[1] R. Agarwal, S. Hristova, D. O’Regan, Stability of generalized proportional caputo fractional dif-
ferential equations by lyapunov functions, Fractal Fract. 6 (2022) 34.
[2] Z. Bai, D. Liu, Modeling seasonal measles transmission in china, Commun. Nonlinear Sci. Numer.
Simul. 25 (2015) 19–26.
[3] D. Baleanu, S. Arshad, A. Jajarmi, W. Shokat, F. Akhavan Ghassabzade, M. Wali, Dynamical
behaviours and stability analysis of a generalized fractional model with a real case study, J. Adv.
Res. 48 (2023) 157–173.
[4] D. Baleanu, A. Jajarmi, S.S. Sajjadi, D. Mozyrska, A new fractional model and optimal control of
a tumor-immune surveillance with non-singular derivative operator, Chaos 29 (2019) 083127.
[5] D. Baleanu, P. Shekari, L. Torkzadeh, H. Ranjbar, A. Jajarmi, K. Nouri, Stability analysis and
system properties of nipah virus transmission: A fractional calculus case study, Chaos Solitons
Fract. 166 (2023) 112990.
[6] M.A. Belay, O.J. Abonyo, D.M. Theuri, Mathematical model of hepatitis B disease with optimal
control and cost-effectiveness analysis, Comput. Math. Methods Med. 29 (2023) 5215494.
[7] A. Bouissa, M. Tahiri, N. Tsouli, M.R. Sidi ammi, Global dynamics of a time-fractional spatio
temporal SIR model with a generalized incidence rate, J. App. Math. Comput. 69 (2023) 4779–
4804.
[8] V. Capasso, G. Serio, A generalization of the kermack-mckendrick deterministic epidemic model,
Math. Biosci. 42 (1978) 43–61.
[9] Z. Chen, Z. Yang, D. Sheng, Numerical analysis of linearly implicit Euler method for age structured
SIS model, J. App. Math. Comput. 70 (2024) 969–996.
[10] Chinese Center for Disease Control and Prevention. Available: www.chinacdc.cn/jkzt/crb/
mz/jszl2205/200904/t2009041524226.htm. National Measles Elimilation Program, 2006–
2012.
[11] M.L. Diagne, H. Rwezaura, S.A. Pedro, J.M. Tchuenche, Theoretical analysis of a measles model
with nonlinear incidence functions, Commun. Nonlinear Sci. Numer. Simul. 117 (2023) 106911.
[12] O. Diekmann, J.A. Heesterbeek, M.G. Roberts, The construction of next-generation matrices for
compartmental epidemic models, J. Roy. Soc. Interface. 7 (2009) 873–885.
[13] D.N. Durrheim, A. Xu, M.G. Baker, L.Y. Hsu, Y. Takashima, China has the momentum to eliminate
measles, Lancet. Reg. Health. West. Pac. 30 (2023) 100669.
[14] M. Fahimi, K. Nouri, L. Torkzadeh, Chaos in a stochastic cancer model, Phys. A 7 (2020) 123810.
[15] J.F. Gmez-Aguilar, J.J. Rosales-Garcia, J.J. Bernal-Alvarado, T. Cordova-Fraga, R. Guzman-
Cabrera, Fractional mechanical oscillators, Rev. Mex. Fis. 58 (2012) 348–352.
[16] Health Organization World. The revision of world population prospects, available: www.
worldometers.info/demographics/life-expectancy. WHO Data, 2022.
[17] M.A. Kuddus, M. Mohiuddin, A. Rahman, Mathematical analysis of a measles transmission dy-
namics model in bangladesh with double dose vaccination, Sci. Rep. 11 (2021) 16571.
[18] G. Lan , B. Sona, S. Yuan, Epidemic threshold and ergodicity of an SEIR model with vertical
transmission under the telegraph noise, Chaos Solitons Fract. 167 (2023) 113017.
[19] H. Liu, Y. Li, Hyers–Ulam stability of linear fractional differential equations with variable coeffi-
cients, Adv. Difference Equ. 8 (2020) 404.
[20] J.P. LaSalle, Stability theory for ordinary differential equations, J. Differential Equations 4 (1968)
57–65.
[21] C. Ma, L. Rodewald, L. Hao, Q. Su, Y. Zhang, N. Wen, C. Fan, H. Yang, H. Luo, H. Wang, J.L.
Goodson, Z. Yin, Z. Feng, Progress toward measles elimination:china-January 2013-June 2019,
China CDC Weekly, 68 (2019) 1112–1116.
[22] C. Milici, G. Draganescu, J.T. Machado, Introduction to Fractional Differential Equations, Springer
International Publishing, Switzerland, 2019.
[23] S.E. Moore, H.L. Nyandjo-Bamen, O. Menoukeu-Pamen, J.K.K. Asamoah, Z. Jin, Global stability
dynamics and sensitivity assessment of COVID-19 with timely-delayed diagnosis in Ghana, Com-
put. Math. Biophys. 10 (2022) 87–104.
[24] F. Ndairou, M. Khalighi, L. Lahti, Ebola epidemic model with dynamic population and memory,
Chaos Solitons Fract. 170 (2023) 113361.
[25] K.S. Nisar, M. Shoaib, M.A.Z. Raja, R. Tabassum, A. Morsy, A novel design of evolutionally
computing to study the quarantine effects on transmission model of Ebola virus disease, Results
Phys. 48 (2023) 106408.
[26] K. Nouri, M. Fahimi, L. Torkzadeh, D. Baleanu, Stochastic epidemic model of Covid-19 via the
reservoir-people transmission network, Comput. Mater. Contin. 72 (2022) 1495–1514.
[27] O.J. Peter, N.D. Fahrani, F. Fatmawati, W. Windarto, C.W. Chukwu, A fractional derivative model-
ing study for measles infection with double dose vaccination, Healthc. Anal. 4 (2023) 100231.
[28] O.J. Peter, H.S. Panigoro, M.A. Ibrahim, O.M. Otunuga, T.A. Ayoola, A.O. Oladapo, Analysis and
dynamics of measles with control strategies: A mathematical modeling approach, Int. J. Dyn. Contr.
11 (2023) 2538–2552.
[29] S. Rezapour, H. Mohammadi, A. Jajarmi, A new mathematical model for Zika virus transmission,
Adv. Differ. Equ. 2020 (2020) 589.
[30] B. Seidu, O.D. Makinde, I.Y. Seini, On the optimal control of HIV-TB Co-infection and improve-
ment of workplace productivity, Discret. dyn. nat. soc. 2023 (2023) 3716235.
[31] A. Singh, P. Deolia, COVID-19 outbreak: A predictive mathematical study incorporating shedding
effect, J. Appl. Math. Comput. 69 (2022) 1239-1268.
[32] C. Thaiprayoon, J. Kongson, W. Sudsutad, J. Alzabut, S. Etemad, S. Rezapour, Analysis of a non-
linear fractional system for zika virus dynamics with sexual transmission route under generalized
caputo-type derivative, J. Appl. Math. Comput. 68 (2022) 4273–4303.
[33] G.T. Tilahun, S. Demie , A. Eyob, Stochastic model of measles transmission dynamics with double
dose vaccination, Infect. Dis. Model. 5 (2020) 478–494.
[34] L. Torkzadeh, M. Fahimi, H. Ranjbar, K. Nouri, Analysis of a stochastic model for a prey predator
system with an indirect effect, Int. J. Comput. Math. 102 (2024) 60–73.
[35] R. Verma, S.P. Tiwari, R.K. Upadhyay, Transmission dynamics of epidemic spread and outbreak of
Ebola in west africa: fuzzy modeling and simulation, J. Appl. Math. Comput. 60 (2019) 637–671.
[36] S. Wang, The Ulam stability of fractional differential equation with the Caputo-Fabrizio derivative,
J. Funct. Spaces 2022 (2022) 7268518.
[37] H. Wang, Z. Zhu, X. Duan, J. song, N. Mao, A. Cui, C. Wang, H. Du, Y. Wang , F. Li, S. Zhou,
D. Feng , C. Li, H. Gao, J. He, L. Li, Y. Lei, H. Zheng, T. Gong, Y. Hu, C. Xu, H. Zhao, Z.
Sun, Y. Chen, X. Tang, M. Chen, L. Deng, S. Wang, X. Tian, T. Zhang, Y. Si, F. Yuan, L. Fan,
K. Mahemutijiang, Z. Chen, H. Chen, W. Xu, Y. Zhang, Transmission pattern of measles virus
circulating in China during 1993–2021: Genotyping evidence supports that China is approaching
measles elimination, Clin. Infect. Dis. 76 (2023) e1140–e1149.
[38] F.A. Wodajo, D.M. Gebru, H.T. Alemneh, Mathematical model analysis of effective intervention
strategies on transmission dynamics of hepatitis B virus, Sci. Rep. 13 (2023) 8337.
[39] H.M. Youssef, N. Alghamdi, M.A. Ezzat, A.A. El-Bary, A.M. Shawky, A proposed modified SEIQR
epidemic model to analyze the COVID-19 spreading in Saudi Arabia, Alex. Eng. J. 61 (2022) 2456–
2470.
[40] Y. Zhao, D. Jiang, The threshold of a stochastic SIS epidemic model with vaccination, Appl. Math.
Comput. 243 (2014) 718–727.
)