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Caputo SIR model for COVID-19 under optimized fractional order. (English) Zbl 1494.92121


MSC:

92D30 Epidemiology
34A08 Fractional ordinary differential equations
34C60 Qualitative investigation and simulation of ordinary differential equation models
92C60 Medical epidemiology
26A33 Fractional derivatives and integrals

References:

[1] Brauer, F.; Castillo-Chavez, C.; Feng, Z., Mathematical Models in Epidemiology (2019), New York: Springer, New York · Zbl 1433.92001 · doi:10.1007/978-1-4939-9828-9
[2] Djordjevic, J.; Silva, C. J.; Torres, D. F.M., A stochastic SICA epidemic model for HIV transmission, Appl. Math. Lett., 84, 168-175 (2018) · Zbl 1470.92293 · doi:10.1016/j.aml.2018.05.005
[3] Ndaïrou, F.; Area, I.; Nieto, J. J.; Silva, C. J.; Torres, D. F.M., Mathematical modeling of Zika disease in pregnant women and newborns with microcephaly in Brazil, Math. Methods Appl. Sci., 41, 8929-8941 (2018) · Zbl 1406.34083 · doi:10.1002/mma.4702
[4] Rachah, A.; Torres, D. F.M., Dynamics and optimal control of Ebola transmission, Math. Comput. Sci., 10, 331-342 (2016) · Zbl 1352.49042 · doi:10.1007/s11786-016-0268-y
[5] Coronavirus disease (COVID-2019) situation reports, World Health Organization. https://www.who.int/317emergencies/diseases/novel-coronavirus-2019/situation-reports/. Assessed 2 August 2020
[6] He, S.; Peng, Y.; Kehui, K., SEIR modeling of the COVID-19 and its dynamics, Nonlinear Dyn., 101, 1667-1680 (2020) · doi:10.1007/s11071-020-05743-y
[7] Fanelli, D.; Piazza, F., Analysis and forecast of COVID-19 spreading in China, Italy and France, Chaos Solitons Fractals, 134, 1-5 (2020) · Zbl 1483.92130 · doi:10.1016/j.chaos.2020.109761
[8] Atangana, A., Modelling the spread of COVID-19 with new fractal-fractional operators: can the lockdown save mankind before vaccination?, Chaos Solitons Fractals, 136, 1-38 (2020) · doi:10.1016/j.chaos.2020.109860
[9] Shaikh, A. S.; Jadhav, K. S.; Timol, V. S.; Nisar, M. G.; Khan, I., Analysis of the COVID-19 pandemic spreading in India by an epidemiological model and fractional differential operator, Preprints, 2020 (2020)
[10] Naveed, M.; Rafiq, M.; Raza, A.; Ahmed, N.; Khan, I.; Nisar, K. S.; Soori, A. H., Mathematical analysis of novel coronavirus (2019-nCov) delay pandemic model, Comput. Mater. Continua, 64, 3, 1401-1414 (2020) · doi:10.32604/cmc.2020.011314
[11] Ahmed, I.; Goufo, E. F.D.; Yusuf, A.; Kumam, P.; Chaipanya, P.; Nonlaopon, K., An epidemic prediction from analysis of a combined HIV-COVID-19 co-infection model via ABC fractional operator, Alex. Eng. J., 60, 2979-2995 (2021) · doi:10.1016/j.aej.2021.01.041
[12] Wikipedia Website. https://en.wikipedia.org/wiki/Coronavirus/
[13] Li, Q.; Guan, X.; Wu, P., Early transmission dynamics in Wuhan, China, of novel coronavirus infected pneumonia, N. Engl. J. Med., 382, 1199-1207 (2020) · doi:10.1056/NEJMoa2001316
[14] Guan, W., Ni, Z., Hu, Y., et al.: Clinical characteristics of 2019 novel coronavirus infection in China. medRxiv (2020). doi:10.1056/NEJMoa2002032
[15] Yang, Y., Lu, Q., Liu, M., et al.: Epidemiological and clinical features of the 2019 novel coronavirus outbreak in China. medRxiv (2020). doi:10.1101/2020.02.10.20021675
[16] Rothe, C.; Schunk, M.; Sothmann, P., Transmission of 2019-nCoV infection from an asymptomatic contact in Germany, N. Engl. J. Med., 382, 970-971 (2020) · doi:10.1056/NEJMc2001468
[17] Diagnosis and treatment of novel coronavirus pneumonia. (Trial version Sixth, in Chinese.)
[18] Wrapp, D.; Wang, N.; Corbett, K., Cryo-EM structure of the 2019-nCoV spike in the prefusion conformation, Science, 367, 6483, 1260-1263 (2020) · doi:10.1126/science.abb2507
[19] Araz, S.İ., Analysis of a Covid-19 model: optimal control, stability and simulations, Alex. Eng. J., 60, 1, 647-658 (2021) · doi:10.1016/j.aej.2020.09.058
[20] Atangana, A., Araz, S.İ.: Mathematical model of Covid-19 spread in Turkey and South Africa: Theory, methods and applications. medRxiv (2020). doi:10.1101/2020.05.08.20095588 · Zbl 1485.92110
[21] Qureshi, S.; Yusuf, A., Modeling chickenpox disease with fractional derivatives: from Caputo to Atangana-Baleanu, Chaos Solitons Fractals, 122, 111-118 (2019) · Zbl 1448.92331 · doi:10.1016/j.chaos.2019.03.020
[22] Qureshi, S.; Yusuf, A., Mathematical modeling for the impacts of deforestation on wildlife species using Caputo differential operator, Chaos Solitons Fractals, 126, 32-40 (2019) · Zbl 1448.92380 · doi:10.1016/j.chaos.2019.05.037
[23] Jajarmi, A.; Yusuf, A.; Baleanu, D.; Inc, M., A new fractional HRSV model and its optimal control: a non-singular operator approach, Physica A, 547 (2020) · Zbl 07530156 · doi:10.1016/j.physa.2019.123860
[24] Abdulhameed, M.; Muhammad, M. M.; Gital, A. Y.; Yakubu, D. G.; Khan, I., Effect of fractional derivatives on transient MHD flow and radiative heat transfer in a micro-parallel channel at high zeta potentials, Physica A, 519, 42-71 (2019) · Zbl 1514.76116 · doi:10.1016/j.physa.2018.12.019
[25] Dubey, V. P.; Kumar, R.; Kumar, D., Analytical study of fractional Bratu-type equation arising in electro-spun organic nanofibers elaboration, Physica A, 521, 762-772 (2019) · Zbl 1514.34018 · doi:10.1016/j.physa.2019.01.094
[26] Chang, A.; Sun, H.; Zhang, Y.; Zheng, C.; Min, F., Spatial fractional Darcy’s law to quantify fluid flow in natural reservoirs, Physica A, 519, 119-126 (2019) · Zbl 1514.76086 · doi:10.1016/j.physa.2018.11.040
[27] Goulart, A. G.; Lazo, M. J.; Suarez, J. M.S., A new parameterization for the concentration flux using the fractional calculus to model the dispersion of contaminants in the planetary boundary layer, Physica A, 518, 38-49 (2019) · Zbl 1514.76085 · doi:10.1016/j.physa.2018.11.064
[28] Qureshi, S.; Chang, M.; Shaikh, A. A., Analysis of series RL and RC circuits with time-invariant source using truncated M, Atangana beta and conformable derivatives, J. Ocean Eng. Sci. (2020) · doi:10.1016/j.joes.2020.11.006
[29] Naik, P. A.; Yavuz, M.; Qureshi, S.; Zu, J.; Townley, S., Modeling and analysis of COVID-19 epidemics with treatment in fractional derivatives using real data from Pakistan, Eur. Phys. J. Plus, 135, 10, 1-42 (2020) · doi:10.1140/epjp/s13360-020-00819-5
[30] Tuan, N. H.; Tri, V. V.; Baleanu, D., Analysis of the fractional corona virus pandemic via deterministic modeling, Math. Methods Appl. Sci., 44, 1, 1086-1102 (2021) · Zbl 1472.34097 · doi:10.1002/mma.6814
[31] Atangana, E.; Atangana, A., Facemasks simple but powerful weapons to protect against COVID-19 spread: can they have sides effects?, Results Phys., 19 (2020) · doi:10.1016/j.rinp.2020.103425
[32] Memon, Z.; Qureshi, S.; Memon, B. R., Assessing the role of quarantine and isolation as control strategies for COVID-19 outbreak: a case study, Chaos Solitons Fractals, 144 (2021) · doi:10.1016/j.chaos.2021.110655
[33] Jajarmi, A.; Ghanbari, B.; Baleanu, D., A new and efficient numerical method for the fractional modeling and optimal control of diabetes and tuberculosis co-existence, Chaos, Interdiscip. J. Nonlinear Sci., 29, 9 (2019) · Zbl 1423.92093 · doi:10.1063/1.5112177
[34] Ameen, I.; Baleanu, D.; Ali, H. M., An efficient algorithm for solving the fractional optimal control of SIRV epidemic model with a combination of vaccination and treatment, Chaos Solitons Fractals, 137 (2020) · Zbl 1489.92134 · doi:10.1016/j.chaos.2020.109892
[35] Arshad, S.; Defterli, O.; Baleanu, D., A second order accurate approximation for fractional derivatives with singular and non-singular kernel applied to a HIV model, Appl. Math. Comput., 374 (2020) · Zbl 1433.34007
[36] Khan, H.; Li, Y.; Khan, A.; Khan, A., Existence of solution for a fractional-order Lotka-Volterra reaction-diffusion model with Mittag-Leffler kernel, Math. Methods Appl. Sci., 42, 9, 3377-3387 (2019) · Zbl 1459.35378 · doi:10.1002/mma.5590
[37] Ulam, S. M., A Collection of Mathematical Problems (1960), New York: Interscience, New York · Zbl 0086.24101
[38] Ulam, S. M., Problems in Modern Mathematics (2004) · Zbl 0137.24201
[39] Asamoah, J. K.K.; Jin, Z.; Sun, G. Q.; Li, M. Y., A deterministic model for Q fever transmission dynamics within dairy cattle herds: using sensitivity analysis and optimal controls, Comput. Math. Methods Med., 2020 (2020) · Zbl 1431.92129 · doi:10.1155/2020/6820608
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