Abstract
In this study, based on our previous study in which the proposed model is derived based on the SIR model and E. M. Rogers’s Diffusion of Innovation Theory, including the aspects of contact and time delay, we examined the mathematical properties, especially the stability of the equilibrium for our proposed mathematical model. By means of the results of the stability in this study, we also used actual data representing transient and resurgent booms, and conducted parameter estimation for our proposed model using Bayesian inference. In addition, we conducted a model fitting to five actual data. By this study, we reconfirmed that we can express the resurgences or minute oscillations of actual data by means of our proposed model.
Highlights
Booms emerge in many fields and are closely tied to our everyday life
In a sense, we can regard an infectious disease as a boom, like influenza or SARS, which is infected by viruses that are transmitted from person to person
May received acclaim for fitting results from an experiment on the Australian sheep blowfly (Lucilia cuprina) conducted by Nicholson [13]. Based on these experimental results, we regarded the definition of a time delay for societal booms as “the time required for a boom adopter associated with contact and resurgence to pick up a boom and take action”, and incorporated the concept of the time delay into the derivation of a mathematical model
Summary
Booms emerge in many fields and are closely tied to our everyday life. For example, a fashion in clothing, makeup, sports, a movie and food (we call “societal booms”). The modern studies on epidemiological booms were developed by Kermack and McKendrick, and others in the early twentieth century [1] This field of study gained attention among researchers owing to the spread of emerging infectious diseases, such as AIDS in the 1980s, that posed risks in developed countries. Nakagiri et al used a system of simultaneous linear differential equations to develop a mathematical model to describe problems in societal booms, and performed a model fitting to actual data. Using actual booms data we evaluate the parameters and examine the fit of our proposed model. Mathematical Model we explain a mathematical model for societal booms which was derived in [9]
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