RESUMEN
Background: We aimed to forecast possible situations of the COVID-19 spreading for Okinawa Prefecture in Japan. Methods: The VSIIR model is proposed to extend the SIIR model to include vaccine effects where the parameter v denotes the vaccination rate and is treated as a control parameter on which possible situations for Okinawa would depend. Results: It is shown that the infection ends without spreading if v > d 1 + d 2 is satisfied where 1 / d i refers to the antibody duration, i = 1 for infection and i = 2 for vaccination, respectively. Conclusion: It is important to set a vaccination policy that can save lives and maintain daily life at the same time.
RESUMEN
A new mathematical model called SIIR model is constructed to describe the spread of infection by taking account of the characteristics of COVID-19 and is verified by the data from Japan. The following features of COVID-19: (a) there exist presymptomatic individuals who have infectivity even during the incubation period, (b) there exist asymptomatic individuals who can freely move around and play crucial roles in the spread of infection, and (c) the duration of immunity may be finite, are incorporated into the SIIR model. The SIIR model has the advantage of being able to explicitly handle asymptomatic individuals who are delayed in discovery or are extremely difficult to be discovered in the real world. It is shown that the conditions for herd immunity in the SIIR model become more severe than those in the SIR model; that is, the presence of asymptomatic individuals increases herd immunity threshold (HIT).
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Spontaneous formation of a cylindrical density cavity, or "plasma hole," has been observed in a rotating magnetized plasma. Density of the plasma hole is one-tenth of that of ambient plasma and is bounded by a steep transition layer of the order of several ion Larmor radii. The flow velocity field associated with the plasma hole is experimentally determined, exhibiting a monopole vortical structure. It is found that the vorticity distribution is localized near the center of the hole and is identified as a Burgers vortex. This is the first experimental observation of a Burgers vortex in a plasma.
RESUMEN
The effects of dynamic payoff matrices on evolution of cooperation are studied based on the prisoner's dilemma game on a two-dimensional square lattice. The study is conducted by simulation and an analytical theory based on mean-field approximation. Payoff matrices are designed to evolve depending on a ratio of defectors (or cooperators) to the whole population. Dynamic payoff matrices are necessary to describe evolution of a society whose payoff may be affected by the results of actions of the members in the society. Introducing such payoff matrices helps to model dynamic aspects of societies.
RESUMEN
A new set of model equations is proposed to describe the evolution of the arms race, by extending Richardson's model with special emphases that (1) power dependent defensive reaction or historical enmity could be a motive force to promote armaments, (2) a deterrent would suppress the growth of armaments, and (3) the defense reaction of one nation against the other nation depends nonlinearly on the difference in armaments between two. The set of equations is numerically solved to exhibit stationary, periodic, and chaotic behavior depending on the combinations of parameters involved. The chaotic evolution is realized when the economic situation of each country involved in the arms race is quite different, which is often observed in the real world. (c) 1998 American Institute of Physics.
