IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v140y2020ics0960077920306536.html
   My bibliography  Save this article

Complex dynamics in susceptible-infected models for COVID-19 with multi-drug resistance

Author

Listed:
  • Matouk, A.E.

Abstract

Nowadays, exploring complex dynamic of epidemic models becomes a focal point for research after the outbreak of COVID-19 pandemic which has no vaccine or fully approved drug treatment up till now. Hence, complex dynamics in a susceptible-infected (SI) model for COVID-19 with multi-drug resistance (MDR) and its fractional-order counterpart are investigated. Existence of positive solution in fractional-order model is discussed. Local stability based on the fractional Routh-Hurwitz (FRH) conditions is considered. Also, new FRH conditions are introduced and proved for the fractional case (0,2]. All these FRH conditions are also applied to discuss local stability of the multi-drug resistance steady states. Chaotic attractors are also found in this model for both integer-order and fractional-order cases. Numerical tools such as Lyapunov exponents, Lyapunov spectrum and bifurcation diagrams are employed to confirm existence of these complex dynamics. This study helps to understand complex behaviors and predict spread of severe infectious diseases such as COVID-19.

Suggested Citation

  • Matouk, A.E., 2020. "Complex dynamics in susceptible-infected models for COVID-19 with multi-drug resistance," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    • Handle: RePEc:eee:chsofr:v:140:y:2020:i:c:s0960077920306536
    DOI: 10.1016/j.chaos.2020.110257
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077920306536
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2020.110257?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Cooper, Ian & Mondal, Argha & Antonopoulos, Chris G., 2020. "A SIR model assumption for the spread of COVID-19 in different communities," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    2. Bagal, Dilip Kumar & Rath, Arati & Barua, Abhishek & Patnaik, Dulu, 2020. "Estimating the parameters of susceptible-infected-recovered model of COVID-19 cases in India during lockdown periods," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    3. Ullah, Saif & Khan, Muhammad Altaf, 2020. "Modeling the impact of non-pharmaceutical interventions on the dynamics of novel coronavirus with optimal control analysis with a case study," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    4. Ghanbari, Behzad, 2020. "On forecasting the spread of the COVID-19 in Iran: The second wave," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    5. A. E. Matouk, 2009. "Chaos Synchronization between Two Different Fractional Systems of Lorenz Family," Mathematical Problems in Engineering, Hindawi, vol. 2009, pages 1-11, May.
    6. Soukhovolsky, Vladislav & Kovalev, Anton & Pitt, Anne & Kessel, Boris, 2020. "A new modelling of the COVID 19 pandemic," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    7. Alkahtani, Badr Saad T. & Alzaid, Sara Salem, 2020. "A novel mathematics model of covid-19 with fractional derivative. Stability and numerical analysis," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    8. Al-khedhairi, A. & Matouk, A.E. & Khan, I., 2019. "Chaotic dynamics and chaos control for the fractional-order geomagnetic field model," Chaos, Solitons & Fractals, Elsevier, vol. 128(C), pages 390-401.
    9. Yadav, Ram Prasad & Renu Verma,, 2020. "A numerical simulation of fractional order mathematical modeling of COVID-19 disease in case of Wuhan China," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    10. Salgotra, Rohit & Gandomi, Mostafa & Gandomi, Amir H., 2020. "Evolutionary modelling of the COVID-19 pandemic in fifteen most affected countries," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    11. Reis, Ruy Freitas & de Melo Quintela, Bárbara & de Oliveira Campos, Joventino & Gomes, Johnny Moreira & Rocha, Bernardo Martins & Lobosco, Marcelo & Weber dos Santos, Rodrigo, 2020. "Characterization of the COVID-19 pandemic and the impact of uncertainties, mitigation strategies, and underreporting of cases in South Korea, Italy, and Brazil," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).
    12. Annas, Suwardi & Isbar Pratama, Muh. & Rifandi, Muh. & Sanusi, Wahidah & Side, Syafruddin, 2020. "Stability analysis and numerical simulation of SEIR model for pandemic COVID-19 spread in Indonesia," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    13. Mahajan, Ashutosh & Sivadas, Namitha A & Solanki, Ravi, 2020. "An epidemic model SIPHERD and its application for prediction of the spread of COVID-19 infection in India," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    14. Atangana, Abdon, 2018. "Non validity of index law in fractional calculus: A fractional differential operator with Markovian and non-Markovian properties," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 688-706.
    15. Bekiros, Stelios & Kouloumpou, Dimitra, 2020. "SBDiEM: A new mathematical model of infectious disease dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).
    16. Sarkar, Kankan & Khajanchi, Subhas & Nieto, Juan J., 2020. "Modeling and forecasting the COVID-19 pandemic in India," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    17. Samui, Piu & Mondal, Jayanta & Khajanchi, Subhas, 2020. "A mathematical model for COVID-19 transmission dynamics with a case study of India," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    18. Mohammad, Mutaz & Trounev, Alexander, 2020. "On the dynamical modeling of COVID-19 involving Atangana–Baleanu fractional derivative and based on Daubechies framelet simulations," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    19. Zhang, Zizhen, 2020. "A novel covid-19 mathematical model with fractional derivatives: Singular and nonsingular kernels," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    20. Chimmula, Vinay Kumar Reddy & Zhang, Lei, 2020. "Time series forecasting of COVID-19 transmission in Canada using LSTM networks," Chaos, Solitons & Fractals, Elsevier, vol. 135(C).
    21. Zhang, Zizhen & Jain, Sonal, 2020. "Mathematical model of Ebola and Covid-19 with fractional differential operators: Non-Markovian process and class for virus pathogen in the environment," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    22. Khan, Firdos & Saeed, Alia & Ali, Shaukat, 2020. "Modelling and forecasting of new cases, deaths and recover cases of COVID-19 by using Vector Autoregressive model in Pakistan," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    23. Papo, David & Righetti, Marco & Fadiga, Luciano & Biscarini, Fabio & Zanin, Massimiliano, 2020. "A minimal model of hospital patients’ dynamics in COVID-19," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    24. Ndaïrou, Faïçal & Area, Iván & Nieto, Juan J. & Torres, Delfim F.M., 2020. "Mathematical modeling of COVID-19 transmission dynamics with a case study of Wuhan," Chaos, Solitons & Fractals, Elsevier, vol. 135(C).
    25. Bozkurt, Fatma & Yousef, Ali & Baleanu, Dumitru & Alzabut, Jehad, 2020. "A mathematical model of the evolution and spread of pathogenic coronaviruses from natural host to human host," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    26. Asamoah, Joshua Kiddy K. & Owusu, Mark A. & Jin, Zhen & Oduro, F. T. & Abidemi, Afeez & Gyasi, Esther Opoku, 2020. "Global stability and cost-effectiveness analysis of COVID-19 considering the impact of the environment: using data from Ghana," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    27. Kaxiras, Efthimios & Neofotistos, Georgios & Angelaki, Eleni, 2020. "The first 100 days: Modeling the evolution of the COVID-19 pandemic," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    28. Mandal, Manotosh & Jana, Soovoojeet & Nandi, Swapan Kumar & Khatua, Anupam & Adak, Sayani & Kar, T.K., 2020. "A model based study on the dynamics of COVID-19: Prediction and control," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).
    29. Atangana, Abdon, 2020. "Modelling the spread of COVID-19 with new fractal-fractional operators: Can the lockdown save mankind before vaccination?," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).
    30. Croccolo, Fabrizio & Roman, H. Eduardo, 2020. "Spreading of infections on random graphs: A percolation-type model for COVID-19," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    31. Tuan, Nguyen Huy & Mohammadi, Hakimeh & Rezapour, Shahram, 2020. "A mathematical model for COVID-19 transmission by using the Caputo fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    32. Basu, Sayantani & Campbell, Roy H., 2020. "Going by the numbers : Learning and modeling COVID-19 disease dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    33. Ahmed, E. & Elgazzar, A.S., 2007. "On fractional order differential equations model for nonlocal epidemics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 379(2), pages 607-614.
    34. Wang, Peipei & Zheng, Xinqi & Li, Jiayang & Zhu, Bangren, 2020. "Prediction of epidemic trends in COVID-19 with logistic model and machine learning technics," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    35. Higazy, M., 2020. "Novel fractional order SIDARTHE mathematical model of COVID-19 pandemic," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    36. Okuonghae, D. & Omame, A., 2020. "Analysis of a mathematical model for COVID-19 population dynamics in Lagos, Nigeria," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    37. Lee, Chaeyoung & Li, Yibao & Kim, Junseok, 2020. "The susceptible-unidentified infected-confirmed (SUC) epidemic model for estimating unidentified infected population for COVID-19," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    38. Fredj, Haifa Ben & Chérif, Farouk, 2020. "Novel Corona virus disease infection in Tunisia: Mathematical model and the impact of the quarantine strategy," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    39. Huang, Yubo & Wu, Yan & Zhang, Weidong, 2020. "Comprehensive identification and isolation policies have effectively suppressed the spread of COVID-19," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    40. Atangana, Abdon & Gómez-Aguilar, J.F., 2018. "Fractional derivatives with no-index law property: Application to chaos and statistics," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 516-535.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Collen Zalengera & Maxon L. Chitawo & Isaac Chitedze & Long Seng To & Vincent Mwale & Kondwani T. Gondwe & Timeyo Maroyi, 2021. "Unbending the Winding Path of a Low-Income Country’s Energy Sector amid the COVID-19 Pandemic: Perspectives from Malawi," Energies, MDPI, vol. 14(21), pages 1-15, November.
    2. Nabin Sapkota & Atsuo Murata & Waldemar Karwowski & Mohammad Reza Davahli & Krzysztof Fiok & Awad M. Aljuaid & Tadeusz Marek & Tareq Ahram, 2022. "The Chaotic Behavior of the Spread of Infection during the COVID-19 Pandemic in Japan," IJERPH, MDPI, vol. 19(19), pages 1-16, October.
    3. Matouk, A.E. & Lahcene, Bachioua, 2023. "Chaotic dynamics in some fractional predator–prey models via a new Caputo operator based on the generalised Gamma function," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    4. Zhangbo Yang & Jiahao Zhang & Shanxing Gao & Hui Wang, 2022. "Complex Contact Network of Patients at the Beginning of an Epidemic Outbreak: An Analysis Based on 1218 COVID-19 Cases in China," IJERPH, MDPI, vol. 19(2), pages 1-17, January.
    5. Du, Yuxian & Lin, Xi & Pan, Ye & Chen, Zhaoxin & Xia, Huan & Luo, Qian, 2023. "Identifying influential airports in airline network based on failure risk factors with TOPSIS," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    6. Lee, Chaeyoung & Kwak, Soobin & Kim, Sangkwon & Hwang, Youngjin & Choi, Yongho & Kim, Junseok, 2021. "Robust optimal parameter estimation for the susceptible-unidentified infected-confirmed model," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).
    7. Hector Eduardo Roman & Fabrizio Croccolo, 2021. "Spreading of Infections on Network Models: Percolation Clusters and Random Trees," Mathematics, MDPI, vol. 9(23), pages 1-22, November.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Gandzha, I.S. & Kliushnichenko, O.V. & Lukyanets, S.P., 2021. "Modeling and controlling the spread of epidemic with various social and economic scenarios," Chaos, Solitons & Fractals, Elsevier, vol. 148(C).
    2. Khan, Hasib & Ahmad, Farooq & Tunç, Osman & Idrees, Muhammad, 2022. "On fractal-fractional Covid-19 mathematical model," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    3. Asamoah, Joshua Kiddy K. & Owusu, Mark A. & Jin, Zhen & Oduro, F. T. & Abidemi, Afeez & Gyasi, Esther Opoku, 2020. "Global stability and cost-effectiveness analysis of COVID-19 considering the impact of the environment: using data from Ghana," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    4. Cooper, Ian & Mondal, Argha & Antonopoulos, Chris G., 2020. "Dynamic tracking with model-based forecasting for the spread of the COVID-19 pandemic," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    5. Li, Tingting & Guo, Youming, 2022. "Optimal control and cost-effectiveness analysis of a new COVID-19 model for Omicron strain," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 606(C).
    6. Kumar Das, Dhiraj & Khatua, Anupam & Kar, T.K. & Jana, Soovoojeet, 2021. "The effectiveness of contact tracing in mitigating COVID-19 outbreak: A model-based analysis in the context of India," Applied Mathematics and Computation, Elsevier, vol. 404(C).
    7. Zhu, Cheng-Cheng & Zhu, Jiang, 2021. "Dynamic analysis of a delayed COVID-19 epidemic with home quarantine in temporal-spatial heterogeneous via global exponential attractor method," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    8. Kalantari, Mahdi, 2021. "Forecasting COVID-19 pandemic using optimal singular spectrum analysis," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    9. Hwang, Eunju, 2022. "Prediction intervals of the COVID-19 cases by HAR models with growth rates and vaccination rates in top eight affected countries: Bootstrap improvement," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    10. Crokidakis, Nuno, 2020. "COVID-19 spreading in Rio de Janeiro, Brazil: Do the policies of social isolation really work?," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).
    11. Ullah, Mohammad Sharif & Higazy, M. & Kabir, K.M. Ariful, 2022. "Dynamic analysis of mean-field and fractional-order epidemic vaccination strategies by evolutionary game approach," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    12. Ahmad, Shabir & Ullah, Aman & Arfan, Muhammad & Shah, Kamal, 2020. "On analysis of the fractional mathematical model of rotavirus epidemic with the effects of breastfeeding and vaccination under Atangana-Baleanu (AB) derivative," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    13. Rabih Ghostine & Mohamad Gharamti & Sally Hassrouny & Ibrahim Hoteit, 2021. "Mathematical Modeling of Immune Responses against SARS-CoV-2 Using an Ensemble Kalman Filter," Mathematics, MDPI, vol. 9(19), pages 1-13, September.
    14. Ahumada, M. & Ledesma-Araujo, A. & Gordillo, L. & Marín, J.F., 2023. "Mutation and SARS-CoV-2 strain competition under vaccination in a modified SIR model," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    15. Chatterjee, Amar Nath & Ahmad, Bashir, 2021. "A fractional-order differential equation model of COVID-19 infection of epithelial cells," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    16. Rabih Ghostine & Mohamad Gharamti & Sally Hassrouny & Ibrahim Hoteit, 2021. "An Extended SEIR Model with Vaccination for Forecasting the COVID-19 Pandemic in Saudi Arabia Using an Ensemble Kalman Filter," Mathematics, MDPI, vol. 9(6), pages 1-16, March.
    17. Khan, Muhammad Altaf & Atangana, Abdon, 2022. "Mathematical modeling and analysis of COVID-19: A study of new variant Omicron," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 599(C).
    18. Jelena Musulin & Sandi Baressi Šegota & Daniel Štifanić & Ivan Lorencin & Nikola Anđelić & Tijana Šušteršič & Anđela Blagojević & Nenad Filipović & Tomislav Ćabov & Elitza Markova-Car, 2021. "Application of Artificial Intelligence-Based Regression Methods in the Problem of COVID-19 Spread Prediction: A Systematic Review," IJERPH, MDPI, vol. 18(8), pages 1-39, April.
    19. Alberto Olivares & Ernesto Staffetti, 2021. "Optimal Control Applied to Vaccination and Testing Policies for COVID-19," Mathematics, MDPI, vol. 9(23), pages 1-22, December.
    20. Çaparoğlu, Ömer Faruk & Ok, Yeşim & Tutam, Mahmut, 2021. "To restrict or not to restrict? Use of artificial neural network to evaluate the effectiveness of mitigation policies: A case study of Turkey," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:140:y:2020:i:c:s0960077920306536. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.