Document Type : Original Article
Authors
1 Physics Department, Institute for Advanced Studies in Basic Sciences
2 Physics Department, Institute for Advanced Studies in Basic Sciences, Zanjan
Abstract
Interaction between two diseases can be as competition and cooperation. In this work, we study these interactions for two diseases that spread simultaneously on a multiplex network. We assume that each disease spreads in one layer of the network with a different structure than the other layer. We consider an asymmetric case in which one disease propagates according to the SIR dynamics, and another one follows the dynamics of the SIS model. By using the heterogeneous mean-field theory, we find the epidemic threshold of each disease in the case of cooperation and competition. We also obtain the phase diagram of the model that contains information about the prevalence of diseases.
Keywords
- R M Anderson and R M May, “Infectious diseases of humans: Dynamics and Control”, Oxford University Press, Oxford (1992).
- W O Kermack and A G McKendrick, R. Soc. London, Ser. A 115 (1927) 700.
- R Pastor-Satorras and A Vespignani. Rev. Lett. 86 (2001) 14.
- R Pastor-Satorras, C Castellano, P Van Mieghem, and AVespignani, Mod. Phys. 87 (2015) 925.
- W Wang, M Tang, H E Stanley, and L A Braunstein, Prog. Phys. 80 (2017) 036603.
- M E J Newman, Rev. Lett. 95 (2005) 108701.
- M E J Newman and C R Ferrario, PLoS ONE 8 (2013) e71321.
- W Cai, L Chen, F Ghanbarnejad, and P Grassberger, Nature Phys. 11 (2015) 936.
9. L Pan, D.Yang, W Wang, S Cai, T Zhou, Y C Lai, Phys. Rev. Research 2 (2020) 023233.
- F Pinotti, F Ghanbarnejad, P Hovel, and C Poletto, Royal Society Open Science 7 (2020) 190305.
- B Karrer and M E J Newman, Rev. E. 84 (2011) 036106.
- C Poletto, S Meloni, V Colizza, Y Moreno and A Vespignani, PLoS Computational Biology 9 (2013) 1003169.
- M M de Oliveira and R Dickman, PloS ONE 12 (2017) e0182672.
- P C Ventura, Y Moreno, and F A Rodrigues, Physical Review Research 3 (2021) 013146.
- P Brodka, K Musial, and J Jankowski, IEEE Access 8 (2020)
- C Granell, S Gomez, and A Arenas, Rev. Lett. 111 (2013) 128701.
- N Azimi-Tafreshi, Rev. E. 93 (2016) 042303.
- Z Wang, M A Andrews, Z X Wu, L Wang, and C T Bauch, Physics of life reviews 15 (2015) 1.
- FVelasquez-Rojas, P C Ventura, C Connaughton, Y Moreno, F A Rodrigues, and F Vazquez, Rev. E. 102 (2020) 022312.
- J Sanz, C Y Xia, S Meloni, and Y Moreno, Rev. X. 4 (2014) 041005.
- M Kivelä, A Arenas, M Barthelemy, J P Gleeson, Y Moreno, and M A Porter, Journal of Complex Networks 2 (2014) 203.
- Q Wu and S Chen, Chaos 30 (2020) 073115.
- M Boguna, and R Pastor-Satorras, Rev. E. 66 (2002) 047104.
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