Citation: Prasantha Bharathi Dhandapani, Dumitru Baleanu, Jayakumar Thippan, Vinoth Sivakumar. On stiff, fuzzy IRD-14 day average transmission model of COVID-19 pandemic disease[J]. AIMS Bioengineering, 2020, 7(4): 208-223. doi: 10.3934/bioeng.2020018
[1] | Antonio DeSimone, Natalie Grunewald, Felix Otto . A new model for contact angle hysteresis. Networks and Heterogeneous Media, 2007, 2(2): 211-225. doi: 10.3934/nhm.2007.2.211 |
[2] | Steinar Evje, Aksel Hiorth . A mathematical model for dynamic wettability alteration controlled by water-rock chemistry. Networks and Heterogeneous Media, 2010, 5(2): 217-256. doi: 10.3934/nhm.2010.5.217 |
[3] | Liping Yu, Hans Kleppe, Terje Kaarstad, Svein M. Skjaeveland, Steinar Evje, Ingebret Fjelde . Modelling of wettability alteration processes in carbonate oil reservoirs. Networks and Heterogeneous Media, 2008, 3(1): 149-183. doi: 10.3934/nhm.2008.3.149 |
[4] | Sharif Ullah, Obaid J. Algahtani, Zia Ud Din, Amir Ali . Numerical analysis of stretching/shrinking fully wet trapezoidal fin. Networks and Heterogeneous Media, 2024, 19(2): 682-699. doi: 10.3934/nhm.2024030 |
[5] | Oliver Kolb, Simone Göttlich, Paola Goatin . Capacity drop and traffic control for a second order traffic model. Networks and Heterogeneous Media, 2017, 12(4): 663-681. doi: 10.3934/nhm.2017027 |
[6] | Henri Berestycki, Jean-Pierre Nadal, Nancy Rodíguez . A model of riots dynamics: Shocks, diffusion and thresholds. Networks and Heterogeneous Media, 2015, 10(3): 443-475. doi: 10.3934/nhm.2015.10.443 |
[7] | Tong Li, Sunčica Čanić . Critical thresholds in a quasilinear hyperbolic model of blood flow. Networks and Heterogeneous Media, 2009, 4(3): 527-536. doi: 10.3934/nhm.2009.4.527 |
[8] | Giuseppe Toscani, Andrea Tosin, Mattia Zanella . Kinetic modelling of multiple interactions in socio-economic systems. Networks and Heterogeneous Media, 2020, 15(3): 519-542. doi: 10.3934/nhm.2020029 |
[9] | Naoki Sato, Toyohiko Aiki, Yusuke Murase, Ken Shirakawa . A one dimensional free boundary problem for adsorption phenomena. Networks and Heterogeneous Media, 2014, 9(4): 655-668. doi: 10.3934/nhm.2014.9.655 |
[10] | Frédéric Coquel, Edwige Godlewski, Jean-Marc Hérard, Jacques Segré . Preface. Networks and Heterogeneous Media, 2010, 5(3): i-ii. doi: 10.3934/nhm.2010.5.3i |
[1] |
Zadeh LA (1965) Fuzzy sets. Inform Contr 8: 338-353. doi: 10.1016/S0019-9958(65)90241-X
![]() |
[2] |
Chang SSL, Zadeh LA (1972) On fuzzy mapping and control. doi: 10.1109/TSMC.1972.5408553
![]() |
[3] |
Buckley JJ, Feuring T (2000) Fuzzy differential equations. Fuzzy Set Syst 110: 43-54. doi: 10.1016/S0165-0114(98)00141-9
![]() |
[4] |
Dubois D, Prade H (1982) Towards fuzzy differential calculus, Part 3: Differentiation. Fuzzy Set Syst 8: 225-233. doi: 10.1016/S0165-0114(82)80001-8
![]() |
[5] |
Lupulescu V (2009) On a class of fuzzy functional differential equations. Fuzzy set Syst 160: 1547-1562. doi: 10.1016/j.fss.2008.07.005
![]() |
[6] |
Kaleva O (1987) Fuzzy differential equations. Fuzzy Set Syst 24: 301-317. doi: 10.1016/0165-0114(87)90029-7
![]() |
[7] |
Kaleva O (1990) The Cauchy problem for fuzzy differential equations. Fuzzy Set Syst 35: 389-386. doi: 10.1016/0165-0114(90)90010-4
![]() |
[8] |
Ma M, Friedman M, Kandel A (1999) Numerical solutions of fuzzy differential equations. Fuzzy Set Syst 105: 133-138. doi: 10.1016/S0165-0114(97)00233-9
![]() |
[9] |
Seikkala S (1987) On the fuzzy initial value problem. Fuzzy Set Syst 24: 319-330. doi: 10.1016/0165-0114(87)90030-3
![]() |
[10] | Diamond P, Kloeden P (1984) Metric Spaces of Fuzzy Sets: Theory and Applications Singapore: World Scientific. |
[11] |
Chalco-Cano Y, Roman-Flores H (2008) On new solutions of fuzzy differential equation. Chaos Soliton Fract 38: 112-119. doi: 10.1016/j.chaos.2006.10.043
![]() |
[12] |
Abbasbandy S, Viranloo TA (2002) Numerical solution of fuzzy differential equation by Taylor method. Comput Meth Appl mat 2: 113-124. doi: 10.2478/cmam-2002-0006
![]() |
[13] | Abbasbandy S, Viranloo TA (2004) Numerical solution of fuzzy differential equation by Runge-Kutta method. Nonlinear Stud 11: 117-129. |
[14] |
Curtiss CF, Hirschfelder JO (1952) Integration of stiff equations. Proc Natl Acad Sci USA 38: 235-243. doi: 10.1073/pnas.38.3.235
![]() |
[15] |
Söderlind G, Jay L, Calvo M (2015) Stiffness 1952–2012: Sixty years in search of a definition. BIT Numer Math 55: 531-558. doi: 10.1007/s10543-014-0503-3
![]() |
[16] |
Shampine LF (1981) Evaluation of a test set for stiff ODE solvers. ACM Trans Math Softw 7: 409-420. doi: 10.1145/355972.355973
![]() |
[17] |
Higham DJ, Trefethen LN (1993) Stiffness of ODEs. BIT 33: 285-303. doi: 10.1007/BF01989751
![]() |
[18] |
Spijker MN (1996) Stiffness in numerical initial-value problems. J Comp Appl Math 72: 393-406. doi: 10.1016/0377-0427(96)00009-X
![]() |
[19] |
Kermack WO, McKendrick AG (1927) A contribution to the mathematical theory of epidemics. Proc Roy Soc Lond A 115: 700-721. doi: 10.1098/rspa.1927.0118
![]() |
[20] |
Palese P, Young JF (1982) Variation of influenza A, B, and C viruses. Science 215: 1468-1474. doi: 10.1126/science.7038875
![]() |
[21] | Allen LJS (2007) An Introduction to Mathematical Biology NJ: Prentice Hall. |
[22] |
He S, Tang S, Rong L (2020) A discrete stochastic model of the COVID-19 outbreak: Forecast and control. MBE 17: 2792-2804. doi: 10.3934/mbe.2020153
![]() |
[23] |
Zhou W, Wang A, Xia F, et al. (2020) Effects of media reporting on mitigating spread of COVID-19 in the early phase of the outbreak. MBE 17: 2693-2707. doi: 10.3934/mbe.2020147
![]() |
[24] |
Yin F, Lv J, Zhang X, et al. (2020) COVID-19 information propagation dynamics in the chinese sina-microblog. MBE 17: 2676-2692. doi: 10.3934/mbe.2020146
![]() |
[25] |
Dai C, Yang J, Wang K (2020) Evaluation of prevention and control interventions and its impact on the epidemic of coronavirus disease 2019 in Chongqing and Guizhou Provinces. MBE 17: 2781-2791. doi: 10.3934/mbe.2020152
![]() |
[26] |
Rong X, Yang L, Chu H, et al. (2020) Effect of delay in diagnosis on transmission of COVID-19. MBE 17: 2725-2740. doi: 10.3934/mbe.2020149
![]() |
[27] |
Tian J, Wu J, Bao Y, et al. (2020) Modeling analysis of COVID-19 based on morbidity data in Anhui, China. MBE 17: 2842-2852. doi: 10.3934/mbe.2020158
![]() |
[28] |
Li C, Xu J, Liu J, et al. (2020) The within-host viral kinetics of SARS-CoV-2. MBE 17: 2853-2861. doi: 10.3934/mbe.2020159
![]() |
[29] |
Volpert V, Banerjee M, Petrovskii S (2020) On a quarantine model of coronavirus infection and data analysis. Math Model Nat Phenom 15: 24. doi: 10.1051/mmnp/2020006
![]() |
[30] | Tang B, Bragazzi NL, Li Q, et al. (2020) An updated estimation of the risk of transmission of the novel coronavirus (2019-nCov). Infect Dis Model 5: 248-225. |
[31] |
Yang Z, Zeng Z, Wang K, et al. (2020) Modified SEIR and AI prediction of the epidemics trend of COVID-19 in China under public health interventions. J Thorac Dis 12: 165-174. doi: 10.21037/jtd.2020.02.64
![]() |
[32] |
Tuli S, Tuli S, Tuli R, et al. (2020) Predicting the growth and trend of COVID-19 pandemic using machine learning and Cloud computing. Internet Thing 11: 100222. doi: 10.1016/j.iot.2020.100222
![]() |
[33] |
Pai C, Bhaskar A, Rawoot V (2020) Investigating the dynamics of COVID-19 pandemic in India under lockdown. Chaos Soliton Fract 138: 109988. doi: 10.1016/j.chaos.2020.109988
![]() |
[34] |
Ribeiro MHDM, Da Silva RG, Mariani VC, et al. (2020) Short-term forecasting COVID-19 cumulative confirmed cases: Perspectives for Brazil. Chaos Soliton Fract 135: 109853. doi: 10.1016/j.chaos.2020.109853
![]() |
[35] |
Khan MA, Atangana A (2020) Modeling the dynamics of novel coronavirus (2019-nCov) with fractional derivative. doi: 10.1016/j.aej.2020.02.033
![]() |
[36] |
Gong X, Fatmawati, Khan MA (2020) A numerical solution of the competition model among bank data in Caputo-Fabrizio derivative. doi: 10.1016/j.aej.2020.02.008
![]() |
[37] |
Jan R, Khan MA, Gómez-Aguilar JF (2020) Asymptomatic carriers in transmission dynamics of dengue with control interventions. Optim Control Appl Meth 41: 430-447. doi: 10.1002/oca.2551
![]() |
[38] |
Khan MA, Ullah S, Ullah S, et al. (2020) Fractional order SEIR model with generalized incidence rate. AIMS Mathematics 5: 2843-2857. doi: 10.3934/math.2020182
![]() |
[39] |
Windarto, Khan MA, Fatmawati (2020) Parameter estimation and fractional derivatives of dengue transmission model. AIMS Mathematics 5: 2758-2779. doi: 10.3934/math.2020178
![]() |
[40] |
Dhandapani PB, Baleanu D, Thippan J, et al. (2019) Fuzzy type RK4 solutions to fuzzy hybrid retarded delay differential equations. Front Phys 7: 168. doi: 10.3389/fphy.2019.00168
![]() |
[41] | Dhandapani PB, Thippan J, Sivakumar V (2019) Numerical solution of fuzzy multiple hybrid single retarded delay differential equations. Int J Recent Technol Eng 8: 1946-1949. |
[42] | Dhandapani PB, Thippan J, Sivakumar V (2019) Numerical solutions of fuzzy multiple hybrid single neutral delay differential equations. Int J Sci Technol Res 8: 520-523. |
[43] | Daily updates of coronavirus COVID-19 pandemic disease.Available from: https://www.worldometers.info/coronavirus/. |
1. | Giovanni Noselli, Antonio DeSimone, A robotic crawler exploiting directional frictional interactions: experiments, numerics and derivation of a reduced model, 2014, 470, 1364-5021, 20140333, 10.1098/rspa.2014.0333 | |
2. | J. Dohmen, N. Grunewald, F. Otto, M. Rumpf, 2008, Chapter 7, 978-3-540-77202-6, 75, 10.1007/978-3-540-77203-3_7 | |
3. | Xiao-Ping Wang, Xianmin Xu, A dynamic theory for contact angle hysteresis on chemically rough boundary, 2017, 37, 1553-5231, 1061, 10.3934/dcds.2017044 | |
4. | P. Gruber, D. Knees, S. Nesenenko, M. Thomas, Analytical and numerical aspects of time-dependent models with internal variables, 2010, 90, 00442267, 861, 10.1002/zamm.200900387 | |
5. | Xianmin Xu, Yinyu Zhao, Xiaoping Wang, Analysis for Contact Angle Hysteresis on Rough Surfaces by a Phase-Field Model with a Relaxed Boundary Condition, 2019, 79, 0036-1399, 2551, 10.1137/18M1182115 | |
6. | Mathilde Reyssat, David Quéré, Contact Angle Hysteresis Generated by Strong Dilute Defects, 2009, 113, 1520-6106, 3906, 10.1021/jp8066876 | |
7. | G. Bellettini, Sh.Yu. Kholmatov, Minimizing movements for mean curvature flow of droplets with prescribed contact angle, 2018, 117, 00217824, 1, 10.1016/j.matpur.2018.06.003 | |
8. | Alessandro Turco, François Alouges, Antonio DeSimone, Wetting on rough surfaces and contact angle hysteresis: numerical experiments based on a phase field model, 2009, 43, 0764-583X, 1027, 10.1051/m2an/2009016 | |
9. | Xianmin Xu, Xiaoping Wang, Analysis of Wetting and Contact Angle Hysteresis on Chemically Patterned Surfaces, 2011, 71, 0036-1399, 1753, 10.1137/110829593 | |
10. | Jiwoong Jang, Capillary-type boundary value problems of mean curvature flows with force and transport terms on a bounded domain, 2023, 62, 0944-2669, 10.1007/s00526-023-02450-5 | |
11. | Antonio DeSimone, Martin Kružík, Domain patterns and hysteresis in phase-transforming solids: Analysis and numerical simulations of a sharp interface dissipative model via phase-field approximation, 2013, 8, 1556-181X, 481, 10.3934/nhm.2013.8.481 | |
12. | Antonio DeSimone, Paolo Gidoni, Giovanni Noselli, Liquid crystal elastomer strips as soft crawlers, 2015, 84, 00225096, 254, 10.1016/j.jmps.2015.07.017 | |
13. | Livio Fedeli, Alessandro Turco, Antonio DeSimone, Metastable equilibria of capillary drops on solid surfaces: a phase field approach, 2011, 23, 0935-1175, 453, 10.1007/s00161-011-0189-6 | |
14. | David Quéré, Wetting and Roughness, 2008, 38, 1531-7331, 71, 10.1146/annurev.matsci.38.060407.132434 | |
15. | Abner J. Salgado, A diffuse interface fractional time-stepping technique for incompressible two-phase flows with moving contact lines, 2013, 47, 0764-583X, 743, 10.1051/m2an/2012047 | |
16. | Giovanni Alberti, Antonio DeSimone, Quasistatic Evolution of Sessile Drops and Contact Angle Hysteresis, 2011, 202, 0003-9527, 295, 10.1007/s00205-011-0427-x | |
17. | William M. Feldman, Limit Shapes of Local Minimizers for the Alt–Caffarelli Energy Functional in Inhomogeneous Media, 2021, 240, 0003-9527, 1255, 10.1007/s00205-021-01635-6 | |
18. | Antonio DeSimone, Livio Fedeli, Alessandro Turco, 2010, Chapter 4, 978-90-481-9194-9, 51, 10.1007/978-90-481-9195-6_4 | |
19. | William M. Feldman, Inwon C. Kim, Liquid Drops on a Rough Surface, 2018, 71, 00103640, 2429, 10.1002/cpa.21793 | |
20. | Mathilde Reyssat, Denis Richard, Christophe Clanet, David Quéré, Dynamical superhydrophobicity, 2010, 146, 1359-6640, 19, 10.1039/c000410n | |
21. | S. Cacace, A. Chambolle, A. DeSimone, L. Fedeli, Macroscopic contact angle and liquid drops on rough solid surfaces via homogenization and numerical simulations, 2013, 47, 0764-583X, 837, 10.1051/m2an/2012048 | |
22. | A. DeSimone, F. Guarnieri, G. Noselli, A. Tatone, Crawlers in viscous environments: Linear vs non-linear rheology, 2013, 56, 00207462, 142, 10.1016/j.ijnonlinmec.2013.02.007 | |
23. | P. Gidoni, G. Noselli, A. DeSimone, Crawling on directional surfaces, 2014, 61, 00207462, 65, 10.1016/j.ijnonlinmec.2014.01.012 |