Dynamical analysis of novel minimal SEIR model incorporating asymptomatic transmission

Document Type : Research Article

Authors

1 Department of Mathematics, Sardar Patel University, Vallabh Vidyanagar, Anand, Gujarat, India. Department of Mathematics, Shri Alpesh N. Patel Post Graduate Institute of Science & Research, Anand.

2 Department of Mathematics, Sardar Patel University, Vallabh Vidyanagar, Gujarat, India.

Abstract

We propose a modified SEIR model that includes asymptomatic transmission directly in the infection term, avoiding the need for a separate asymptomatic compartment while keeping the model realistic. The basic reproduction number ($\mathcal{R}_0$) is calculated to measure the potential for disease spread. Local stability analysis shows that the disease-free equilibrium is stable when $\mathcal{R}_0 < 1$ and unstable when $\mathcal{R}_0 > 1$, while the endemic equilibrium is locally stable in the latter case. A forward bifurcation at $\mathcal{R}_0 = 1$ is identified, indicating a smooth transition from the disease-free equilibrium to a unique endemic equilibrium without coexistence of the two equilibria. Global stability results show that the disease-free state is globally asymptotically stable for $\mathcal{R}_0 \leq 1$, and the endemic state is globally asymptotically stable for $\mathcal{R}_0 > 1$. Simulations using early COVID‑19 data support these findings, showing that higher asymptomatic transmission prolongs outbreaks, increases peaks, and delays elimination. Evaluation of control strategies reveals that isolation is more effective than testing alone, and their combination produces the greatest overall reduction in disease spread under appropriate assumptions.

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References

[1] J.P. Arcede, R.L. Caga-Anan, C.Q. Mentuda, Y. Mammeri, Accounting for symptomatic and asymptomatic in a SEIR-type model of COVID-19, Math. Model. Nat. Phenom. 15 (2020) 34.
[2] L. Basnarkov, SEAIR epidemic spreading model of COVID-19, Chaos Solitons Fract. 142 (2021) 110394.
[3] F. Brauer, C. Castillo-Chavez, Mathematical Models in Population Biology and Epidemiology, Springer, 2012.
[4] L.E. Brümmer, S. Katzenschlager, M. Gaeddert, C. Erdmann, S. Schmitz, M. Bota, M. Grilli, J. Larmann, M.A. Weigand, N.R. Pollock, Diagnostic accuracy of rapid antigen tests in symptomatic and asymptomatic SARS-CoV-2 infections, PLoS Med. 20 (2023) e1004108.
[5] N. Cangiotti, M. Capolli, M. Sensi, S. Sottile, A survey on Lyapunov functions for epidemic compartmental models, Boll. Unione Mat. Ital. 17 (2024) 241–257.
[6] C. Castillo-Chavez, B. Song, Dynamical models of tuberculosis and their applications, Math. Biosci. Eng. 1 (2004) 361–404.
[7] C. Cohen, J. Kleynhans, J. Moyes, M.L. McMorrow, F.K. Treurnicht, O. Hellferscee, A. Mathunjwa, A. von Gottberg, N. Wolter, N.A. Martinson, Asymptomatic transmission and high community burden of seasonal influenza in South Africa, Lancet Glob. Health 9 (2021) e863–e874.
[8] K.L. Cooke, Functional-differential equations: some models and perturbation problems, Differential Equations and Dynamical Systems, Proc. Int. Symp., Univ. of Puerto Rico (1967) 27–30.
[9] M.C. Gómez, E. Ibargüen Mondragón, Global stability analysis for a SEI model with nonlinear incidence rate and asymptomatic infectious state, Appl. Math. Comput. 402 (2021) 126130.
[10] J.A.P. Heesterbeek, A brief history of R0 and a recipe for its calculation, Acta Biotheor. 50 (2002) 189–204.
[11] Z. Hu, C. Song, C. Xu, Clinical characteristics of 24 asymptomatic infections with COVID-19, Infect. Dis. Poverty 9 (2020) 1–9.
[12] S.-B. Hsu, Y.-H. Hsieh, On the role of asymptomatic infection in transmission dynamics of infectious diseases, Bull. Math. Biol. 70 (2008) 134–155.
[13] S. Kadyrov, Y. Aitzhanov, Z.I. Muminov, Global stability analysis of a novel epidemic model with separate compartments for symptomatic and asymptomatic cases, Lobachevskii J. Math. 46 (2025) 683–696.
[14] W.O. Kermack, A.G. McKendrick, G.T. Walker, A contribution to the mathematical theory of epidemics, Proc. Roy. Soc. Lond. Ser. A 115 (1927) 700–721.
[15] W.O. Kermack, A.G. McKendrick, G.T. Walker, Contributions to the mathematical theory of epidemics. II — The problem of endemicity, Proc. Roy. Soc. Lond. Ser. A 138 (1932) 55–83.
[16] W.O. Kermack, A.G. McKendrick, G.T. Walker, Contributions to the mathematical theory of epidemics. III — Further studies of the problem of endemicity, Proc. Roy. Soc. Lond. Ser. A 141 (1933) 94–122.
[17] S. Lamei, Dynamical behavior of a multi-group stochastic SEIR system with symptomatic and asymptomatic individuals, J. Math. Model. 13 (2025) 767–786.
[18] J. La Salle, S. Lefschetz, Stability by Liapunov's Direct Method, Academic Press, 1961.
[19] T.W. Leulseged, D.G. Alemahu, I.S. Hassen, E.H. Maru, W.C. Zewde, N.W. Chamiso, K.T. Yegele, D.S. Abebe, F.M. Abdi, E.Y. Minyelshewa, T.G. Gerbi, H.T. Hagos, Factors associated with development of symptomatic disease in Ethiopian COVID-19 patients, BMC Infect. Dis. 21 (2021) 759.
[20] Q. Li, X. Guan, P. Wu, X. Wang, L. Zhou, Y. Tong, R. Ren, K.S.M. Leung, E.H.Y. Lau, J.Y. Wong, Early transmission dynamics in Wuhan, China, of novel coronavirus–infected pneumonia, N. Engl. J. Med. 382 (2020) 1199–1207.
[21] Z. Liu, T. Zhou, Analysis of global stability of an epidemic model with asymptomatic infected persons, Adv. Contin. Discrete Models 2025 (2025) 85.
[22] J. Pan, Z. Chen, Y. He, T. Liu, X. Cheng, J. Xiao, H. Feng, Why controlling the asymptomatic infection is important: A modelling study with stability and sensitivity analysis, Fractal Fract. 6 (2022) 197.
[23] S.Y. Park, Y.-M. Kim, S. Yi, S. Lee, B.-J. Na, C.B. Kim, J.-I. Kim, H.S. Kim, Y.B. Kim, Y. Park, Coronavirus disease outbreak in call center, South Korea, Emerg. Infect. Dis. 26 (2020) 1666.
[24] E. Schuit, C. Vilaplana, J. Dinnes, J.J. Deeks, J. Domen, A. Lentferink, P. Olliaro, A. van den Bruel, L. Hooft, P.M. Bossuyt, Serial self-testing using antigen rapid diagnostic tests in symptomatic and asymptomatic SARS-CoV-2 infections, Lancet Microbe 4 (2023) e623–e633.
[25] Z. Shuai, Global stability of infectious disease models using Lyapunov functions, SIAM J. Appl. Math. 73 (2013) 1513–1532.
[26] M.W. Tenforde, Symptom duration and risk factors for delayed return to usual health among outpatients with COVID-19 in a multistate health care systems network, MMWR Morb. Mortal. Wkly. Rep. 69 (2020).
[27] N. van der Moeren, G. Zwart, E. Lodder, H. van Esch, J. Stohr, B.B. Oude Munnink, A.A. van der Eijk, R. Molenkamp, S.D. Pas, M.P. Koopmans, Performance evaluation of the BD Veritor SARS-CoV-2 antigen rapid test, Clin. Microbiol. Infect. 28 (2022) 1266–1272.
[28] J. Watmough, Role of incidence function in vaccine-induced backward bifurcation in some HIV models, Math. Biosci. 210 (2007) 436–463.
[29] J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosci. 180 (2002) 29–48.
[30] World Health Organization, Novel Coronavirus (2019-nCoV) Situation Report–142, WHO, 2020.
[31] World Health Organization, Crude Birth Rate (births per 1000 population), WHO, 2020.
[32] M. Yanes-Lane, N. Winters, F. Fregonese, M. Bastos, S. Perlman-Arrow, J.R. Campbell, D. Menzies, Proportion of asymptomatic infection among COVID-19 positive persons and their transmission potential, PLOS One 15 (2020) e0241536.
[33] P. Zhang, Q. Zhang, X. Wei, Q. Cui, Modeling and analysis of a class of epidemic models with asymptomatic infection and transmission heterogeneity, J. Appl. Math. Comput. (2025) 1–28.
[34] C.Q. Zhu, S.D. Gao, Y. Xu, X.H. Yang, F.Q. Ye, L.L. Ai, R.C. Lv, B. Zhang, Y. Li, H. Lv, A COVID-19 case report from asymptomatic contact, Infect. Dis. Poverty 9 (2020) 70.
Journal of Mathematical Modeling
Volume 14, Issue 2
May 2026
Pages 741-760

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