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Eradication Suggestions For Infectious Diseases Based on the Fractional Guinea-Worm Disease Model

Year 2024, Volume: 45 Issue: 2, 343 - 351, 30.06.2024

Bahar Acay Öztürk

https://doi.org/10.17776/csj.1380228

Abstract

Guine-worm disease (GWD) is considered one of the most fascinating infectious diseases that almost no one is aware of. On the other hand, unfortunately, there is no medicine or vaccine to treat this tropical disease transmitted through drinking water. However, GWD is about to be miraculously eradicated. This feature makes it the first parasitic disease to be eradicated without biomedical interventions. Accordingly, this situation brings the question: How can a disease be eradicated without medicine, vaccine or immunity? In light of this question, the current study offers recommendations on how to stop the spread of infectious diseases. One of the best ways to eliminate existing diseases is to benefit from the strategies followed for diseases that have been eradicated. Our results obtained by utilizing the fractional Caputo derivative show that behavior change programs aimed at reducing or stopping the spread of infectious diseases are effective tools in eradicating the disease

Keywords

Caputo fractional operator Fractional modeling Guinea-worm disease Non-local derivative Mathematical biology

References

  • [1] Kilbas, A. A., Srivastava, H. M., Trujillo, J. J., Theory and Applications of Fractional Differential Equations, Elsevier, (2006) 1-523.
  • [2] Podlubny, I. Fractional Differential Equations: An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of their Solution and Some of their Applications, Elsevier, (1998) 1-340.
  • [3] Gu, Y., Khan, M., Zarin, R., Khan, A., Yusuf, A., Humphries, U. W., Mathematical Analysis of a New Nonlinear Dengue Epidemic Model via Deterministic and Fractional Approach, Alex. Eng. J., 67 (2023) 1-21.
  • [4] Smith, R., Modelling Disease Ecology with Mathematics, Springfield: American Institute of Mathematical Sciences, (2008).
  • [5] Mandal, S., Sarkar, R. R., Sinha, S., Mathematical Models of Malaria-a Review, Malaria J., 10(1) (2011) 1-19.
  • [6] Hethcote, H. W., The Mathematics of Infectious Diseases, SIAM review, 42(4) (2000) 599-653.
  • [7] Brauer, F., Compartmental models in epidemiology, Mathematical Epidemiology, (2008) 19-79.
  • [8] Cohen, J. M., “Remarkable Solutions to Impossible Problems”: Lessons for Malaria from the Eradication of Smallpox, Malaria J., 18 (2019) 1-16.
  • [9] Bernoulli, D., Blower, S., An Attempt at a New Analysis of the Mortality Caused by Smallpox and of the Advantages of Inoculation to Prevent it, Rev. Med. Virol., 14(5) (2004) 275.
  • [10] Gonzalez-Silva, M., Rabinovich, N. R., Some Lessons for Malaria from the Global Polio Eradication Initiative, Malaria J., 20(1) (2021) 210.
  • [11] Mustapha, U. T., Qureshi, S., Yusuf, A., Hincal, E., Fractional modeling for the spread of Hookworm infection under Caputo operator, Chaos, Solitons Fract., 137 (2023) 109878.
  • [12] Berhe, H. W., Qureshi, S., Shaikh, A. A., Deterministic Modeling of Dysentery Diarrhea Epidemic under Fractional Caputo Differential Operator via Real Statistical Analysis, Chaos, Solitons Fract., 131 (2020) 109536.
  • [13] Qureshi, S., Yusuf, A., Mathematical Modeling for the Impacts of Deforestation on Wildlife Species Using Caputo Differential Operator, Chaos, Solitons Fract., 126 (2019) 32-40.
  • [14] Acay, B., Inc, M., Khan, A., Yusuf, A., Fractional Methicillin-Resistant Staphylococcus Aureus Infection Model under Caputo Operator, J. Appl. Math. Comput., 67(1-2) (2021) 755-783.
  • [15] Acay, B., Inc, M., Mustapha, U. T., Yusuf, A., Fractional Dynamics and Analysis for a Lana Fever Infectious Ailment with Caputo Operator, Chaos, Solitons Fract., 153 (2021) 111605.
  • [16] Inc, M., Acay, B., Berhe, H. W., Yusuf, A., Khan, A., Yao, S. W., Analysis of Novel Fractional COVID-19 Model with Real-Life Data Application, Results Phys., 23 (2021) 103968.
  • [17] Yusuf, A., Acay, B., Mustapha, U. T., Inc, M., Baleanu, D., Mathematical Modeling of Pine Wilt Disease with Caputo Fractional Operator. Chaos, Solitons Fract., 143 (2021) 110569.
  • [18] Jena, R. M., Chakraverty, S., Yavuz, M., Abdeljawad, T., A New Modeling and Existence–Uniqueness Analysis for Babesiosis Disease of Fractional Order, Mod. Phys. Lett. B, 35(30) (2021) 2150443.
  • [19] Johansyah, M. D., Sambas, A., Qureshi, S., Zheng, S., Abed-Elhameed, T. M., Vaidyanathan, S., Sulaiman, I. M., Investigation of the Hyperchaos and Control in the Fractional Order Financial System with Profit Margin, Partial Differ. Equ. Appl. Math., (2024) 100612.
  • [20] Şenol, M., Gençyiğit, M., Koksal, M. E., Qureshi, S., New Analytical and Numerical Solutions to the (2+ 1)-Dimensional Conformable cpKP–BKP Equation Arising in Fluid Dynamics, plasma physics, and nonlinear optics, Opt. Quant. Electron., 56(3) (2024) 352.
  • [21] Awadalla, M., Alahmadi, J., Cheneke, K. R., Qureshi, S., Fractional Optimal Control Model and Bifurcation Analysis of Human Syncytial Respiratory Virus Transmission Dynamics, Fractal Fract., 8(1) (2024) 44.
  • [22] Qureshi, S., Argyros, I. K., Soomro, A., Gdawiec, K., Shaikh, A. A., Hincal, E., A New Optimal Root-Finding Iterative Algorithm: Local and Semilocal Analysis With Polynomiography, Numer. Algorithms, (2023) 1-31.
  • [23] Abdulganiy, R. I., Ramos, H., Osilagun, J. A., Okunuga, S. A., Qureshi, S., A Functionally-Fitted Block Hybrid Falkner Method for Kepler Equations and Related Problems, Comput. and Appl. Math., 42(8) (2023) 327.
  • [24] Qureshi, S., Soomro, A., Naseem, A., Gdawiec, K., Argyros, I. K., Alshaery, A. A., Secer, A., From Halley to Secant: Redefining root finding with memory‐based methods including convergence and stability, Math. Method Appl. Sci., 7(47) (2024) 5509-5531.
  • [25] Evirgen, F., Esmehan, U. Ç. A. R., Sümeyra, U. Ç. A. R., 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) (2023) 58-72.
  • [26] ur Rahman, M., Arfan, M., Baleanu, D., Piecewise Fractional Analysis of the Migration Effect in Plant-Pathogen-Herbivore Interactions, Bull. Math. Biol., 1(1) (2023) 1-23.
  • [27] Joshi, H., Yavuz, M., Transition Dynamics Between a Novel Coinfection Model of Fractional-Order for COVID-19 and Tuberculosis via a Treatment Mechanism, Eur. Phys. J. Plus., 138(5) (2023) 468.

Year 2024, Volume: 45 Issue: 2, 343 - 351, 30.06.2024

Bahar Acay Öztürk

https://doi.org/10.17776/csj.1380228

Abstract

References

  • [1] Kilbas, A. A., Srivastava, H. M., Trujillo, J. J., Theory and Applications of Fractional Differential Equations, Elsevier, (2006) 1-523.
  • [2] Podlubny, I. Fractional Differential Equations: An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of their Solution and Some of their Applications, Elsevier, (1998) 1-340.
  • [3] Gu, Y., Khan, M., Zarin, R., Khan, A., Yusuf, A., Humphries, U. W., Mathematical Analysis of a New Nonlinear Dengue Epidemic Model via Deterministic and Fractional Approach, Alex. Eng. J., 67 (2023) 1-21.
  • [4] Smith, R., Modelling Disease Ecology with Mathematics, Springfield: American Institute of Mathematical Sciences, (2008).
  • [5] Mandal, S., Sarkar, R. R., Sinha, S., Mathematical Models of Malaria-a Review, Malaria J., 10(1) (2011) 1-19.
  • [6] Hethcote, H. W., The Mathematics of Infectious Diseases, SIAM review, 42(4) (2000) 599-653.
  • [7] Brauer, F., Compartmental models in epidemiology, Mathematical Epidemiology, (2008) 19-79.
  • [8] Cohen, J. M., “Remarkable Solutions to Impossible Problems”: Lessons for Malaria from the Eradication of Smallpox, Malaria J., 18 (2019) 1-16.
  • [9] Bernoulli, D., Blower, S., An Attempt at a New Analysis of the Mortality Caused by Smallpox and of the Advantages of Inoculation to Prevent it, Rev. Med. Virol., 14(5) (2004) 275.
  • [10] Gonzalez-Silva, M., Rabinovich, N. R., Some Lessons for Malaria from the Global Polio Eradication Initiative, Malaria J., 20(1) (2021) 210.
  • [11] Mustapha, U. T., Qureshi, S., Yusuf, A., Hincal, E., Fractional modeling for the spread of Hookworm infection under Caputo operator, Chaos, Solitons Fract., 137 (2023) 109878.
  • [12] Berhe, H. W., Qureshi, S., Shaikh, A. A., Deterministic Modeling of Dysentery Diarrhea Epidemic under Fractional Caputo Differential Operator via Real Statistical Analysis, Chaos, Solitons Fract., 131 (2020) 109536.
  • [13] Qureshi, S., Yusuf, A., Mathematical Modeling for the Impacts of Deforestation on Wildlife Species Using Caputo Differential Operator, Chaos, Solitons Fract., 126 (2019) 32-40.
  • [14] Acay, B., Inc, M., Khan, A., Yusuf, A., Fractional Methicillin-Resistant Staphylococcus Aureus Infection Model under Caputo Operator, J. Appl. Math. Comput., 67(1-2) (2021) 755-783.
  • [15] Acay, B., Inc, M., Mustapha, U. T., Yusuf, A., Fractional Dynamics and Analysis for a Lana Fever Infectious Ailment with Caputo Operator, Chaos, Solitons Fract., 153 (2021) 111605.
  • [16] Inc, M., Acay, B., Berhe, H. W., Yusuf, A., Khan, A., Yao, S. W., Analysis of Novel Fractional COVID-19 Model with Real-Life Data Application, Results Phys., 23 (2021) 103968.
  • [17] Yusuf, A., Acay, B., Mustapha, U. T., Inc, M., Baleanu, D., Mathematical Modeling of Pine Wilt Disease with Caputo Fractional Operator. Chaos, Solitons Fract., 143 (2021) 110569.
  • [18] Jena, R. M., Chakraverty, S., Yavuz, M., Abdeljawad, T., A New Modeling and Existence–Uniqueness Analysis for Babesiosis Disease of Fractional Order, Mod. Phys. Lett. B, 35(30) (2021) 2150443.
  • [19] Johansyah, M. D., Sambas, A., Qureshi, S., Zheng, S., Abed-Elhameed, T. M., Vaidyanathan, S., Sulaiman, I. M., Investigation of the Hyperchaos and Control in the Fractional Order Financial System with Profit Margin, Partial Differ. Equ. Appl. Math., (2024) 100612.
  • [20] Şenol, M., Gençyiğit, M., Koksal, M. E., Qureshi, S., New Analytical and Numerical Solutions to the (2+ 1)-Dimensional Conformable cpKP–BKP Equation Arising in Fluid Dynamics, plasma physics, and nonlinear optics, Opt. Quant. Electron., 56(3) (2024) 352.
  • [21] Awadalla, M., Alahmadi, J., Cheneke, K. R., Qureshi, S., Fractional Optimal Control Model and Bifurcation Analysis of Human Syncytial Respiratory Virus Transmission Dynamics, Fractal Fract., 8(1) (2024) 44.
  • [22] Qureshi, S., Argyros, I. K., Soomro, A., Gdawiec, K., Shaikh, A. A., Hincal, E., A New Optimal Root-Finding Iterative Algorithm: Local and Semilocal Analysis With Polynomiography, Numer. Algorithms, (2023) 1-31.
  • [23] Abdulganiy, R. I., Ramos, H., Osilagun, J. A., Okunuga, S. A., Qureshi, S., A Functionally-Fitted Block Hybrid Falkner Method for Kepler Equations and Related Problems, Comput. and Appl. Math., 42(8) (2023) 327.
  • [24] Qureshi, S., Soomro, A., Naseem, A., Gdawiec, K., Argyros, I. K., Alshaery, A. A., Secer, A., From Halley to Secant: Redefining root finding with memory‐based methods including convergence and stability, Math. Method Appl. Sci., 7(47) (2024) 5509-5531.
  • [25] Evirgen, F., Esmehan, U. Ç. A. R., Sümeyra, U. Ç. A. R., 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) (2023) 58-72.
  • [26] ur Rahman, M., Arfan, M., Baleanu, D., Piecewise Fractional Analysis of the Migration Effect in Plant-Pathogen-Herbivore Interactions, Bull. Math. Biol., 1(1) (2023) 1-23.
  • [27] Joshi, H., Yavuz, M., Transition Dynamics Between a Novel Coinfection Model of Fractional-Order for COVID-19 and Tuberculosis via a Treatment Mechanism, Eur. Phys. J. Plus., 138(5) (2023) 468.
There are 27 citations in total.

Details

Primary Language English
Subjects Numerical Solution of Differential and Integral Equations, Biological Mathematics
Journal Section Natural Sciences
Authors

Bahar Acay Öztürk 0000-0002-2350-4872

Publication Date June 30, 2024
Submission Date October 23, 2023
Acceptance Date February 26, 2024
Published in Issue Year 2024Volume: 45 Issue: 2

Cite

APA Acay Öztürk, B. (2024). Eradication Suggestions For Infectious Diseases Based on the Fractional Guinea-Worm Disease Model. Cumhuriyet Science Journal, 45(2), 343-351. https://doi.org/10.17776/csj.1380228
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