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Journal of Environmental Accounting and Management
António Mendes Lopes (editor), Jiazhong Zhang(editor)
António Mendes Lopes (editor)

University of Porto, Portugal


Jiazhong Zhang (editor)

School of Energy and Power Engineering, Xi'an Jiaotong University, Xi'an, Shaanxi Province 710049, China

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Existence and Uniqueness of Climate-Based Periodic Chikungunya Fractional Order Model with Incubation Period

Journal of Environmental Accounting and Management 10(1) (2022) 19--30 | DOI:10.5890/JEAM.2022.03.003

J. Dianavinnarasi, J.Jency Mariyal , A. Pratap

Department of Mathematics, Alagappa University, Karaikudi-630 004, India

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Chikungunya fever is caused by CHIKV, which uses the Aedes albopictus and Aedes aegypti mosquito population as a vector. According to WHO, mosquito-borne diseases cause millions of deaths. In this paper, the existence and uniqueness results of the temperature dependent Chikungunya virus dynamical model using fractional calculus and some fixed point theorems are derived. The Caputo-Fabrizio operator without singular kernel is used to obtain the solution of the proposed model.


  1. [1] Caputo, M. and Fabrizio, M. (2015), A new definition of fractional derivative without singular kernel, Progr. Fract. Differ. Appl., 1, 73-85.
  2. [2] Dumont, Y., Chiroleu, F., and Domerg, C. (2008), On a temporal model for the Chikungunya disease: modeling, theory and numerics, Math. Biosci., 213(1), 80-91.
  3. [3] nia, Tong and Ng, (2009)]{3} Kam, Y.W., Ong, E.K.S., R{e}nia, L., Tong, J.C. and Ng, L.F.P. (2009), Immuno-biology of Chikungunya and implications for disease intervention, Microbes Infect., 11(14), 1186-1196.
  4. [4]  Kaur, N., Jain, J., Kumar, A., Narang, M., Zakaria, M.K., Marcello, A., Kumar, D., Gaind, R., and Sunil, S. (2017), Chikungunya outbreak in Delhi, India, 2016: report on coinfection status and comorbid conditions in patients, New Microbes New Infec., 20, 39-42.
  5. [5]  Losada, J. and Nieto, J.J. (2015), Properties of the new fractional derivative without singular kernel, Progr. Fract.Differ. Appl., 1, 87-92.
  6. [6]  Nunes, M.R.T., Faria, N.R., Vasconcelos, J.M.D., Golding, N., Kraemer, M.U., Oliveira, L.F.D., Silva, D.E.A.D., Silva, E.V.P.D., and Silva, S.P.D. (2015), Emergence and potential for spread of Chikungunya virus in Brazil, BMC Med., 13(1), 1-11.
  7. [7]  Powers, A.M., Brault, A.C., Tesh, R.B. and Weaver, S.C. (2000), Re-emergence of Chikungunya and O'nyong-nyong viruses: evidence for distinct geographical lineages and distant evolutionary relationships, J. Gen. Virol., 81(2), 471-479.
  8. [8]  Rezza, G., Nicoletti, L., Angelini, R., Romi, R., Finarelli, A.C., Panning, M., Cordioli, P., Fortuna, C., Boros, S., and Magurano, F. (2007), Infection with Chikungunya virus in Italy: an outbreak in a temperate region, Lancet, 370(9602), 1840-1846.
  9. [9]  Sergon, K., Yahaya, A.A., Brown, J., Bedja, S.A., Mlindasse, M., Agata, N., Allaranger, Y., Ball, M.D., and Powers, A.M. (2007), Seroprevalence of Chikungunya virus infection on Grande Comore Island, Union of the Comoros, Am. J. Trop. Med. Hyg., 76(6), 1189-1193.
  10. [10]  Sergon, K., Njuguna, C., Kalani, R., Ofula, V., Onyango, C., Konongoi, L.S., Bedno, S., Burke, H., Dumilla, A.M., and Konde, J. (2008), Seroprevalence of Chikungunya virus (CHIKV) infection on Lamu Island, Kenya, October 2004, Am. J. Trop. Med. Hyg., 78(2), 333-337.
  11. [11]  Simon, F., Javelle, E., Oliver, M., Leparcgoffart, I., and Marimoutou, C. (2011), Chikungunya virus infection, Curr. Infect. Dis. Rep., 13(3), 218-228.
  12. [12]  Thiberville, S.D., Moyen, N., Dupuis-Maguiraga, L., Nougairede, A., Gould, E.A., Roques, P., and Lamballerie, X.D. (2013), Chikungunya fever: epidemiology, clinical syndrome, pathogenesis and therapy, Antiviral Res., 99(3), 345-370.
  13. [13]  Weaver, S.C. (2006), Evolutionary influences in arboviral disease, Curr. Top. Microbiol. Immunol., 299(2), 285-314.
  14. [14]  WHO(Accessed 24 January 2019),Chikungunya,