. Results in Physics, 24, 104098, (2021).
Layton, A.T. and Sadria, M. Understanding the dynamics of SARS-CoV-2 variants of concern in Ontario, Canada: a modeling study. Scientific Reports, 12, 2114, (2022).
Duran, S., Durur, H., Yavuz, M. and Yokus, A. Discussion of numerical and analytical techniques for the emerging fractional order murnaghan model in materials science. Optical and Quantum Electronics, 55, 571, (2023).
Sun, G.Q., Xie, J.H., Huang, S.H., Jin, Z., Li, M.T. and Liu, L. Transmission dynamics of cholera: mathematical modeling and control strategies. Communications in Nonlinear Scienceand Numerical Simulation, 45, 235-244, (2017).
Senderovich, Y., Izhaki, I. and Halpern, M. Fish as reservoirs and vectors of Vibrio cholerae. PloS one, 5(1), e8607, (2010).
Islam, M.S., Zaman, M.H., Islam, M.S., Ahmed, N. and Clemens, J.D. Environmental reservoirs of Vibrio cholerae. Vaccine, 38, A52-A62, (2020).
Chac, D., Dunmire, C.N., Singh, J. and Weil, A.A. Update on environmental and host factors impacting the risk of Vibrio cholerae infection. ACS Infectious Diseases, 7(5), 1010-1019, (2021).
Tilahun, G.T., Woldegerima, W.A. and Wondifraw, A. Stochastic and deterministic mathematical model of cholera disease dynamics with direct transmission. Advances in Difference Equations, 2020, 670, (2020).
Adewole, M.O. and Faniran, T.S. Analysis of Cholera model with treatment noncompliance. International Journal of Nonlinear Analysis and Applications, 13(1), 29-43, (2022).
Diethelm, K. and Ford, N.J. Analysis of fractional differential equations. Journal of Mathematical Analysis and Applications, 265(2), 229-248, (2002).
Kilbas, A.A., Srivastava, H.M. and Trujillo, J.J. Theory and Applications of Fractional Differential Equations (Vol. 204). Elsevier: Netherlands, (2006).
Uçar, S., Evirgen, F., Özdemir, N. and Hammouch, Z. Mathematical analysis and simulation of a giving up smoking model within the scope of non-singular derivative. In Proceedings, Institute of Mathematics and Mechanics, National Academy of Sciences of Azerbaijan (Vol. 48) pp. 84–99, Baku, Azerbaijan, (2022).
Uçar, S. Existence and uniqueness results for a smoking model with determination and education in the frame of non-singular derivatives. Discrete and Continuous Dynamical Systems Series S, 14(7), 2571-2589, (2021).
Uçar, E. and Özdemir, N. A fractional model of cancer-immune system with Caputo and Caputo–Fabrizio derivatives. The European Physical Journal Plus, 136, 1-17, (2021).
Yokus, A., Durur, H., Kaya, D., Ahmad, H. and Nofal, T.A. Numerical comparison of Caputo and Conformable derivatives of time fractional Burgers-Fisher equation. Results in Physics, 25, 104247, (2021).
Ahmad, S., Dong, Q.I.U. and Rahman, M.U. Dynamics of a fractional-order COVID-19 model under the nonsingular kernel of Caputo-Fabrizio operator. Mathematical Modelling and Numerical Simulation with Applications, 2(4), 228-243, (2022).
Atede, A.O., Omame, A. and Inyama, S.C. A fractional order vaccination model for COVID- 19 incorporating environmental transmission: a case study using Nigerian data. Bulletin of Biomathematics, 1(1), 78-110, (2023).
Ullah, S., Khan, M.A., Farooq, M., Hammouch, Z. and Baleanu, D. A fractional model for the dynamics of tuberculosis infection using Caputo-Fabrizio derivative. Discrete and Continous Dynamical System Series S, 13(3), (2020).
Özköse, F., Habbireeh, R. and Şenel, M.T. A novel fractional order model of SARS-CoV-2 and Cholera disease with real data. Journal of Computational and Applied Mathematics, 423, 114969, (2023).
Ahmed, I., Goufo, E.F.D., Yusuf, A., Kumam, P., Chaipanya, P. and Nonlaopon, K. An epidemic prediction from analysis of a combined HIV-COVID-19 co-infection model via ABC-fractional operator. Alexandria Engineering Journal, 60(3), 2979-2995, (2021).
Ahmed, I., Yusuf, A., Sani, M.A., Jarad, F., Kumam, W. and Thounthong, P. Analysis of a Caputo HIV and malaria co-infection epidemic model. Thai Journal of Mathematics, 19(3), 897-912, (2021).
Din, A., Li, Y., Yusuf, A., Liu, J. and Aly, A.A. Impact of information intervention on stochastic hepatitis B model and its variable-order fractional network. The European Physical Journal Special Topics, 231, 1859-1873, (2022).
Addai, E., Zhang, L., Preko, A.K. and Asamoah, J.K.K. Fractional order epidemiological model of SARS-CoV-2 dynamism involving Alzheimer’s disease. Healthcare Analytics, 2, 100114, (2022).
Hanif, A., Butt, A.I.K., Ahmad, S., Din, R.U. and Inc, M. A new fuzzy fractional order model of transmission of Covid-19 with quarantine class. The European Physical Journal Plus, 136, 1179, (2021).
Uçar, S., Özdemir, N., Koca, I. and Altun, E. Novel analysis of the fractional glucose–insulin regulatory system with non-singular kernel derivative. The European Physical Journal Plus, 135, 414, (2020).
Duran, S., Yokuş, A. and Durur, H. Surface wave behavior and refraction simulation on the ocean for the fractional Ostrovsky–Benjamin–Bona–Mahony equation. Modern Physics Letters B, 35(31), 2150477, (2021).
Durur, H., Yokuş, A. and Yavuz, M. Behavior analysis and asymptotic stability of the traveling wave solution of the Kaup-Kupershmidt equation for conformable derivative. In Fractional Calculus: New Applications in Understanding Nonlinear Phenomena (Vol. 3) pp. 162-185, (2022).
Joshi, H., Yavuz, M. and Stamova, I. Analysis of the disturbance effect in intracellular calcium dynamic on fibroblast cells with an exponential kernel law. Bulletin of Biomathematics, 1(1), 24-39, (2023).
Rashid, S., Jarad, F., Alsubaie, H., Aly, A.A. and Alotaibi, A. A novel numerical dynamics of fractional derivatives involving singular and nonsingular kernels: designing a stochastic cholera epidemic model. AIMS Mathematics, 8(2), 3484-3522, (2023).
Baleanu, D., Jajarmi, A., Mohammadi, H. and Rezapour, S. A new study on the mathematical modelling of human liver with Caputo–Fabrizio fractional derivative. Chaos, Solitons and Fractals, 134, 109705, (2020).
Losada, J. and Nieto, J.J. Properties of a new fractional derivative without singular kernel. Progress in Fractional Differentiation and Applications, 1(2), 87-92, (2015).
Eustace, K.A., Osman, S. and Wainaina, M. Mathematical modelling and analysis of the dynamics of cholera. Global Journal of Pure and Applied Mathematics, 14(9), 1259-1275, (2018).
Atangana, A. and Owolabi, K.M. New numerical approach for fractional differential equations. Mathematical Modelling of Natural Phenomena, 13(1), 3, (2018).
Evirgen, F., Uçar, E., Uçar, S. and Özdemir, N. Modelling influenza A disease dynamics under Caputo-Fabrizio fractional derivative with distinct contact rates. Mathematical Modelling and Numerical Simulation with Applications, 3(1), 58-72, (2023).

A Caputo-Fabrizio fractional-order cholera model and its sensitivity analysis

Yıl 2023, Cilt: 3 Sayı: 2, 170 - 187, 30.06.2023

Idris Ahmed Ali Akgül Fahd Jarad Poom Kumam Kamsing Nonlaopon

https://doi.org/10.53391/mmnsa.1293162

Cited By: 5

Öz

In recent years, the availability of advanced computational techniques has led to a growing emphasis on fractional-order derivatives. This development has enabled researchers to explore the intricate dynamics of various biological models by employing fractional-order derivatives instead of traditional integer-order derivatives. This paper proposes a Caputo-Fabrizio fractional-order cholera epidemic model. Fixed-point theorems are utilized to investigate the existence and uniqueness of solutions. A recent and effective numerical scheme is employed to demonstrate the model's complex behaviors and highlight the advantages of fractional-order derivatives. Additionally, a sensitivity analysis is conducted to identify the most influential parameters.

Anahtar Kelimeler

Cholera, mathematical model, fixed point theorems, sensitivity analysis, numerical simulations

Kaynakça

Acosta, C.J., Galindo, C.M., Kimario, J., Senkoro, K., Urassa, H., Casals, C. et al. Cholera outbreak in southern Tanzania: risk factors and patterns of transmission. Emerging Infectious Diseases, 7, 583-587, (2001).
Luquero, F.J., Rondy, M., Boncy, J., Munger, A., Mekaoui, H., Rymshaw, E. et al. Mortality rates during cholera epidemic, Haiti, 2010–2011. Emerging Infectious Diseases, 22(3), 410-416, (2016).
Mgonja, D.S., Massawe, E.S. and Makinde, O.D. Computational modelling of Cholera Bacteriophage with treatment. Open Journal of Epidemiology, 5(3), 172-186, (2015).
Moore, M., Gould, P. and Keary, B.S. Global urbanization and impact on health. International Journal of Hygiene and Environmental Health, 206(4-5), 269-278, (2003).
Biswas, D. and Pal, S. Role of awareness to control transmission of HIV/AIDS epidemic with treatment and sensitivity analysis. Journal of Statistics and Management Systems, 25(3), 617-644, (2022).
Abimbade, S.F., Olaniyi, S., Ajala, O.A. and Ibrahim, M.O. Optimal control analysis of a tuberculosis model with exogenous re-infection and incomplete treatment. Optimal Control Applications and Methods, 41(6), 2349-2368, (2020).
Mukandavire, Z., Garira, W. and Tchuenche, J.M. Modelling effects of public health educational campaigns on HIV/AIDS transmission dynamics. Applied Mathematical Modelling, 33(4), 2084-2095, (2009).
Ahmed, I., Yusuf, A., Ibrahim, A., Kumam, P., and Ibrahim, M. J. A mathematical model of the ongoing coronavirus disease (COVID-19) pandemic: a case study in Turkey. Science and Technology Asia, 27(4), 248-258, (2022).
Peter, O.J., Qureshi, S., Yusuf, A., Al-Shomrani, M. and Idowu, A.A. A new mathematical model of COVID-19 using real data from Pakistan. Results in Physics, 24, 104098, (2021).
Layton, A.T. and Sadria, M. Understanding the dynamics of SARS-CoV-2 variants of concern in Ontario, Canada: a modeling study. Scientific Reports, 12, 2114, (2022).
Duran, S., Durur, H., Yavuz, M. and Yokus, A. Discussion of numerical and analytical techniques for the emerging fractional order murnaghan model in materials science. Optical and Quantum Electronics, 55, 571, (2023).
Sun, G.Q., Xie, J.H., Huang, S.H., Jin, Z., Li, M.T. and Liu, L. Transmission dynamics of cholera: mathematical modeling and control strategies. Communications in Nonlinear Scienceand Numerical Simulation, 45, 235-244, (2017).
Senderovich, Y., Izhaki, I. and Halpern, M. Fish as reservoirs and vectors of Vibrio cholerae. PloS one, 5(1), e8607, (2010).
Islam, M.S., Zaman, M.H., Islam, M.S., Ahmed, N. and Clemens, J.D. Environmental reservoirs of Vibrio cholerae. Vaccine, 38, A52-A62, (2020).
Chac, D., Dunmire, C.N., Singh, J. and Weil, A.A. Update on environmental and host factors impacting the risk of Vibrio cholerae infection. ACS Infectious Diseases, 7(5), 1010-1019, (2021).
Tilahun, G.T., Woldegerima, W.A. and Wondifraw, A. Stochastic and deterministic mathematical model of cholera disease dynamics with direct transmission. Advances in Difference Equations, 2020, 670, (2020).
Adewole, M.O. and Faniran, T.S. Analysis of Cholera model with treatment noncompliance. International Journal of Nonlinear Analysis and Applications, 13(1), 29-43, (2022).
Diethelm, K. and Ford, N.J. Analysis of fractional differential equations. Journal of Mathematical Analysis and Applications, 265(2), 229-248, (2002).
Kilbas, A.A., Srivastava, H.M. and Trujillo, J.J. Theory and Applications of Fractional Differential Equations (Vol. 204). Elsevier: Netherlands, (2006).
Uçar, S., Evirgen, F., Özdemir, N. and Hammouch, Z. Mathematical analysis and simulation of a giving up smoking model within the scope of non-singular derivative. In Proceedings, Institute of Mathematics and Mechanics, National Academy of Sciences of Azerbaijan (Vol. 48) pp. 84–99, Baku, Azerbaijan, (2022).
Uçar, S. Existence and uniqueness results for a smoking model with determination and education in the frame of non-singular derivatives. Discrete and Continuous Dynamical Systems Series S, 14(7), 2571-2589, (2021).
Uçar, E. and Özdemir, N. A fractional model of cancer-immune system with Caputo and Caputo–Fabrizio derivatives. The European Physical Journal Plus, 136, 1-17, (2021).
Yokus, A., Durur, H., Kaya, D., Ahmad, H. and Nofal, T.A. Numerical comparison of Caputo and Conformable derivatives of time fractional Burgers-Fisher equation. Results in Physics, 25, 104247, (2021).
Ahmad, S., Dong, Q.I.U. and Rahman, M.U. Dynamics of a fractional-order COVID-19 model under the nonsingular kernel of Caputo-Fabrizio operator. Mathematical Modelling and Numerical Simulation with Applications, 2(4), 228-243, (2022).
Atede, A.O., Omame, A. and Inyama, S.C. A fractional order vaccination model for COVID- 19 incorporating environmental transmission: a case study using Nigerian data. Bulletin of Biomathematics, 1(1), 78-110, (2023).
Ullah, S., Khan, M.A., Farooq, M., Hammouch, Z. and Baleanu, D. A fractional model for the dynamics of tuberculosis infection using Caputo-Fabrizio derivative. Discrete and Continous Dynamical System Series S, 13(3), (2020).
Özköse, F., Habbireeh, R. and Şenel, M.T. A novel fractional order model of SARS-CoV-2 and Cholera disease with real data. Journal of Computational and Applied Mathematics, 423, 114969, (2023).
Ahmed, I., Goufo, E.F.D., Yusuf, A., Kumam, P., Chaipanya, P. and Nonlaopon, K. An epidemic prediction from analysis of a combined HIV-COVID-19 co-infection model via ABC-fractional operator. Alexandria Engineering Journal, 60(3), 2979-2995, (2021).
Ahmed, I., Yusuf, A., Sani, M.A., Jarad, F., Kumam, W. and Thounthong, P. Analysis of a Caputo HIV and malaria co-infection epidemic model. Thai Journal of Mathematics, 19(3), 897-912, (2021).
Din, A., Li, Y., Yusuf, A., Liu, J. and Aly, A.A. Impact of information intervention on stochastic hepatitis B model and its variable-order fractional network. The European Physical Journal Special Topics, 231, 1859-1873, (2022).
Addai, E., Zhang, L., Preko, A.K. and Asamoah, J.K.K. Fractional order epidemiological model of SARS-CoV-2 dynamism involving Alzheimer’s disease. Healthcare Analytics, 2, 100114, (2022).
Hanif, A., Butt, A.I.K., Ahmad, S., Din, R.U. and Inc, M. A new fuzzy fractional order model of transmission of Covid-19 with quarantine class. The European Physical Journal Plus, 136, 1179, (2021).
Uçar, S., Özdemir, N., Koca, I. and Altun, E. Novel analysis of the fractional glucose–insulin regulatory system with non-singular kernel derivative. The European Physical Journal Plus, 135, 414, (2020).
Duran, S., Yokuş, A. and Durur, H. Surface wave behavior and refraction simulation on the ocean for the fractional Ostrovsky–Benjamin–Bona–Mahony equation. Modern Physics Letters B, 35(31), 2150477, (2021).
Durur, H., Yokuş, A. and Yavuz, M. Behavior analysis and asymptotic stability of the traveling wave solution of the Kaup-Kupershmidt equation for conformable derivative. In Fractional Calculus: New Applications in Understanding Nonlinear Phenomena (Vol. 3) pp. 162-185, (2022).
Joshi, H., Yavuz, M. and Stamova, I. Analysis of the disturbance effect in intracellular calcium dynamic on fibroblast cells with an exponential kernel law. Bulletin of Biomathematics, 1(1), 24-39, (2023).
Rashid, S., Jarad, F., Alsubaie, H., Aly, A.A. and Alotaibi, A. A novel numerical dynamics of fractional derivatives involving singular and nonsingular kernels: designing a stochastic cholera epidemic model. AIMS Mathematics, 8(2), 3484-3522, (2023).
Baleanu, D., Jajarmi, A., Mohammadi, H. and Rezapour, S. A new study on the mathematical modelling of human liver with Caputo–Fabrizio fractional derivative. Chaos, Solitons and Fractals, 134, 109705, (2020).
Losada, J. and Nieto, J.J. Properties of a new fractional derivative without singular kernel. Progress in Fractional Differentiation and Applications, 1(2), 87-92, (2015).
Eustace, K.A., Osman, S. and Wainaina, M. Mathematical modelling and analysis of the dynamics of cholera. Global Journal of Pure and Applied Mathematics, 14(9), 1259-1275, (2018).
Atangana, A. and Owolabi, K.M. New numerical approach for fractional differential equations. Mathematical Modelling of Natural Phenomena, 13(1), 3, (2018).
Evirgen, F., Uçar, E., Uçar, S. and Özdemir, N. Modelling influenza A disease dynamics under Caputo-Fabrizio fractional derivative with distinct contact rates. Mathematical Modelling and Numerical Simulation with Applications, 3(1), 58-72, (2023).

Toplam 42 adet kaynakça vardır.

Ayrıntılar

Birincil Dil	İngilizce
Konular	Biyoinformatik ve Hesaplamalı Biyoloji, Biyolojik Matematik
Bölüm	Araştırma Makalesi
Yazarlar	Idris Ahmed 0000-0003-0901-1673 Ali Akgül 0000-0001-9832-1424 Fahd Jarad 0000-0002-3303-0623 Poom Kumam 0000-0002-5463-4581 Kamsing Nonlaopon 0000-0002-7469-5402
Erken Görünüm Tarihi	30 Haziran 2023
Yayımlanma Tarihi	30 Haziran 2023
Gönderilme Tarihi	5 Mayıs 2023
Yayımlandığı Sayı	Yıl 2023 Cilt: 3 Sayı: 2

Kaynak Göster

APA	Ahmed, I., Akgül, A., Jarad, F., Kumam, P., vd. (2023). A Caputo-Fabrizio fractional-order cholera model and its sensitivity analysis. Mathematical Modelling and Numerical Simulation With Applications, 3(2), 170-187. https://doi.org/10.53391/mmnsa.1293162