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Analysis of a nonlinear fractional system for Zika virus dynamics with sexual transmission route under generalized Caputo-type derivative

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Abstract

This paper establishes a mathematical model of the Zika virus infection with the sexual transmission route under the generalized Caputo-type fractional derivative. The model consists of a system of eleven nonlinear fractional differential equations. The existence and uniqueness results are derived by applying Banach’s and Schaüder’s fixed point theorems. The different types of Ulam’s stability results for the fractional model are examined. The corrector-predictor algorithm has been applied to illustrate the approximated solutions and analyze the dynamical behavior of the fractional model under consideration. In addition, various numerical simulations are presented corresponding to different fractional-orders in \(\alpha \in [0,1]\).

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References

  1. Rezapour, S., Imran, A., Hussain, A., Martinez, F., Etemad, S., Kaabar, M.K.A.: Condensing functions and approximate endpoint criterion for the existence analysis of quantum integro-difference FBVPs. Symmetry 13(3), 469 (2021). https://doi.org/10.3390/sym13030469

    Article  Google Scholar 

  2. Matar, M.M., Abbas, M.I., Alzabut, J., Kaabar, M.K.A., Etemad, S., Rezapour, S.: Investigation of the p-Laplacian nonperiodic nonlinear boundary value problem via generalized Caputo fractional derivatives. Adv. Diff. Eq. 2021, 68 (2021). https://doi.org/10.1186/s13662-021-03228-9

    Article  MathSciNet  MATH  Google Scholar 

  3. Thabet, S.T.M., Etemad, S., Rezapour, S.: On a coupled Caputo conformable system of pantograph problems. Turkish J. Math. 45(1), 496–519 (2021). https://doi.org/10.3906/mat-2010-70

    Article  MathSciNet  MATH  Google Scholar 

  4. Baleanu, D., Etemad, S., Rezapour, S.: On a fractional hybrid integro-differential equation with mixed hybrid integral boundary value conditions by using three operators. Alexandria Eng. J. 59(5), 3019–3027 (2020). https://doi.org/10.1016/j.aej.2020.04.053

    Article  Google Scholar 

  5. Baleanu, D., Rezapour, S., Saberpour, Z.: On fractional integro-differential inclusions via the extended fractional Caputo-Fabrizio derivation. Boundary Value Prob. 2019, 79 (2019). https://doi.org/10.1186/s13661-019-1194-0

    Article  MathSciNet  Google Scholar 

  6. Aydogan, S.M., Baleanu, D., Mousalou, A., Rezapour, S.: On high order fractional integro-differential equations including the Caputo-Fabrizio derivative. Boundary Value Prob. 2018, 90 (2018). https://doi.org/10.1186/s13661-018-1008-9

    Article  MathSciNet  MATH  Google Scholar 

  7. Baleanu, D., Jajarmi, A., Mohammadi, H., Rezapour, S.: A new study on the mathematical modelling of human liver with Caputo-Fabrizio fractional derivative. Chaos, Solitons and Fractals 134,(2020). https://doi.org/10.1016/j.chaos.2020.109705

  8. Baleanu, D., Mohammadi, H., Rezapour, S.: Analysis of the model of HIV-1 infection of \(CD4^{+}\) T-cell with a new approach of fractional derivative. Adv. Diff. Eq. 2020, 71 (2020). https://doi.org/10.1186/s13662-020-02544-w

    Article  MathSciNet  MATH  Google Scholar 

  9. Baleanu, D., Mohammadi, H., Rezapour, S.: A fractional differential equation model for the COVID-19 transmission by using the Caputo-Fabrizio derivative. Adv. Diff. Eq. 2020, 299 (2020). https://doi.org/10.1186/s13662-020-02762-2

    Article  MathSciNet  MATH  Google Scholar 

  10. Baleanu, D., Etemad, S., Rezapour, S.: A hybrid Caputo fractional modeling for thermostat with hybrid boundary value conditions. Boundary Value Prob. 2020, 64 (2020). https://doi.org/10.1186/s13661-020-01361-0

    Article  MathSciNet  MATH  Google Scholar 

  11. Baleanu, D., Mohammadi, H., Rezapour, S.: A mathematical theoretical study of a particular system of Caputo-Fabrizio fractional differential equations for the Rubella disease model. Adv. Diff. Eq. 2020, 184 (2020). https://doi.org/10.1186/s13662-020-02614-z

    Article  MathSciNet  MATH  Google Scholar 

  12. Rabaan, A.A., Bazzi, A.M., Al-Ahmed, S.H., Al-Ghaith, M.M., Al-Tawfiq, J.A.: Overview of Zika infection, epidemiology, transmission and control measures. J. Infect. Public Health 10(2), 141–149 (2017). https://doi.org/10.1016/j.jiph.2016.05.007

    Article  Google Scholar 

  13. Kindhauser, M.K., Allen, T., Frank, V., Santhana, R.S., Dye, C.: Zika: the origin and spread of a mosquito-borne virus. Bull. World Health Organiz. 94(9), 675–686 (2016). https://doi.org/10.2471/BLT.16.171082

    Article  Google Scholar 

  14. Lanciotti, R.S., Kosoy, O.L., Laven, J.J., Velez, J.O., Lambert, A.J., Johnson, A.J., Stanfield, S.M., Duffy, M.R.: Genetic and serologic properties of Zika virus associated with an epidemic, Yap State, Micronesia, 2007. Emerg. Infect. Dis. 14(8), 1232–1239 (2008). https://doi.org/10.3201/eid1408.080287

    Article  Google Scholar 

  15. Musso, D., Roche, C., Robin, E., Nhan, T., Teissier, A., Cao-Lorneau, V.M.: Potential sexual transmission of zika virus. Emerg. Infect. Dis. 21(2), 359–361 (2015). https://doi.org/10.3201/eid2102.141363

    Article  Google Scholar 

  16. Besnard, M., Lastere, S., Teissier, A., Cao-Lormeau, V., Musso, D., Cao-Lorneau, V.M.: Evidence of perinatal transmission of zika virus, French Polynesia, December 2013 and February 2014. Euro Surv. 19(13), 20751 (2014). https://doi.org/10.2807/1560-7917.ES2014.19.13.20751

    Article  Google Scholar 

  17. Musso, D., Nhan, T., Roche, C., Bierlaire, D., Zisou, K., Shan Yan, A., Cao-Lorneau, V.M., Broult, J.: Potential for Zika virus transmission through blood transfusion demonstrated during an outbreak in French Polynesia, November 2013 to February 2014. Euro Surv. 19(14), 20761 (2014). https://doi.org/10.2807/1560-7917.ES2014.19.14.20761

    Article  Google Scholar 

  18. Calvet, G., Aguiar, R.S., Melo, A.S.O., Sampaio, S.A., de Filippis, I., Fabri, A., Araujo, E.S.M., de Sequeira, P.C., de Mendonça, M.C.L., ad D. A. Tschoeke, L.d., Schrago, C.G., Thompson, F.L., Brasil, P., Dos Santos, F.B., Nogueira, R.M.R., Tanuri, A., de Filippis, A.M.B.: Detection and sequencing of Zika virus from amniotic fluid of fetuses with microcephaly in Brazil: a case study. Lancet Infect. Dis. 16(6), 653–660 (2016). https://doi.org/10.1016/S1473-3099(16)00095-5

  19. Krauer, F., Riesen, M., Reveiz, L., Oladapo, O.T., Martinez-Vega, R., Porgo, T.V., Haefliger, A., Broutet, N.J., Low, N.: Zika virus infection as a cause of congenital brain abnormalities and Guillain-Barre syndrome: systematic review. Plos Med. 14(1), 5207634 (2017). https://doi.org/10.1371/journal.pmed.1002203

    Article  Google Scholar 

  20. Okyere, E., Olaniyi, S., Bonyah, E.: Mathematical model for Zika virus dynamics with sexual transmission route. Sci. African 9, 00532 (2020). https://doi.org/10.1016/j.sciaf.2020.e00532

    Article  Google Scholar 

  21. Danbaba, U., Garba, S.M.: Modeling the transmission dynamics of Zika with sterile insect technique. Math. Methods Appl. Sci. 41(18), 8871–8896 (2018). https://doi.org/10.1002/mma.5336

    Article  MathSciNet  MATH  Google Scholar 

  22. Bonyah, E., Khan, M.A., Okosun, K.O., Gomez-Aguitar, J.F.: On the co-infection of dengue fever and Zika virus. Optim. Control Appl. Methods 40(3), 394–421 (2019). https://doi.org/10.1002/oca.2483

    Article  MathSciNet  MATH  Google Scholar 

  23. Zhao, H., Wang, L., Oliva, S.M., Zhu, H.: Modeling and dynamics analysis of Zika transmission with limited medical resourses. Bull. Math. Biol. 8, 99 (2020). https://doi.org/10.1007/s11538-020-00776-1

    Article  MATH  Google Scholar 

  24. Alkahtani, B.S.T., Alzaid, S.S.: Stochastic mathematical model of Chikungunya spread with the global derivative. Result. Phys. 20, 103680 (2021). https://doi.org/10.1016/j.rinp.2020.103680

  25. Ali, Z., Rabiei, F., Shah, K., Khodadadi, T.: Qualitative analysis of fractal-fractional order COVID-19 mathematical model with case study of Wuhan. Alexandria Eng. J. 60(1), 477–489 (2021). https://doi.org/10.1016/j.aej.2020.09.020

    Article  Google Scholar 

  26. Razzaq, O.A., Rehman, D.U., Khan, N.A., Ahmadian, A., Ferrara, M.: Optimal surveillance mitigation of COVID-19 disease outbreak: fractional order optimal control of compartment model. Result. Phys. 20,(2021). https://doi.org/10.1016/j.rinp.2020.103715

  27. Ahmad, S., Ullah, R., Baleanu, D.: Mathematical analysis of tuberculosis control model using nonsingular kernel type Caputo derivative. Adv. Diff. Eq. 2021, 26 (2021). https://doi.org/10.1186/s13662-020-03191-x

    Article  MathSciNet  MATH  Google Scholar 

  28. Bonyah, E., Sagoe, A.K., Kumar, D., Deniz, S.: Fractional optimal control dynamics of coronavirus model with Mittag-Leffler law. Ecol. Complex. 45, 100880 (2021). https://doi.org/10.1016/j.ecocom.2020.100880

    Article  Google Scholar 

  29. Ali, Z., Rabiei, F., Shah, K., Khodadadi, T.: Fractal-fractional order dynamical behavior of an HIV/AIDS epidemic mathematical model. Eur. Phys. J. Plus 136, 36 (2021). https://doi.org/10.1140/epjp/s13360-020-00994-5

    Article  Google Scholar 

  30. Alrabaiah, H., Zeb, A., Alzahrani, E., Shah, K.: Dynamical analysis of fractional-order tobacco smoking model containing snuffing class. Alexandria Eng. J. 60(4), 3669–3678 (2021). https://doi.org/10.1016/j.aej.2021.02.005

    Article  Google Scholar 

  31. Deressa, C.T., Duressa, G.F.: Analysis of Atangana-Baleanu fractional-order SEAIR epidemic model with optimal control. Adv. Diff. Eq. 2021, 174 (2021). https://doi.org/10.1186/s13662-021-03334-8

    Article  MathSciNet  MATH  Google Scholar 

  32. Mohammadi, H., Kumar, S., Rezapour, S., Etemad, S.: A theoretical study of the Caputo-Fabrizio fractional modeling for hearing loss due to Mumps virus with optimal control. Chaos, Solitons and Fractals 144, 110668 (2021). https://doi.org/10.1016/j.chaos.2021.110668

    Article  MathSciNet  Google Scholar 

  33. Ucar, E., Ozdemir, N.: A fractional model of cancer-immune system with Caputo and Caputo-Fabrizio derivatives. Eur. Phys. J. Plus 136, 43 (2021). https://doi.org/10.1140/epjp/s13360-020-00966-9

    Article  Google Scholar 

  34. Zeb, A., Nazir, G., Shah, K., Alzahrani, E.: Theoretical and semi-analytical results to a biological model under Atangana-Baleanu-Caputo fractional derivative. Adv. Diff. Eq. 2020, 654 (2020). https://doi.org/10.1186/s13662-020-03117-7

    Article  MathSciNet  MATH  Google Scholar 

  35. Khan, S.A., Shah, K., Kumam, P., Seadawy, A., Zaman, G., Shah, Z.: Study of mathematical model of Hepatitis B under Caputo-Fabrizo derivative. AIMS Math.6(1), 195–209 (20201). https://doi.org/10.3934/math.2021013

  36. Abdeljawad, T., Jarad, F., Alzabut, J.: Fractional proportional differences with memory. Eur. Phys. J. Special Topic. 226, 3333–3354 (2017). https://doi.org/10.1140/epjst/e2018-00053-5

    Article  Google Scholar 

  37. Ahmad, M., Zada, A., Alzabut, J.: Hyers-Ulam stability of a coupled system of fractional differential equations of Hilfer-Hadamard type. Demonst. Math. 52(1), 283–295 (2019). https://doi.org/10.1515/dema-2019-0024

    Article  MathSciNet  MATH  Google Scholar 

  38. Dianavinnarasi, J., Raja, R., Alzabut, J., Cao, J., Niezabitowski, M., Bagdasar, O.: Application of Caputo-Fabrizio operator to suppress the Aedes Aegypti mosquitoes via Wolbachia: An LMI approach. Math. Comput. Simulat. (2021). https://doi.org/10.1016/j.matcom.2021.02.002

  39. Bozkurt, F., Yousef, A., Baleanu, D., Alzabut, J.: A mathematical model of the evolution and spread of pathogenic coronaviruses from natural host to human host. Chaos, Solitons and Fractals 138, 109931 (2020). https://doi.org/10.1016/j.chaos.2020.109931

    Article  MathSciNet  Google Scholar 

  40. Seemab, A., Ur-Rehman, M., Alzabut, J., Hamdi, A.: On the existence of positive solutions for generalized fractional boundary value problems. Boundary Value Prob. 2019, 186 (2019). https://doi.org/10.1186/s13661-019-01300-8

    Article  MathSciNet  Google Scholar 

  41. Pratap, A., Raja, R., Alzabut, J., Dianavinnarasi, J., Cao, J., Rajchakit, G.: Finite-time Mittag-Leffler stability of fractional-order quaternion-valued memristive neural networks with impulses. Neural Process. Lett. 51, 1485–1526 (2020). https://doi.org/10.1007/s11063-019-10154-1

    Article  Google Scholar 

  42. Iswarya, M., Raja, R., Rajchakit, G., Cao, J., Alzabut, J., Huang, C.: Existence, uniqueness and exponential stability of periodic solution for discrete-time delayed BAM neural networks based on coincidence degree theory and graph theoretic method. Mathematics 7(11), 1055 (2019). https://doi.org/10.3390/math7111055

    Article  Google Scholar 

  43. Akinyemi, L., Iyiola, O.S.: Exact and approximate solutions of time-fractional models arising from physics via Shehu transform. Math. Methods Appl. Sci. 43(12), 7442–7464 (2020). https://doi.org/10.1002/mma.6484

    Article  MathSciNet  MATH  Google Scholar 

  44. Owusu-Mensah, I., Akinyemi, L., Oduro, B., Iyiola, O.S.: A fractional order approach to modeling and simulations of the novel COVID-19. Adv. Diff. Eq. 2020, 683 (2021). https://doi.org/10.1186/s13662-020-03141-7

    Article  MathSciNet  MATH  Google Scholar 

  45. Iyiola, O.S., Oduro, B., Akinyemi, L.: Analysis and solutions of generalized Chagas vectors re-infestation model of fractional order type. Chaos, Solitons and Fractals 145, 110797 (2021). https://doi.org/10.1016/j.chaos.2021.110797

    Article  MathSciNet  Google Scholar 

  46. Akinyemi, L., Senol, M., Huseen, S.N.: Modified homotopy methods for generalized fractional perturbed Zakharov-Kuznetsov equation in dusty plasma. Adv. Diff. Eq. 2021, 45 (2021). https://doi.org/10.1186/s13662-020-03208-5

    Article  MathSciNet  MATH  Google Scholar 

  47. Khalil, M., Arafa, A.A.M., Sayed, A.: A variable fractional order network model of Zika virus. J. Fract. Calculus Appl. 9(1), 204–221 (2018)

    MathSciNet  MATH  Google Scholar 

  48. Khan, M.A., Ullah, S., Farhan, M.: The dynamics of Zika virus with Caputo fractional derivative. AIMS Math. 4(1), 134–146 (2019). https://doi.org/10.3934/Math.2019.1.134

    Article  MathSciNet  MATH  Google Scholar 

  49. Rezapour, S., Mohammadi, H., Jajarmi, A.: A new mathematical model for Zika virus transmission. Adv. Diff. Eq. 2020, 589 (2020). https://doi.org/10.1186/s13662-020-03044-7

    Article  MathSciNet  MATH  Google Scholar 

  50. Erturk, V.S., Kumar, P.: Solution of a COVID-19 model via new generalized Caputo-type fractional derivatives. Chaos, Solitons and Fractals 139, 110280 (2020). https://doi.org/10.1016/j.chaos.2020.110280

    Article  MathSciNet  MATH  Google Scholar 

  51. Katugampola, U.N.: New approach to generalized fractional integral. Appl. Math. Comput. 218(3), 860–865 (2011). https://doi.org/10.1016/j.amc.2011.03.062

    Article  MathSciNet  MATH  Google Scholar 

  52. Katugampola, U.N.: A new approach to generalized fractional derivatives. Bull. Math. Anal. Appl. 6(4), 1–15 (2014)

    MathSciNet  MATH  Google Scholar 

  53. Odibat, Z., Baleanu, D.: Numerical simulation of initial value problems with generalized Caputo-type fractional derivatives. Appl. Numer. Math. 156, 94–105 (2020). https://doi.org/10.1016/j.apnum.2020.04.015

    Article  MathSciNet  MATH  Google Scholar 

  54. Li, C., Zeng, F.: The finite difference methods for fractional ordinary differential equations. Numer. Funct. Anal. Optim. 34(2), 149–179 (2013). https://doi.org/10.1080/01630563.2012.706673

    Article  MathSciNet  MATH  Google Scholar 

  55. Zhao, X.Q.: Dynamical Systems in Population Biology. Springer, Cham, Baltimore (2017). https://doi.org/10.1007/978-3-319-56433-3

  56. Deimling, K.: Multi-valued Differential Equations. Walter de Gruyter, Berlin (1992)

    Book  MATH  Google Scholar 

  57. Granas, A., Dugundji, J.: Fixed Point Theory. Springer, New York (2003)

    Book  MATH  Google Scholar 

  58. Rus, I.A.: Ulam stabilities of ordinary differential equations in a Banach space. Carpathian J. Math. 26(1), 103–107 (2010). https://www.jstor.org/stable/43999438

  59. Wikipedia: List of sovereign states and dependent territories by birth rate. https://en.wikipedia.org/wiki/List\_of\_sovereign\_states\_and\_dependent\_territories\_by\_birth\_rate accessed 01.02.16 (2015)

  60. Dumont, Y., Chiroleu, Y.F., Domerg, C.: On a temporal model for the Chikungunya disease: modeling, theory and numerics. Math. Biosci. 213(1), 80–91 (2008). https://doi.org/10.1016/j.mbs.2008.02.008

    Article  MathSciNet  MATH  Google Scholar 

  61. Dumont, Y., Chiroleu, Y.F.: Vector control for the Chikungunya disease. Math. Biosci. Eng. 7(2), 313–345 (2010). https://doi.org/10.3934/mbe.2010.7.313

    Article  MathSciNet  MATH  Google Scholar 

  62. Manore, C., Hickmann, J., Xu, J.S., Wearing, H., Hyman, J.: Comparing Dengue and Chikungunya emergence and endemic transmission in A. aegypti and A. aalbopictus. J. Theor. Biol. 356 174–191 (2014). https://doi.org/10.1016/j.jtbi.2014.04.033

  63. Poletti, P., Messeri, G., Ajelli, M., Vallorani, R., Rizzo, C., Merler, S.: Comparative role of Aedes albopictus and Aedes aegypti in the emergence of dengue and Chikungunya in Central Africa. PLoS One 6(5), 18860 (2011). https://doi.org/10.1371/journal.pone.0018860

    Article  Google Scholar 

  64. Turell, M.J., Beaman, J.R., Tammariello, R.F.: Susceptibility of selected strains of Aedes aegypti and Aedes albopictus Diptera: Culicidae to Chikungunya virus. J. Med. Entomol. 29(1), 49–53 (1992). https://doi.org/10.1093/jmedent/29.1.49

    Article  Google Scholar 

  65. Bewick, S., Fagan, W.F., Calabrese, J., Agusto, F.: Zika virus: endemic versus epidemic dynamics and implications for disease spread in the Americas. bioRxiv, 041897 (2016). https://doi.org/10.1101/041897

  66. World Health Organization: Microcephaly Brazil: disease outbreak news. http://www.who.int/csr/don/8-january-2016-brazil-microcephaly/en accessed 01.02.16 (2016)

  67. Gray, R.H., Wawer, M.J., Brookmeyer, R., Sewankambo, N.K., Serwadda, D., Wabwire-Mangen, F., Lutalo, T., Li, X., vanCott, T., Quinn, T.: Probability of HIV-1 transmission per coital act in monogamous, heterosexual, HIV-1-discordant couples in Rakai. Uganda. The Lancet 357(9263), 1149–1153 (2001). https://doi.org/10.1016/S0140-6736(00)04331-2

    Article  Google Scholar 

  68. Putnam, J.L., Scott, T.W.: Blood feeding behavior of Dengue-2 virus-infected Aedes aegypti. Am. J. Tropic. Med. Hygiene 52(3), 225–227 (1995). https://doi.org/10.4269/ajtmh.1995.52.225

    Article  Google Scholar 

  69. Trpis, M., Haussermann, W.: Dispersal and other population parameters of Aedes aegypti in an African village and their possible significance in epidemiology of vector-borne diseases. Am. J. Tropic. Med. Hygiene 35(6), 1263–1279 (1986). https://doi.org/10.4269/ajtmh.1986.35.1263

    Article  Google Scholar 

  70. Newton, E.A.C., Reiter, P.: A model of the transmission of Dengue fever with an evaluation of the impact of ultra-low volume (ULV) insecticide applications on Dengue epidemics. Am. J. Tropic. Med. Hygiene 47(6), 709–720 (1992). https://doi.org/10.4269/ajtmh.1992.47.709

    Article  Google Scholar 

  71. Paupy, C., Ollomo, B., Kamgang, B., Moutailler, S., Rousset, D., Demanou, M., Herve, J.P., Leroy, E., Simard, F.: Comparative role of Aedes albopictus and Aedes aegypti in the emergence of dengue and Chikungunya in Central Africa. Vector Borne Zoonotic Dis. 10(3), 259–266 (2010). https://doi.org/10.1089/vbz.2009.0005

    Article  Google Scholar 

  72. Dubrulle, M., Mousson, L., Moutailler, S., Vazeille, M., Failloux, A.B.: Chikungunya virus and Aedes mosquitoes: saliva is infectious as soon as two days after oral infection. PLoS One 4(6), 5895 (2009). https://doi.org/10.1371/journal.pone.0005895

    Article  Google Scholar 

  73. Moulay, D., Aziz-Alaoui, M.A., Cadivel, M.: The Chikungunya disease: modeling, vector and transmission global dynamics. Math. Biosci. 229(1), 50–63 (2011). https://doi.org/10.1016/j.mbs.2010.10.008

    Article  MathSciNet  MATH  Google Scholar 

  74. Sebastian, M.R., Lodha, R., Kabra, S.K.: Chikungunya infection in children. Indian J. Pediatric. 76, 185 (2009). https://doi.org/10.1007/s12098-009-0049-6

    Article  Google Scholar 

  75. Sheppard, P.M., Macdonald, W.M., Tonn, R.J., Grabs, B.: The dynamics of an adult population of Aedes aegypti in relation to Dengue haemorrhagic fever in Bangkok. J. Animal Ecol. 38(3), 661–702 (1969). https://doi.org/10.2307/3042

    Article  Google Scholar 

  76. Trpis, M., Haussermann, W., Craig, G.B.: Estimates of population size, dispersal, and longevity of domestic Aedes aegypti by mark-release-recapture in the village of Shauri Moyo in eastern Kenya. J. Med. Entomol. 32(1), 27–33 (1995). https://doi.org/10.1093/jmedent/32.1.27

    Article  Google Scholar 

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Acknowledgements

The fifth and sixth authors were supported by Azarbaijan Shahid Madani University. The authors express their gratitude to dear unknown referees for their helpful suggestions which improved the final version of this paper.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Burapha University, Chonburi, 20131, Thailand

    Chatthai Thaiprayoon & Jutarat Kongson

  2. Center of Excellence in Mathematics, CHE, Sri Ayutthaya Rd., Bangkok, 10400, Thailand

    Chatthai Thaiprayoon & Jutarat Kongson

  3. Department of Applied Statistics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok, 10800, Thailand

    Weerawat Sudsutad

  4. Department of Mathematics and General Sciences, Prince Sultan University, Riyadh, 11586, Saudi Arabia

    Jehad Alzabut

  5. Group of Mathematics, Faculty of Engineering, Ostim Technical University, Ankara, 06374, Turkey

    Jehad Alzabut

  6. Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran

    Sina Etemad & Shahram Rezapour

  7. Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan

    Shahram Rezapour

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  1. Chatthai Thaiprayoon
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Thaiprayoon, C., Kongson, J., Sudsutad, W. et al. Analysis of a nonlinear fractional system for Zika virus dynamics with sexual transmission route under generalized Caputo-type derivative. J. Appl. Math. Comput. 68, 4273–4303 (2022). https://doi.org/10.1007/s12190-021-01663-1

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  • DOI: https://doi.org/10.1007/s12190-021-01663-1

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