Research Article
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Year 2023, Volume: 3 Issue: 2, 170 - 187, 30.06.2023
https://doi.org/10.53391/mmnsa.1293162

Abstract

References

  • 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

Year 2023, Volume: 3 Issue: 2, 170 - 187, 30.06.2023
https://doi.org/10.53391/mmnsa.1293162

Abstract

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.

References

  • 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).
There are 42 citations in total.

Details

Primary Language English
Subjects Bioinformatics and Computational Biology, Biological Mathematics
Journal Section Research Articles
Authors

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

Early Pub Date June 30, 2023
Publication Date June 30, 2023
Submission Date May 5, 2023
Published in Issue Year 2023 Volume: 3 Issue: 2

Cite

APA Ahmed, I., Akgül, A., Jarad, F., Kumam, P., et al. (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


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