Processing math: 100%
Search Advanced

AIMS Materials Science

2016, Volume 3, Issue 3: 881-907. doi: 10.3934/matersci.2016.3.881
Previous Article Next Article
Review Topical Sections

Moving surfaces and interfaces : application to damage, fracture and wearcontact

  • Institut GeM, Ecole Centrale de Nantes CNRS UMR6183, F-44321 Nantes Cedex 3, IMSIAEdF-CEA-CNRS UMR9219, Universit´e Paris Saclay, 828 Bvd Mar´echaux, F-91762 PalaiseauCedex, France
  • Received: 30 May 2016 Accepted: 12 July 2016 Published: 14 July 2016

  • The full scenario of the degradation of solids under mechanical loading is described by modelling the gradual loss of rigidity. This common approach is purely local. Another way to describe the damage evolution is to consider the propagation of the surface separating sound material and damaged material. When this surface is moving, a flux of matter is induced, that is useful for describing the loss of material during wear mechanisms or brittle fracture. The article proposes modelling of moving surface and interface in order to describe such behaviours. The problem of evolution is written, analysis of stability and bifurcation of the propagation is also presented. Applications to brittle fracture, transition from fracture to damage and wear contact are briefly investigated.

    Citation: Claude Stolz. Moving surfaces and interfaces : application to damage, fracture and wearcontact[J]. AIMS Materials Science, 2016, 3(3): 881-907. doi: 10.3934/matersci.2016.3.881

    Related Papers:

    [1] Joan Ponce, Horst R. Thieme . Can infectious diseases eradicate host species? The effect of infection-age structure. Mathematical Biosciences and Engineering, 2023, 20(10): 18717-18760. doi: 10.3934/mbe.2023830
    [2] Peter Rashkov, Ezio Venturino, Maira Aguiar, Nico Stollenwerk, Bob W. Kooi . On the role of vector modeling in a minimalistic epidemic model. Mathematical Biosciences and Engineering, 2019, 16(5): 4314-4338. doi: 10.3934/mbe.2019215
    [3] Yukihiko Nakata, Ryosuke Omori . The change of susceptibility following infection can induce failure to predict outbreak potential by R0. Mathematical Biosciences and Engineering, 2019, 16(2): 813-830. doi: 10.3934/mbe.2019038
    [4] Jianquan Li, Zhien Ma, Fred Brauer . Global analysis of discrete-time SI and SIS epidemic models. Mathematical Biosciences and Engineering, 2007, 4(4): 699-710. doi: 10.3934/mbe.2007.4.699
    [5] Yilei Tang, Dongmei Xiao, Weinian Zhang, Di Zhu . Dynamics of epidemic models with asymptomatic infection and seasonal succession. Mathematical Biosciences and Engineering, 2017, 14(5&6): 1407-1424. doi: 10.3934/mbe.2017073
    [6] Carlos M. Hernández-Suárez, Carlos Castillo-Chavez, Osval Montesinos López, Karla Hernández-Cuevas . An application of queuing theory to SIS and SEIS epidemic models. Mathematical Biosciences and Engineering, 2010, 7(4): 809-823. doi: 10.3934/mbe.2010.7.809
    [7] Anthony Morciglio, R. K. P. Zia, James M. Hyman, Yi Jiang . Understanding the oscillations of an epidemic due to vaccine hesitancy. Mathematical Biosciences and Engineering, 2024, 21(8): 6829-6846. doi: 10.3934/mbe.2024299
    [8] Liqiong Pu, Zhigui Lin . A diffusive SIS epidemic model in a heterogeneous and periodically evolvingenvironment. Mathematical Biosciences and Engineering, 2019, 16(4): 3094-3110. doi: 10.3934/mbe.2019153
    [9] Masoud Saade, Samiran Ghosh, Malay Banerjee, Vitaly Volpert . An epidemic model with time delays determined by the infectivity and disease durations. Mathematical Biosciences and Engineering, 2023, 20(7): 12864-12888. doi: 10.3934/mbe.2023574
    [10] Hai-Feng Huo, Qian Yang, Hong Xiang . Dynamics of an edge-based SEIR model for sexually transmitted diseases. Mathematical Biosciences and Engineering, 2020, 17(1): 669-699. doi: 10.3934/mbe.2020035
  • The full scenario of the degradation of solids under mechanical loading is described by modelling the gradual loss of rigidity. This common approach is purely local. Another way to describe the damage evolution is to consider the propagation of the surface separating sound material and damaged material. When this surface is moving, a flux of matter is induced, that is useful for describing the loss of material during wear mechanisms or brittle fracture. The article proposes modelling of moving surface and interface in order to describe such behaviours. The problem of evolution is written, analysis of stability and bifurcation of the propagation is also presented. Applications to brittle fracture, transition from fracture to damage and wear contact are briefly investigated.


    [1] Francfort GA, Marigo JJ (1998) Revisiting brittle fracture as an energy minimization problem. J Mech Phys Solids 46: 1319-1342. doi: 10.1016/S0022-5096(98)00034-9
    [2] Peerlings R, Geers M, de Borst R, et al. (2001) A critical comparison of non-local and gradientenhanced softening continua. Int J Solids Struct 38: 7723-7746. doi: 10.1016/S0020-7683(01)00087-7
    [3] Hakim V, Karma A (2009) A law of crack motion and phase-field models of fracture. J Mech Phys Solids 57: 342-368. doi: 10.1016/j.jmps.2008.10.012
    [4] Bourdin B, Francfort GA, Marigo JJ (2008) The variational approach to fracture. J Elasticity 91: 5-148. doi: 10.1007/s10659-007-9107-3
    [5] Bui HD (1980) Solution explicite d'un problème de frontière libre en élastoplasticité avec endommagement. C R Acad des Sciences de Paris, série B 290: 345-348.
    [6] Bui HD, Ehrlacher A (1980) Propagation dynamique d'une zone endommagée dans un solide élastique fragile en mode III et en régime permanent. C R Acad des Sciences de Paris, Série B 290 : 273-276.
    [7] Gurtin ME (1995) The nature of configurational forces. Arch Rat Mech 131: 67-100. doi: 10.1007/BF00386071
    [8] Dragon-Louiset M, Stolz C (1999) A thermodynamical approach to contact wear. C R Acad des Sciences de Paris, S´erie IIb 327: 1275-1280.
    [9] Bui HD, Dang Van Ky, Stolz C (1981) Variational-principles applicable to rate boundary-valueproblems of elastic-brittle solids with damaged zone. C R Acad des Sciences de Paris, Série II 292: 251-254.
    [10] Pradeilles-Duval RM, Stolz C (1995) Mechanical transformations and discontinuities along a moving surface. J Mech Phys Solids 43: 91-121. doi: 10.1016/0022-5096(94)00061-9
    [11] Stolz C (2007) Bifurcation of equilibrium solutions and defects nucleation. Int J Fracture 147: 103-107. doi: 10.1007/s10704-007-9147-5
    [12] Stolz C (2010) Thermodynamical description of running discontinuties: application to friction and wear. Entropy 12: 1418-1439. doi: 10.3390/e12061418
    [13] Stolz C, Moës N (2012) A new model of damage: a moving thick layer approach. Int J Fracture 174: 49-60. doi: 10.1007/s10704-012-9693-3
    [14] Abeyaratne R, Knowles J (1990) On the driving traction acting on a surface of strain discontinuity in a continuum. J Mech Phys Solids 38: 345-360. doi: 10.1016/0022-5096(90)90003-M
    [15] Son QN, Pradeilles RM, Stolz C (1989) On a regularized propagation law in fracture and brittle damage. C R Acad des Sciences de Paris, Série II 309: 1515-1520.
    [16] Gurtin ME, Podio-Giugli P (1996) Configurational forces and the basic laws for crack propagation. J Mech Phys Solids 44: 905-927. doi: 10.1016/0022-5096(96)00014-2
    [17] Hill R (1986) Energy momentum tensors in elastostatics: some reflections on the general theory. J Mech Phys Solids 34: 305-317. doi: 10.1016/0022-5096(86)90022-0
    [18] Hutchinson J, Thouless MD, Liniger EG (1992) Growth and configurational stability of circular buckling driven film delamination. Acta Metall Mat 40: 295-308. doi: 10.1016/0956-7151(92)90304-W
    [19] Pradeilles RM, Stolz C (1991) Sur le problème d'évolution des solides à changement de phase irréversibles. C R Acad des Sciences de Paris, Série II 313: 297-302.
    [20] Storakers B, Andersson B (1988) Non linear theory applied to delamination in composites. J Mech Phys Solids 36: 689-718. doi: 10.1016/0022-5096(88)90004-X
    [21] Stolz C (2011) Analysis of stability and bifurcation in non-linear mechanics with dissipation. Entropy 13: 332-366. doi: 10.3390/e13020332
    [22] Pradeilles-Duval RM (2004) Quasi-static evolution of delaminated structures: analysis of stability and bifurcation. Int J Solids Struct 41: 103-130. doi: 10.1016/j.ijsolstr.2003.07.006
    [23] Stolz C. (2004), Energy methods in Non linear Mechanics, Lectures Notes 11,Warsawa, IPPT Pan
    [24] Neuber H (1968) A physically non linear notch and crack model. J Mech Phys Solids 16: 289-294. doi: 10.1016/0022-5096(68)90037-9
    [25] Rice J (1966) Contained plastic deformation near cracks and notches under longitudinal shear. Int J Fracture Mech 2: 426-447.
    [26] Stolz C (2015) Asymptotic fields ahead a crack for a class of non-linear materils under mode III. Mechanics of Materials 90: 102-110. doi: 10.1016/j.mechmat.2015.04.005
    [27] Knowles JK, Sternberg E (1980) Discontinuous deformation gradients near the tip of a crack in finite anti-plane shear: an example. J Elasticity 10: 81-110. doi: 10.1007/BF00043136
    [28] Rice J (1967) Stresses due to sharp notch in a work hardening elastic plastic material loaded by a longitudinal shear. J Appl Mech 34: 287-298. doi: 10.1115/1.3607681
    [29] Knowles JK, Sternberg E (1981) Anti-plane shear fields with discontinuous gradients near the tip of a crack in finite elastostatics. J Elasticity 11: 129-164. doi: 10.1007/BF00043857
    [30] Stolz C (2010) Closed form solution for the finite anti-plane shear field for a class of incompressible brittle solids. Comptes Rendus Mécanique 338-12: 663-669.
    [31] Stolz C, Parrilla-Gomez A (2015) Antiplane shear field for a class of hyperelastic incompressible brittle material: analytical and numerical approaches. J Mech Mater Struct 10: 395-410. doi: 10.2140/jomms.2015.10.395
    [32] Dragon-Louiset M (2001) On a predictive macroscopic contact-sliding wear model based on micro-mechanical consideration.. Int J Solids Struct 38: 1625-1639. doi: 10.1016/S0020-7683(00)00065-2
    [33] Bui HD, Dang Van K (1976) Contribution à l'étude théorique du contact élastique d'un frotteur cylindrique glissant sur un massif élastique. Industrie Minérale, No Sp´ecial Rh´eologie IV: 1-8.

  • This article has been cited by:

    1. Fred Brauer, General compartmental epidemic models, 2010, 31, 0252-9599, 289, 10.1007/s11401-009-0454-1
    2. Jianquan Li, Yijun Lou, Characteristics of an epidemic outbreak with a large initial infection size, 2016, 10, 1751-3758, 366, 10.1080/17513758.2016.1205223
    3. Jing-An Cui, Fangyuan Chen, Effects of isolation and slaughter strategies in different species on emerging zoonoses, 2017, 14, 1551-0018, 1119, 10.3934/mbe.2017058
    4. Xinxin Wang, Shengqiang Liu, Lin Wang, Weiwei Zhang, An Epidemic Patchy Model with Entry–Exit Screening, 2015, 77, 0092-8240, 1237, 10.1007/s11538-015-0084-6
    5. Fred Brauer, Carlos Castillo-Chavez, Zhilan Feng, 2019, Chapter 4, 978-1-4939-9826-5, 117, 10.1007/978-1-4939-9828-9_4
    6. Marek Trawicki, Deterministic Seirs Epidemic Model for Modeling Vital Dynamics, Vaccinations, and Temporary Immunity, 2017, 5, 2227-7390, 7, 10.3390/math5010007
    7. Rosalyn J. Moran, Erik D. Fagerholm, Maell Cullen, Jean Daunizeau, Mark P. Richardson, Steven Williams, Federico Turkheimer, Rob Leech, Karl J. Friston, Estimating required ‘lockdown’ cycles before immunity to SARS-CoV-2: model-based analyses of susceptible population sizes, ‘S0’, in seven European countries, including the UK and Ireland, 2020, 5, 2398-502X, 85, 10.12688/wellcomeopenres.15886.1
    8. Raul Nistal, Manuel de la Sen, Santiago Alonso-Quesada, Asier Ibeas, 2014, A nonlinear SEIR epidemic model with feedback vaccination control, 978-3-9524269-1-3, 158, 10.1109/ECC.2014.6862291
    9. Assessing the effect of non-pharmaceutical interventions on containing an emerging disease, 2012, 9, 1551-0018, 147, 10.3934/mbe.2012.9.147
    10. Ryosuke Omori, Hiroshi Nishiura, Theoretical basis to measure the impact of short-lasting control of an infectious disease on the epidemic peak, 2011, 8, 1742-4682, 10.1186/1742-4682-8-2
    11. Zhipeng Qiu, Zhilan Feng, Transmission Dynamics of an Influenza Model with Vaccination and Antiviral Treatment, 2010, 72, 0092-8240, 1, 10.1007/s11538-009-9435-5
    12. David Berger, Kyle Herkenhoff, Simon Mongey, An SEIR Infectious Disease Model with Testing and Conditional Quarantine, 2020, 1556-5068, 10.2139/ssrn.3561142
    13. David Berger, Kyle Herkenhoff, Chengdai Huang, Simon Mongey, Testing and reopening in an SEIR model, 2020, 10942025, 10.1016/j.red.2020.11.003
    14. S. Towers, J. Chen, C. Cruz, J. Melendez, J. Rodriguez, A. Salinas, F. Yu, Y. Kang, Quantifying the relative effects of environmental and direct transmission of norovirus, 2018, 5, 2054-5703, 170602, 10.1098/rsos.170602
    15. Ryosuke Omori, Yukihiko Nakata, Heidi L. Tessmer, Satowa Suzuki, Keigo Shibayama, The determinant of periodicity in Mycoplasma pneumoniae incidence: an insight from mathematical modelling, 2015, 5, 2045-2322, 10.1038/srep14473
    16. Chengjun Sun, Ying-Hen Hsieh, Global analysis of an SEIR model with varying population size and vaccination, 2010, 34, 0307904X, 2685, 10.1016/j.apm.2009.12.005
    17. Calistus N. Ngonghala, Enahoro Iboi, Steffen Eikenberry, Matthew Scotch, Chandini Raina MacIntyre, Matthew H. Bonds, Abba B. Gumel, Mathematical assessment of the impact of non-pharmaceutical interventions on curtailing the 2019 novel Coronavirus, 2020, 325, 00255564, 108364, 10.1016/j.mbs.2020.108364
    18. N. Sherborne, K. B. Blyuss, I. Z. Kiss, Dynamics of Multi-stage Infections on Networks, 2015, 77, 0092-8240, 1909, 10.1007/s11538-015-0109-1
    19. Ping Yan, Zhilan Feng, Variability order of the latent and the infectious periods in a deterministic SEIR epidemic model and evaluation of control effectiveness, 2010, 224, 00255564, 43, 10.1016/j.mbs.2009.12.007
    20. Saikat Batabyal, Arthita Batabyal, Mathematical computations on epidemiology: a case study of the novel coronavirus (SARS-CoV-2), 2021, 1431-7613, 10.1007/s12064-021-00339-5
    21. Mohammad A. Safi, Mudassar Imran, Abba B. Gumel, Threshold dynamics of a non-autonomous SEIRS model with quarantine and isolation, 2012, 131, 1431-7613, 19, 10.1007/s12064-011-0148-6
    22. Ceyhun Eksin, Martial Ndeffo-Mbah, Joshua S. Weitz, Reacting to outbreaks at neighboring localities, 2021, 520, 00225193, 110632, 10.1016/j.jtbi.2021.110632
    23. Fred Brauer, Mathematical epidemiology is not an oxymoron, 2009, 9, 1471-2458, 10.1186/1471-2458-9-S1-S2
    24. Fengqin Zhang, Jianquan Li, Jia Li, Epidemic characteristics of two classic SIS models with disease-induced death, 2017, 424, 00225193, 73, 10.1016/j.jtbi.2017.04.029
    25. K. M. Ariful Kabir, Jun Tanimoto, Evolutionary game theory modelling to represent the behavioural dynamics of economic shutdowns and shield immunity in the COVID-19 pandemic, 2020, 7, 2054-5703, 201095, 10.1098/rsos.201095
    26. Impact of discontinuous treatments on disease dynamics in an SIR epidemic model, 2012, 9, 1551-0018, 97, 10.3934/mbe.2012.9.97
    27. Jingan Cui, Yanan Zhang, Zhilan Feng, Influence of non-homogeneous mixing on final epidemic size in a meta-population model, 2019, 13, 1751-3758, 31, 10.1080/17513758.2018.1484186
    28. Qianqian Cui, Qiang Zhang, Zhipeng Qiu, Xiaomin Yang, Transmission Dynamics of an Epidemic Model with Vaccination, Treatment and Isolation, 2019, 42, 0126-6705, 885, 10.1007/s40840-017-0519-3
    29. E. Tagliazucchi, P. Balenzuela, M. Travizano, G.B. Mindlin, P.D. Mininni, Lessons from being challenged by COVID-19, 2020, 137, 09600779, 109923, 10.1016/j.chaos.2020.109923
    30. Mohammad A. Safi, Abba B. Gumel, Dynamics analysis of a quarantine model in two patches, 2015, 38, 01704214, 349, 10.1002/mma.3072
    31. Jean Dolbeault, Gabriel Turinici, E. Augeraud, M. Banerjee, J.-S. Dhersin, A. d'Onofrio, T. Lipniacki, S. Petrovskii, Chi Tran, A. Veber-Delattre, E. Vergu, V. Volpert, Heterogeneous social interactions and the COVID-19 lockdown outcome in a multi-group SEIR model, 2020, 15, 0973-5348, 36, 10.1051/mmnp/2020025
    32. Chengjun Sun, Wei Yang, Global results for an SIRS model with vaccination and isolation, 2010, 11, 14681218, 4223, 10.1016/j.nonrwa.2010.05.009
    33. Abba B. Gumel, Enahoro A. Iboi, Calistus N. Ngonghala, Elamin H. Elbasha, A primer on using mathematics to understand COVID-19 dynamics: Modeling, analysis and simulations, 2021, 6, 24680427, 148, 10.1016/j.idm.2020.11.005
    34. Muntasir Alam, K M Ariful Kabir, Jun Tanimoto, Based on mathematical epidemiology and evolutionary game theory, which is more effective: quarantine or isolation policy?, 2020, 2020, 1742-5468, 033502, 10.1088/1742-5468/ab75ea
    35. Suli Liu, Michael Y. Li, Epidemic models with discrete state structures, 2021, 01672789, 132903, 10.1016/j.physd.2021.132903
    36. Yi Wang, Jinde Cao, Global stability of general cholera models with nonlinear incidence and removal rates, 2015, 352, 00160032, 2464, 10.1016/j.jfranklin.2015.03.030
    37. Hongbin Guo, Michael Y. Li, Zhisheng Shuai, Global Dynamics of a General Class of Multistage Models for Infectious Diseases, 2012, 72, 0036-1399, 261, 10.1137/110827028
    38. Fuzhong Nian, Anhui Cong, Rendong Liu, Information propagation based on historical memory, 2019, 30, 0129-1831, 2050005, 10.1142/S0129183120500059
    39. Mustafa Turkyilmazoglu, Explicit formulae for the peak time of an epidemic from the SIR model, 2021, 01672789, 132902, 10.1016/j.physd.2021.132902
    40. KM Ariful Kabir, Atiqur Chowdhury, Jun Tanimoto, An evolutionary game modeling to assess the effect of border enforcement measures and socio-economic cost: Export-importation epidemic dynamics, 2021, 146, 09600779, 110918, 10.1016/j.chaos.2021.110918
    41. Dylan H. Morris, Fernando W. Rossine, Joshua B. Plotkin, Simon A. Levin, Optimal, near-optimal, and robust epidemic control, 2021, 4, 2399-3650, 10.1038/s42005-021-00570-y
    42. Vijay Kumar, Jyoti Chawla, Rajeev Kumar, Arti Saxena, 2021, Chapter 6, 978-3-030-67050-4, 99, 10.1007/978-3-030-67051-1_6
    43. Torsten Thalheim, Tyll Krüger, Jörg Galle, Indirect Virus Transmission via Fomites Can Counteract Lock-Down Effectiveness, 2022, 19, 1660-4601, 14011, 10.3390/ijerph192114011
    44. Yanjun Zhao, Huilai Li, Wenxuan Li, Yang Wang, Global stability of a SEIR epidemic model with infectious force in latent period and infected period under discontinuous treatment strategy, 2021, 14, 1793-5245, 2150034, 10.1142/S1793524521500340
    45. Ashutosh Trivedi, Nanda Kishore Sreenivas, Shrisha Rao, Modeling the Spread and Control of COVID-19, 2021, 9, 2079-8954, 53, 10.3390/systems9030053
    46. Hyun Ho Shin, Carlos Sauer Ayala, Pastor Pérez-Estigarribia, Sebastián Grillo, Leticia Segovia-Cabrera, Miguel García-Torres, Carlos Gaona, Sandra Irala, María Esther Pedrozo, Guillermo Sequera, José Luis Vázquez Noguera, Eduardo De Los Santos, A Mathematical Model for COVID-19 with Variable Transmissibility and Hospitalizations: A Case Study in Paraguay, 2021, 11, 2076-3417, 9726, 10.3390/app11209726
    47. Daniele Proverbio, Françoise Kemp, Stefano Magni, Andreas Husch, Atte Aalto, Laurent Mombaerts, Alexander Skupin, Jorge Gonçalves, Jose Ameijeiras-Alonso, Christophe Ley, Michele Tizzoni, Dynamical SPQEIR model assesses the effectiveness of non-pharmaceutical interventions against COVID-19 epidemic outbreaks, 2021, 16, 1932-6203, e0252019, 10.1371/journal.pone.0252019
    48. 2022, chapter 3, 9781799883432, 56, 10.4018/978-1-7998-8343-2.ch003
    49. Nana Kena Frempong, Theophilus Acheampong, Ofosuhene O. Apenteng, Emmanuel Nakua, John H. Amuasi, Bing Xue, Does the data tell the true story? A modelling assessment of early COVID-19 pandemic suppression and mitigation strategies in Ghana, 2021, 16, 1932-6203, e0258164, 10.1371/journal.pone.0258164
    50. Lee Benson, Ross S. Davidson, Darren M. Green, Andrew Hoyle, Mike R. Hutchings, Glenn Marion, Claudio José Struchiner, When and why direct transmission models can be used for environmentally persistent pathogens, 2021, 17, 1553-7358, e1009652, 10.1371/journal.pcbi.1009652
    51. K. M. Ariful Kabir, Tori Risa, Jun Tanimoto, Prosocial behavior of wearing a mask during an epidemic: an evolutionary explanation, 2021, 11, 2045-2322, 10.1038/s41598-021-92094-2
    52. Kaitlyn Muller, Peter A. Muller, Mathematical modelling of the spread of COVID-19 on a university campus, 2021, 6, 24680427, 1025, 10.1016/j.idm.2021.08.004
    53. Yanjun Zhao, Wenxuan Li, Yang Wang, 2023, 9780323995573, 323, 10.1016/B978-0-32-399557-3.00017-X
    54. Yan Chen, Haitao Song, Shengqiang Liu, Evaluations of COVID-19 epidemic models with multiple susceptible compartments using exponential and non-exponential distribution for disease stages, 2022, 7, 24680427, 795, 10.1016/j.idm.2022.11.004
    55. Florin Avram, Rim Adenane, David I. Ketcheson, A Review of Matrix SIR Arino Epidemic Models, 2021, 9, 2227-7390, 1513, 10.3390/math9131513
    56. Andreas Hornstein, Quarantine, Contact Tracing, and Testing: Implications of an Augmented SEIR Model, 2022, 22, 1935-1690, 53, 10.1515/bejm-2020-0168
    57. SURYADEEPTO NAG, SIDDHARTHA P. CHAKRABARTY, MODELING THE DYNAMICS OF COVID-19 TRANSMISSION IN INDIA: SOCIAL DISTANCING, REGIONAL SPREAD AND HEALTHCARE CAPACITY, 2022, 30, 0218-3390, 647, 10.1142/S0218339022500231
    58. Cameron J. Browne, Hayriye Gulbudak, Joshua C. Macdonald, Differential impacts of contact tracing and lockdowns on outbreak size in COVID-19 model applied to China, 2022, 532, 00225193, 110919, 10.1016/j.jtbi.2021.110919
    59. Florin Avram, Rim Adenane, Andrei Halanay, New Results and Open Questions for SIR-PH Epidemic Models with Linear Birth Rate, Loss of Immunity, Vaccination, and Disease and Vaccination Fatalities, 2022, 14, 2073-8994, 995, 10.3390/sym14050995
    60. M. Aykut Attar, Ayça Tekin-Koru, Latent social distancing: Identification, causes and consequences, 2022, 46, 09393625, 100944, 10.1016/j.ecosys.2022.100944
    61. Rajan Gupta, Gaurav Pandey, Saibal K. Pal, Comparative analysis of epidemiological models for COVID-19 pandemic predictions, 2021, 5, 2470-9360, 69, 10.1080/24709360.2021.1913709
    62. Md. Mamun-Ur-Rashid Khan, Md. Rajib Arefin, Jun Tanimoto, Investigating the trade-off between self-quarantine and forced quarantine provisions to control an epidemic: An evolutionary approach, 2022, 432, 00963003, 127365, 10.1016/j.amc.2022.127365
    63. Zuzana Chladná, Jana Kopfová, Dmitry Rachinskii, Pavel Štepánek, Effect of Quarantine Strategies in a Compartmental Model with Asymptomatic Groups, 2021, 1040-7294, 10.1007/s10884-021-10059-5
    64. Muhammad Abdurrahman Rois, Cicik Alfiniyah, Chidozie W. Chukwu, Dynamic analysis and optimal control of COVID-19 with comorbidity: A modeling study of Indonesia, 2023, 8, 2297-4687, 10.3389/fams.2022.1096141
    65. Florin Avram, Rim Adenane, Lasko Basnarkov, Gianluca Bianchin, Dan Goreac, Andrei Halanay, An Age of Infection Kernel, an R Formula, and Further Results for Arino–Brauer A, B Matrix Epidemic Models with Varying Populations, Waning Immunity, and Disease and Vaccination Fatalities, 2023, 11, 2227-7390, 1307, 10.3390/math11061307
    66. Sarita Bugalia, Jai Prakash Tripathi, Assessing potential insights of an imperfect testing strategy: Parameter estimation and practical identifiability using early COVID-19 data in India, 2023, 10075704, 107280, 10.1016/j.cnsns.2023.107280
    67. K. M. Ariful Kabir, Mohammad Sharif Ullah, Jun Tanimoto, Analyzing the Costs and Benefits of Utilizing a Mixed-Strategy Approach in Infectious Disease Control under a Voluntary Vaccination Policy, 2023, 11, 2076-393X, 1476, 10.3390/vaccines11091476
    68. Preeti Deolia, Anuraj Singh, Analysing the probable insights of ADE in dengue vaccination embodying sequential Zika infection and waning immunity, 2024, 139, 2190-5444, 10.1140/epjp/s13360-023-04813-5
    69. Mohamad Tafrikan, Yolanda Norasia, Aly Syafrudin, Muhammad Abdurrahman Rois, 2024, 3104, 0094-243X, 020009, 10.1063/5.0194546
    70. Mohammad Sharif Ullah, K.M. Ariful Kabir, Behavioral game of quarantine during the monkeypox epidemic: Analysis of deterministic and fractional order approach, 2024, 10, 24058440, e26998, 10.1016/j.heliyon.2024.e26998
    71. Qian Li, Biao Tang, Yanni Xiao, Multiple epidemic waves in a switching system with multi-thresholds triggered alternate control, 2024, 0924-090X, 10.1007/s11071-024-09533-8
    72. Renfei Wang, Yilin Li, Dayu Wu, Yong Zou, Ming Tang, Shuguang Guan, Ying Liu, Zhen Jin, Efim Pelinovsky, Mikhail Kirillin, Elbert Macau, Impact of agent-based intervention strategies on the COVID-19 pandemic in large-scale dynamic contact networks, 2024, 03784371, 129852, 10.1016/j.physa.2024.129852
    73. Atiqur Chowdhury, K M Ariful Kabir, Jun Tanimoto, How quarantine and social distancing policy can suppress the outbreak of novel coronavirus in developing or under poverty level countries: a mathematical and statistical analysis, 2021, 10, 2378315X, 145, 10.15406/bbij.2021.10.00341
    74. Muhammad Abdurrahman Rois, Cicik Alfiniyah, Santi Martini, Dipo Aldila, Farai Nyabadza, Modeling and optimal control of COVID-19 with comorbidity and three-dose vaccination in Indonesia, 2024, 25889338, 10.1016/j.jobb.2024.06.004
    75. Mahmoud A. Ibrahim, Threshold dynamics in a periodic epidemic model with imperfect quarantine, isolation and vaccination, 2024, 9, 2473-6988, 21972, 10.3934/math.20241068
    76. Florin Avram, Rim Adenane, Lasko Basnarkov, Some Probabilistic Interpretations Related to the Next-Generation Matrix Theory: A Review with Examples, 2024, 12, 2227-7390, 2425, 10.3390/math12152425
    77. Romelito L. Lapitan, Precognition of Known And Unknown Biothreats: A Risk-Based Approach, 2024, 1530-3667, 10.1089/vbz.2023.0169
    78. Lukasz Rachel, The second wave, 2024, 1434-4742, 10.1007/s10058-024-00374-w
    79. Kiriti Bhusan Mahato, Mst Sebi Khatun, K.M. Ariful Kabir, Pritha Das, Dynamical behaviors and social efficiency deficit analysis of an epidemic model with three combined strategies, 2024, 03784371, 130315, 10.1016/j.physa.2024.130315
    80. Abhi Chakraborty, Md. Fahimur Rahman Shuvo, Faiza Farheen Haque, K. M. Ariful Kabir, Analyzing disease control through testing game approach embedded with treatment and vaccination strategies, 2025, 15, 2045-2322, 10.1038/s41598-024-84746-w
    81. Martina Alutto, Leonardo Cianfanelli, Giacomo Como, Fabio Fagnani, On the Dynamic Behavior of the Network SIR Epidemic Model, 2025, 12, 2325-5870, 177, 10.1109/TCNS.2024.3448136
  • Reader Comments
  • © 2016 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索
AIMS Materials Science
1.4 3.6

Metrics

Article views(4992) PDF downloads(1055) Cited by(0)

Article has an altmetric score of 1
Article has an altmetric score of 1
Preview PDF
Download XML
Export Citation
Article outline
Abstract
References

Figures and Tables

Figures(7)

Other Articles By Authors

Related pages

Tools

Copyright © AIMS Press

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog