Some mathematical boom equation of SEIR type with diffusion, which appears as a model of social and economical boom for the spread of trend-causing, is treated. The asymptotic properties of the diffusive equation are studied by applying the strong maximum principle, strong fading memory property and luxury Liapunov functions.
References
[1]
Nakagiri, Y. and Kurita, O. (2004) On a Differential Equation Model of Booms. Transactions of the Operations Research Society of Japan, 47, 83-105. https://doi.org/10.15807/torsj.47.83
[2]
Ota, Y. and Mizutani, N. (2020) Estimating Parameters in Mathematical Model for Societal Booms through Bayesian Inference Approach. Mathematical and Computational Applications, 25, Article 42. https://doi.org/10.3390/mca25030042
[3]
Ohta, Y. and Mizutani, N. (2021) On a Proposal of Mathematical Model in Human Social Trend-Using Innovator Theory and Time-Delay Equations. Transactions of the Operations Research Society of Japan, 64, 22-45. https://doi.org/10.15807/torsj.64.22
[4]
Ueda, Y. and Asahi, Y. (2014) Twitter (On the Build and Validate a Twitter User Interest Transfer Model). Communications of the Operations Research Society of Japan, 59, 219-228.
[5]
Hamaya, Y. and Saito, K. (2023) Global Attractivity of a Delayed Seir Epidemic Model of COVID-19 With Diffusion. Journal of Mathematical Sciences, 271, 378-399. https://doi.org/10.1007/s10958-023-06527-6
[6]
Kermack, W.O. and McKendrick, A.G. (1927) A Contribution to the Mathematical Theory of Epidemics. Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character, 115, 700-721. https://doi.org/10.1098/rspa.1927.0118
[7]
Brauer, F. and Castillo-Chavez, C. (2012) Continuous Population Models. In: Brauer, F. and Castillo-Chavez, C., Eds., Mathematical Models in Population Biology and Epidemiology, Springer, 3-47. https://doi.org/10.1007/978-1-4614-1686-9_1
[8]
Hamaya, Y. (1999) On the Asymptotic Behavior of a Diffusive Epidemic Model (AIDS). Nonlinear Analysis: Theory, Methods & Applications, 36, 685-696. https://doi.org/10.1016/s0362-546x(98)00118-7
[9]
Inaba, H. (2020) Mathematical Models for Demography and Epidemics. Expanded Edition, University of Tokyo Press.
[10]
Saito, K. and Hamaya, Y. (2023) On the Asymptotic Stability of Discrete Crocodilians Model. Advances in Pure Mathematics, 13, 211-225. https://doi.org/10.4236/apm.2023.135015
[11]
Zhang, Y., Yu, X., Sun, H.G., Tick, G.R., Wei, W. and Jin, B. (2020) COVID-19 Infection and Recovery in Various Countries: Modeling the Dynamics and Evaluating the Non-Pharmaceutical Mitigation Scenarios. arXiv:203.13901
[12]
Anderson, R.M. and May, R.M. (1979) Population Biology of Infectious Diseases: Part I. Nature, 280, 361-367. https://doi.org/10.1038/280361a0
[13]
Takeuchi, Y. and Ma, W. (1999) Stability Analysis on a Delayed SIR Epidemic Model with Density Dependent Birth Process. Dynamical Systems and Continuous, Discrete and Impulsive Systems, 5, 171-184.
[14]
Hamaya, Y. and Arai, T. (2010) Permanence of an SIR Epidemic Model with Diffusion. Nonlinear Studies, 17, 69-79.
[15]
Saito, K. (2023) On the Global Stability of an SIR Epidemic Discrete Model. International Journal of Mathematical Analysis, 17, 119-132.
[16]
Granovetter, M. and Soong, R. (1983) Threshold Models of Diffusion and Collective Behavior. The Journal of Mathematical Sociology, 9, 165-179. https://doi.org/10.1080/0022250x.1983.9989941
[17]
Matui, Y. (1994) Social Psychology of Fans and Booms. Japanese Science Cop.
[18]
Monneyron, F. (2009) Sociology of Fashion. Hakusuisya.
[19]
Nakajima, J. (1998) Media and Trendy Psychology. Kaneko Shoten.
[20]
Serizawa, S. (1990) Social Phenomenology of Booms. Chikuma Shoten.
[21]
Rogers, E.M. (2003) The Diffusion of Innovations. 5th Edition, The Free Press.
[22]
Hamaya, Y. and Saito, K. (2016) Global Asymptotic Stability of a Delayed SIR Epidemic Model with Diffusion. Libertas Mathematica, 36, 53-72.
[23]
Pazy, A. (1983) Semigroups of Linear Operators and Applications to Partial Differential Equations. Springer-Verlag.
[24]
Redlinger, R. (1985) On Volterra’s Population Equation with Diffusion. SIAM Journal on Mathematical Analysis, 16, 135-142. https://doi.org/10.1137/0516008
[25]
Protter, M.H. and Weinberger, H.F. (1984) Maximum Principles in Differential Equations. Springer-Verlag New York Inc.
[26]
Gopalsamy, K. (1992) Stability and Oscillations in Delay Differential Equations of Population Dynamics. Kluwer Academic Publishers.
[27]
Murakami, S. and Hamaya, Y. (1995) Global Attractivity in an Integrodifferential Equation with Diffusion. Differential Equations and Dynamical Systems, 3, 35-42.
[28]
Saito, K., Kohno, T. and Hamaya, Y. (2017) Global Stability of a Delayed SIR Epidemic Model with Diffusion. International Journal of Differential Equations and Applications, 16, 123-145.
