In confronting the critical challenge of disease outbreak management, health authorities consistently encourage individuals to voluntarily disclose a potential exposure to infection and adhere to self-quarantine protocols by assuring medical care (hospital beds, oxygen, and constant health monitoring) and helplines for severe patients. These have been observed during pandemics; for example, COVID-19 phases in many middle-income countries, such as India, promoted quarantine and reduced stigma. Here, we present a game-theoretic model to elucidate the behavioural interactions in infection disclosure during an outbreak. By employing a fractional derivative approach to model disease propagation, we determine the minimum level of voluntary disclosure required to disrupt the chain of transmission and allow the epidemic to fade. Our findings suggest that higher transmission rates and an increased perceived severity of infection may change the externality of the disclosing strategy, leading to an increase in the proportion of individuals who choose disclosure, and ultimately reducing disease incidence. We estimate the behavioural parameters and transmission rates by fitting the model to COVID-19 hospitalized cases in Chile, South America. The results from our paper underscore the potential for promoting the voluntary disclosure of infection during emerging outbreaks through effective risk communication, thereby emphasizing the severity of the disease and providing accurate information to the public about capacities within hospitals and medical care facilities.
Citation: Pranav Verma, Viney Kumar, Samit Bhattacharyya. Modelling behavioural interactions in infection disclosure during an outbreak: An evolutionary game theory approach[J]. Mathematical Biosciences and Engineering, 2025, 22(8): 1931-1955. doi: 10.3934/mbe.2025070
| [1] | Alice Fiaschi . Rate-independent phase transitions in elastic materials: A Young-measure approach. Networks and Heterogeneous Media, 2010, 5(2): 257-298. doi: 10.3934/nhm.2010.5.257 |
| [2] | 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. Networks and Heterogeneous Media, 2013, 8(2): 481-499. doi: 10.3934/nhm.2013.8.481 |
| [3] | G. Dal Maso, Antonio DeSimone, M. G. Mora, M. Morini . Globally stable quasistatic evolution in plasticity with softening. Networks and Heterogeneous Media, 2008, 3(3): 567-614. doi: 10.3934/nhm.2008.3.567 |
| [4] | G. Dal Maso, Antonio DeSimone, M. G. Mora, M. Morini . Time-dependent systems of generalized Young measures. Networks and Heterogeneous Media, 2007, 2(1): 1-36. doi: 10.3934/nhm.2007.2.1 |
| [5] | Michela Eleuteri, Luca Lussardi, Ulisse Stefanelli . A rate-independent model for permanent inelastic effects in shape memory materials. Networks and Heterogeneous Media, 2011, 6(1): 145-165. doi: 10.3934/nhm.2011.6.145 |
| [6] | Flavia Smarrazzo, Alberto Tesei . Entropy solutions of forward-backward parabolic equations with Devonshire free energy. Networks and Heterogeneous Media, 2012, 7(4): 941-966. doi: 10.3934/nhm.2012.7.941 |
| [7] | Adrian Muntean, Toyohiko Aiki . Preface to ``The Mathematics of Concrete". Networks and Heterogeneous Media, 2014, 9(4): i-ii. doi: 10.3934/nhm.2014.9.4i |
| [8] | Gianni Dal Maso, Francesco Solombrino . Quasistatic evolution for Cam-Clay plasticity: The spatially homogeneous case. Networks and Heterogeneous Media, 2010, 5(1): 97-132. doi: 10.3934/nhm.2010.5.97 |
| [9] | Mauro Garavello . Boundary value problem for a phase transition model. Networks and Heterogeneous Media, 2016, 11(1): 89-105. doi: 10.3934/nhm.2016.11.89 |
| [10] | Martin Heida, Stefan Neukamm, Mario Varga . Stochastic two-scale convergence and Young measures. Networks and Heterogeneous Media, 2022, 17(2): 227-254. doi: 10.3934/nhm.2022004 |
In confronting the critical challenge of disease outbreak management, health authorities consistently encourage individuals to voluntarily disclose a potential exposure to infection and adhere to self-quarantine protocols by assuring medical care (hospital beds, oxygen, and constant health monitoring) and helplines for severe patients. These have been observed during pandemics; for example, COVID-19 phases in many middle-income countries, such as India, promoted quarantine and reduced stigma. Here, we present a game-theoretic model to elucidate the behavioural interactions in infection disclosure during an outbreak. By employing a fractional derivative approach to model disease propagation, we determine the minimum level of voluntary disclosure required to disrupt the chain of transmission and allow the epidemic to fade. Our findings suggest that higher transmission rates and an increased perceived severity of infection may change the externality of the disclosing strategy, leading to an increase in the proportion of individuals who choose disclosure, and ultimately reducing disease incidence. We estimate the behavioural parameters and transmission rates by fitting the model to COVID-19 hospitalized cases in Chile, South America. The results from our paper underscore the potential for promoting the voluntary disclosure of infection during emerging outbreaks through effective risk communication, thereby emphasizing the severity of the disease and providing accurate information to the public about capacities within hospitals and medical care facilities.
| [1] |
J. Huang, Y. Qian, Y. Yan, H. Liang, L. Zhao, Addressing hospital overwhelm during the COVID-19 pandemic by using a primary health care-based integrated health system: Modeling study, JMIR Med. Inform., 12 (2024), 54355. https://doi.org/10.2196/54355 doi: 10.2196/54355
|
| [2] |
H. Lau, T. Khosrawipour, P. Kocbach, H. Ichii, J. Bania, V. Khosrawipour, Evaluating the massive underreporting and undertesting of COVID-19 cases in multiple global epicenters, Pulmonology, 27 (2021), 110–115. https://doi.org/10.1016/j.pulmoe.2020.05.015 doi: 10.1016/j.pulmoe.2020.05.015
|
| [3] | Statista, Impact of coronavirus (COVID-19) on securing ICU beds in hospitals across India as of April 2021, 2021. Available from: https://www.statista.com/statistics/1231043/india-covid-19-impact-on-securing-icu-beds-in-hospitals/. |
| [4] |
X. Wang, J. Wang, J. Shen, J. S. Ji, L. Pan, H. Liu, et al., Facilities for centralized isolation and quarantine for the observation and treatment of patients with COVID-19, Engineering, 7 (2021), 908–913. https://doi.org/10.1016/j.eng.2021.03.010 doi: 10.1016/j.eng.2021.03.010
|
| [5] |
W. Zhu, M. Zhang, J. Pan, Y. Yao, W. Wang, Effects of prolonged incubation period and centralized quarantine on the COVID-19 outbreak in Shijiazhuang, China: A modeling study, BMC Med., 19 (2021), 308. https://doi.org/10.1186/s12916-021-02178-z doi: 10.1186/s12916-021-02178-z
|
| [6] |
A. Satapathi, N. K. Dhar, A. R. Hota, V. Srivastava, Coupled evolutionary behavioral and disease dynamics under reinfection risk, IEEE Trans. Control Network Syst., 11 (2024), 795–807. https://doi.org/10.1109/TCNS.2023.3312250 doi: 10.1109/TCNS.2023.3312250
|
| [7] |
S. Funk, M. Salathé, V. A. A. Jansen, Modelling the influence of human behaviour on the spread of infectious diseases: A review, J. R. Soc. Interface, 7 (2010), 1247–1256. https://doi.org/10.1098/rsif.2010.0142 doi: 10.1098/rsif.2010.0142
|
| [8] |
M. Martcheva, N. Tuncer, C. N. Ngonghala, Effects of social-distancing on infectious disease dynamics: An evolutionary game theory and economic perspective, J. Biol. Dyn., 15 (2021), 342–366. https://doi.org/10.1080/17513758.2021.1946177 doi: 10.1080/17513758.2021.1946177
|
| [9] |
M. Alam, J. Tanimoto, A game-theoretic modeling approach to comprehend the advantage of dynamic health interventions in limiting the transmission of multi-strain epidemics, J. Appl. Math. Phys., 10 (2022), 3700–3748. https://doi.org/10.4236/jamp.2022.1012248 doi: 10.4236/jamp.2022.1012248
|
| [10] | P. Premkumar, J. B. Chakrabarty, A. Rajeev, Impact of sustained lockdown during COVID-19 pandemic on behavioural dynamics through evolutionary game theoretic model, Ann. Oper. Res., (2023). https://doi.org/10.1007/s10479-023-05743-2 |
| [11] | H. Khazaei, K. Paarporn, A. Garcia, C. Eksin, Disease spread coupled with evolutionary social distancing dynamics can lead to growing oscillations, in 2021 60th IEEE Conference on Decision and Control (CDC), (2021), 4280–4286. https://doi.org/10.1109/CDC45484.2021.9683594 |
| [12] |
A. O. Yunus, M. O. Olayiwola, K. A. Adedokun, J. A. Adedeji, I. A. Alaje, Mathematical analysis of fractional-order caputo's derivative of coronavirus disease model via laplace adomian decomposition method, Beni-Suef Univ. J. Basic Appl. Sci., 11 (2022), 144. https://doi.org/10.1186/s43088-022-00326-9 doi: 10.1186/s43088-022-00326-9
|
| [13] |
M. Wali, S. Arshad, J. Huang, Stability analysis of an axtended SEIR COVID-19 fractional model with vaccination efficiency, Comput. Math. Methods Med., 2022 (2022), 3754051. https://doi.org/10.1155/2022/3754051 doi: 10.1155/2022/3754051
|
| [14] | K. Oldham, J. Spanier, The Fractional Calculus Theory and Applications of Differentiation and Integration to Arbitrary Order, Elsevier, 1974. |
| [15] |
H. M. Srivastava, Fractional-order derivatives and integrals: Introductory overview and recent developments, Kyungpook Math. J., 60 (2020), 73–116. https://doi.org/10.5666/KMJ.2020.60.1.73 doi: 10.5666/KMJ.2020.60.1.73
|
| [16] |
S. He, H. Wang, K. Sun, Solutions and memory effect of fractional-order chaotic system: A review, Chin. Phys. B, 31 (2022), 060501. https://doi.org/10.1088/1674-1056/ac43ae doi: 10.1088/1674-1056/ac43ae
|
| [17] |
M. R. Islam, A. Peace, D. Medina, T. Oraby, Integer versus fractional order SEIR deterministic and stochastic models of measles, Int. J. Environ. Res. Public Health, 17 (2020), 2014. https://doi.org/10.3390/ijerph17062014 doi: 10.3390/ijerph17062014
|
| [18] |
C. T. Bauch, Imitation dynamics predict vaccinating behaviour, Proc. R. Soc. B, 272 (2005), 1669–1675. https://doi.org/10.1098/rspb.2005.3153 doi: 10.1098/rspb.2005.3153
|
| [19] |
X. Wang, J. Wang, J. Shen, J. S. Ji, L. Pan, H. Liu, et al., Facilities for centralized isolation and quarantine for the observation and treatment of patients with COVID-19, Engineering, 7 (2021), 908–913. https://doi.org/10.1016/j.eng.2021.03.010 doi: 10.1016/j.eng.2021.03.010
|
| [20] | J. Hofbauer, K. Sigmund, Evolutionary Games and Population Dynamics, Cambridge University Press, 1998. https://doi.org/10.1017/CBO9781139173179 |
| [21] |
S. He, Y. Peng, K. Sun, SEIR modeling of the COVID-19 and its dynamics, Nonlinear Dyn., 101 (2020), 1667–1680. https://doi.org/10.1007/s11071-020-05743-y doi: 10.1007/s11071-020-05743-y
|
| [22] |
R. Niu, E. W. M. Wong, Y. Chan, M. A. V. Wyk, G. Chen, Modeling the COVID-19 pandemic using an SEIHR model with human migration, IEEE Access, 8 (2020), 195503–195514. https://doi.org/10.1109/ACCESS.2020.3032584 doi: 10.1109/ACCESS.2020.3032584
|
| [23] |
F. Ndaïrou, I. Area, J. J. Nieto, D. F. M. Torres, Mathematical modeling of COVID-19 transmission dynamics with a case study of Wuhan, Chaos Solitons Fractals, 135 (2020), 109846. https://doi.org/10.1016/j.chaos.2020.109846 doi: 10.1016/j.chaos.2020.109846
|
| [24] |
H. Alrabaiah, M. Arfan, K. Shah, I. Mahariq, A. Ullah, A comparative study of spreading of novel corona virus disease by using fractional order modified SEIR model, Alexandria Eng. J., 60 (2021), 573–585. https://doi.org/10.1016/j.aej.2020.09.036 doi: 10.1016/j.aej.2020.09.036
|
| [25] | S. Y. Chae, K. Lee, H. M. Lee, N. Jung, Q. A. Le, B. J. Mafwele, et al., Estimation of infection rate and predictions of disease spreading based on initial individuals infected with COVID-19, Front. Phys., 8 (2020). https://doi.org/10.3389/fphy.2020.00311 |
| [26] |
H. Sun, Y. Qiu, H. Yan, Y. Huang, Y. Zhu, J. Gu, et al., Tracking reproductivity of COVID-19 epidemic in China with varying coefficient SIR model, J. Data Sci., 18 (2020), 455–472. https://doi.org/10.6339/JDS.202007_18(3).0010 doi: 10.6339/JDS.202007_18(3).0010
|
| [27] |
P. Ashcroft, S. Lehtinen, D. C. Angst, N. Low, S. Bonhoeffer, Quantifying the impact of quarantine duration on COVID-19 transmission, Elife, 10 (2021), 63704. https://doi.org/10.7554/eLife.63704 doi: 10.7554/eLife.63704
|
| [28] | E. Mathieu, H. Ritchie, L. Rodés-Guirao, C. Appel, D. Gavrilov, C. Giattino, et al., COVID-19 Pandemic, 2020. Available from: https://ourworldindata.org/coronavirus. |
| [29] |
S. Lumme, R. Sund, A. H. Leyland, I. Keskimäki, A Monte Carlo method to estimate the confidence intervals for the concentration index using aggregated population register data, Health Serv. Outcomes Res. Method., 15 (2015), 82–98. https://doi.org/10.1007/s10742-015-0137-1 doi: 10.1007/s10742-015-0137-1
|
| [30] |
E. L. Ionides, C. Breto, J. Park, R. A. Smith, A. A. King, Monte Carlo profile confidence intervals for dynamic systems, J. R. Soc. Interface, 14 (2017), 20170126. https://doi.org/10.1098/rsif.2017.0126. doi: 10.1098/rsif.2017.0126
|
| [31] |
B. Sen-Crowe, M. Sutherland, M. McKenney, A. Elkbuli, A closer look into global hospital beds capacity and resource shortages during the COVID-19 pandemic, J. Surg. Res., 260 (2021), 56–63. https://doi.org/10.1016/j.jss.2020.11.062 doi: 10.1016/j.jss.2020.11.062
|
| [32] |
P. Rzymski, N. Kasianchuk, D. Sikora, B. Poniedziałek, COVID-19 vaccinations and rates of infections, hospitalizations, ICU admissions, and deaths in Europe during SARS-CoV-2 omicron wave in the first quarter of 2022, J. Med. Virol., 95 (2023), 28131. https://doi.org/10.1002/jmv.28131 doi: 10.1002/jmv.28131
|
| [33] |
R. Silaghi-Dumitrescu, I. Patrascu, M. Lehene, I. Bercea, Comorbidities of COVID-19 patients, Medicina, 59 (2023), 1393. https://doi.org/10.3390/medicina59081393 doi: 10.3390/medicina59081393
|
| [34] |
C. N. Ngonghala, P. Goel, D. Kutor, S. Bhattacharyya, Human choice to self-isolate in the face of the COVID-19 pandemic: A game dynamic modelling approach, J. Theor. Biol., 32 (2020), 100397. https://doi.org/10.1016/j.jtbi.2021.110692 doi: 10.1016/j.jtbi.2021.110692
|
| [35] |
C. M. Saad-Roy, A. Traulsen, Dynamics in a behavioral-epidemiological model for individual adherence to a nonpharmaceutical intervention, Proc. Natl. Acad. Sci., 120 (2023), 2311584120. https://doi.org/10.1073/pnas.2311584120 doi: 10.1073/pnas.2311584120
|
| [36] |
M. Farman, A. Akgül, A. Ahmad, S. Imtiaz, Analysis and dynamical behavior of fractional-order cancer model with vaccine strategy, Math. Methods Appl. Sci., 43 (2020), 4871–4882. https://doi.org/10.1002/mma.6240 doi: 10.1002/mma.6240
|
| [37] |
E. Addai, L. Zhang, J. K. K. Asamoah, J. F. Essel, A fractional order age-specific smoke epidemic model, Appl. Math. Modell., 119 (2023), 99–118. https://doi.org/10.1016/j.apm.2023.02.019 doi: 10.1016/j.apm.2023.02.019
|
| [38] |
J. Chen, C. Xia, M. Perc, The SIQRS propagation model with quarantine on simplicial complexes, IEEE Trans. Comput. Soc. Syst., 11 (2024), 4267–4278. https://doi.org/10.1109/TCSS.2024.3351173 doi: 10.1109/TCSS.2024.3351173
|
| [39] |
O. Diekmann, J. A. P. Heesterbeek, M. G. Roberts, The construction of next-generation matrices for compartmental epidemic models, J. R. Soc. Interface, 7 (2010), 873–885. https://doi.org/10.1098/rsif.2009.0386 doi: 10.1098/rsif.2009.0386
|
 mbe-22-08-070-supplementary.pdf |
 |
| 1. | Alice Fiaschi, Dorothee Knees, Ulisse Stefanelli, Young-Measure Quasi-Static Damage Evolution, 2012, 203, 0003-9527, 415, 10.1007/s00205-011-0474-3 | |
| 2. | Alice Fiaschi, Young-measure quasi-static damage evolution: The nonconvex and the brittle cases, 2013, 6, 1937-1179, 17, 10.3934/dcdss.2013.6.17 | |
| 3. | Alexander Mielke, Tomàš Roubíček, 2015, Chapter 2, 978-1-4939-2705-0, 45, 10.1007/978-1-4939-2706-7_2 | |
| 4. | Alice Fiaschi, Dorothee Knees, Sina Reichelt, Global higher integrability of minimizers of variational problems with mixed boundary conditions, 2013, 401, 0022247X, 269, 10.1016/j.jmaa.2012.11.040 | |
| 5. | Alice Fiaschi, Quasistatic evolution for a phase-transition model: a Young measure approach, 2011, 34, 09367195, 124, 10.1002/gamm.201110020 |
Figures(12) / Tables(6)
Pranav Verma, Viney Kumar, Samit Bhattacharyya. Modelling behavioural interactions in infection disclosure during an outbreak: An evolutionary game theory approach[J]. Mathematical Biosciences and Engineering, 2025, 22(8): 1931-1955. doi: 10.3934/mbe.2025070
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