Abstract：Existing infectious disease models are usually based on compartment models and model optimisation is performed by adjusting the number of compartments and transfer paths. However, the finite states delineated by the compartment model often do not adequately reflect the actual states that individuals live in the real world. In this study, we model infectious disease based on quantum mechanics and use quantum superposition states to represent individual states, achieving a more accurate representation of individual states. Firstly, this paper analyses the individual infection process and evolution of the model, and derives the basic reproduction number and disease-free equilibrium point of the model. Secondly, the model simulation is carried out on a quantum circuit, and the parameter sensitivity of the model is analysed and the reasonableness of the model is verified. The simulation results show that the predictions of the model are consistent with the general law of virus propagation and can be implemented to simulate the structure of the compartment model. Finally, the applicability of the model is further verified by simulating real COVID-19 epidemic data.
何为源, 宾晟, 孙更新. 基于量子力学的传染病模型构建与研究[J]. 复杂系统与复杂性科学, 2026, 23(4): 51-61.
HE Weiyuan, BIN Sheng, SUN Gengxin. Construction and Research of Infectious Disease Model Based on Quantum Mechanics[J]. Complex Systems and Complexity Science, 2026, 23(4): 51-61.
[1] Amouch M, Karim N. Modeling the dynamic of COVID-19 with different types of transmissions[J]. Chaos, Solitons & Fractals, 2021, 150: 111188. [2] Pei S, Makse H A. Spreading dynamics in complex networks[J]. Journal of Statistical Mechanics: Theory and Experiment, 2013, 2013(12): P12002. [3] Kermack W O, Mckendrick A G, Walker G T. A contribution to the mathematical theory of epidemics[J]. Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character, 1997, 115(772): 700-721. [4] Geng X, Katul G G, Gerges F, et al. A kernel-modulated SIR model for Covid-19 contagious spread from county to continent[J]. Proceedings of the National Academy of Sciences, 2021, 118(21): e2023321118. [5] Ram V, Schaposnik L P. A modified age-structured SIR model for COVID-19 type viruses[J]. Scientific Reports, 2021, 11(1): 15194. [6] Cai M, Karniadakis G E, Li C. Fractional SEIR model and data-driven predictions of COVID-19 dynamics of omicron variant[J]. Chaos: an Interdisciplinary Journal of Nonlinear Science, 2022, 32(7): 071101. [7] Kiselev I N, Akberdin I R, Kolpakov F A. Delay-differential SEIR modeling for improved modelling of infection dynamics[J]. Scientific Reports, 2023, 13(1): 13439. [8] Wang J, Wang Z, Yu P, et al. The SEIR dynamic evolutionary model with markov chains in hyper networks[J]. Sustainability, 2022, 14(20): 13036. [9] Zhang J, Jin T. A stochastic semi-parametric SEIR model with infectivity in an incubation period[J]. Mathematics, 2024, 12(10): 1580. [10] Basnarkov L. SEAIR Epidemic spreading model of COVID-19[J]. Chaos, Solitons & Fractals, 2021, 142: 110394. [11] Ndaïrou F, Area I, Nieto J J, et al. Mathematical modeling of COVID-19 transmission dynamics with a case study of Wuhan[J]. Chaos, Solitons & Fractals, 2020, 135: 109846. [12] Babaei A, Ahmadi M, Jafari H, et al. A mathematical model to examine the effect of quarantine on the spread of coronavirus[J]. Chaos, Solitons & Fractals, 2021, 142: 110418. [13] Tyagi S, Martha S C, Abbas S, et al. Mathematical modeling and analysis for controlling the spread of infectious diseases[J]. Chaos, Solitons & Fractals, 2021, 144: 110707. [14] Garira W, Maregere B. The transmission mechanism theory of disease dynamics: its aims, assumptions and limitations[J]. Infectious Disease Modelling, 2023, 8(1): 122-144. [15] Wang X, Lyu Y, Yao C, et al. Simulating the spread of infection in networks with quantum computers[J]. Physical Review Applied, 2023, 19(6): 064035. [16] Gomatam R V. Quantum theory and the observation problem[J]. Journal of Consciousness Studies, 1999, 6(11/12):173-190. [17] Schubert D, Richter J, Jin F, et al. Quantum versus classical dynamics in spin models: chains, ladders, and square lattices[J]. Physical Review B, 2021, 104(5): 054415. [18] Yanofsky N S. An introduction to Quantum computing[DB/OL].[2024-06-09]. http://link.springer.com/10.1007/978-94-007-0080-2_10. [19] Wang Y. Quantum computation and quantum information[J]. Statistical Science, 2012, 27(3): 373-394. [20] Galindo A, Martín-delgado M A. Information and computation: classical and quantum aspects[J]. Reviews of Modern Physics, 2002, 74(2): 347-423. [21] Javadi-abhari A, Treinish M, Krsulich K, et al. Quantum Computing with Qiskit[M/OL].[2024-06-09]. http://arxiv.org/abs/2405.08810. [22] Jones T C, Biele G, Mühlemann B, et al. Estimating infectiousness throughout SARS-CoV-2 infection course[J]. Science, 2021, 373(6551): eabi5273. [23] Alene M, Yismaw L, Assemie M A, et al. Serial interval and incubation period of COVID-19: a systematic review and meta-analysis[J]. BMC Infectious Diseases, 2021, 21(1): 257. [24] Tindale L C, Stockdale J E, Coombe M, et al. Evidence for transmission of COVID-19 prior to symptom onset[DB/OL].[2024-01-02]. https://elifesciences.org/articles/57149. [25] Memoli M J, Athota R, Reed S, et al. The natural history of influenza infection in the severely immunocompromised vs nonimmunocompromised hosts[J]. Clinical Infectious Diseases, 2014, 58(2): 214-224. [26] Chen X, Liu S, Goraya M U, et al. Host immune response to influenza a virus infection[J]. Frontiers in Immunology, 2018, 9: 320. [27] Lessler J, Reich N G, Brookmeyer R, et al. Incubation periods of acute respiratory viral infections: a systematic review[J]. The Lancet Infectious Diseases, 2009, 9(5): 291-300. [28] Gendelman H E, Narayan O, Molineaux S, et al. Slow, persistent replication of lentiviruses: role of tissue macrophages and macrophage precursors in bone marrow.[J]. Proceedings of the National Academy of Sciences, 1985, 82(20): 7086-7090. [29] Telo Da Gama M M, Nunes A. Epidemics in small world networks[J]. The European Physical Journal B-Condensed Matter and Complex Systems, 2006, 50(1): 205-208. [30] Barabási A L, Albert R. Emergence of scaling in random networks[J]. Science, 1999, 286(5439): 509-512. [31] Harapan H, Itoh N, Yufika A, et al. Coronavirus disease 2019 (COVID-19): a literature review[J]. Journal of Infection and Public Health, 2020, 13(5): 667-673. [32] Gunzler D D, Sehgal A R. Time-Varying COVID-19 Reproduction Number in the United States[M/OL]. (2020-04-15)[2024-06-01]. http://medrxiv.org/lookup/doi/10.1101/2020.04.10.20060863. [33] Alimohamadi Y, Taghdir M, Sepandi M. Estimate of the basic reproduction number for COVID-19: a systematic review and meta-analysis[J]. Journal of Preventive Medicine and Public Health, 2020, 53: 151-157. [34] Linton N, Kobayashi T, Yang Y, et al. Incubation period and other epidemiological characteristics of 2019 novel coronavirus infections with right truncation: a statistical analysis of publicly available case data[J]. Journal of Clinical Medicine, 2020, 9(2): 538. [35] Tolossa T, Wakuma B, Seyoum Gebre D, et al. Time to recovery from COVID-19 and its predictors among patients admitted to treatment center of wollega university referral hospital, western ethiopia: survival analysis of retrospective cohort study[J]. Plos One, 2021, 16(6): e0252389.
