113 citations · 241 across the 14 of their papers we have counts for
14 papers
Stochastic Modeling of an Infectious Disease, Part III-B: Analysis of the Time-Nonhomogeneous BDI Process and Simulation Experiments of both BD and BDI Processes
Hisashi Kobayashi
In Section 1, we revisit the partial differential equation (PDE) for the probability generating function (PGF) of the time-nonhomogeneous BDI (birth-and-death-with-immigration) pro…
Stochastic Modeling of an Infectious Disease Part II: Simulation Experiments and Verification of the Analysis
Hisashi Kobayashi
In Part 1, we introduced a stochastic model of an infectious disease, based on the BDI (birth and death with immigration) process. We showed that random processes defined by this m…
Stochastic Modeling of an Infectious Disease Part III-A: Analysis of Time-Nonhomogeneous Models
Hisashi Kobayashi
We extend our BDI (birth-death-immigration) process based stochastic model of an infectious disease to time-nonhomogeneous cases. First, we discuss the deterministic model, and der…
Stochastic Modeling of an Infectious Disease, Part I: Understand the Negative Binomial Distribution and Predict an Epidemic More Reliably
Hisashi Kobayashi
Why are the epidemic patterns of COVID-19 so different among different cities or countries which are similar in their populations, medical infrastructures, and people's behavior? W…
Some results on the and functions associated with Riemann's function
Hisashi Kobayashi
We report on some properties of the function and its value on the critical line, . First, we present some identities that hold for the lo…
Local Extrema of the Function and The Riemann Hypothesis
Hisashi Kobayashi
In the present paper we obtain a necessary and sufficient condition to prove the Riemann hypothesis in terms of certain properties of local extrema of the function $Ξ(t)=ξ(\tfrac{1…