scholarly journals Two Multi-Sigmoidal Diffusion Models for the Study of the Evolution of the COVID-19 Pandemic

Mathematics ◽  
2021 ◽  
Vol 9 (19) ◽  
pp. 2409
Author(s):  
Antonio Barrera ◽  
Patricia Román-Román ◽  
Juan José Serrano-Pérez ◽  
Francisco Torres-Ruiz
Keyword(s):  
Bayesian Methods ◽  
Stochastic Models ◽  
Diffusion Processes ◽  
Point Estimation ◽  
Practical Case ◽  
Polynomial Functions ◽  
First Passage ◽  
Specific Data ◽  
Passage Times

A proposal is made to employ stochastic models, based on diffusion processes, to represent the evolution of the SARS-CoV-2 virus pandemic. Specifically, two diffusion processes are proposed whose mean functions obey multi-sigmoidal Gompertz and Weibull-type patterns. Both are constructed by introducing polynomial functions in the ordinary differential equations that originate the classical Gompertz and Weibull curves. The estimation of the parameters is approached by maximum likelihood. Various associated problems are analyzed, such as the determination of initial solutions for the necessary numerical methods in practical cases, as well as Bayesian methods to determine the degree of the polynomial. Additionally, strategies are suggested to determine the best model to fit specific data. A practical case is developed from data originating from several Spanish regions during the first two waves of the COVID-19 pandemic. The determination of the inflection time instants, which correspond to the peaks of infection and deaths, is given special attention. To deal with this particular issue, point estimation as well as first-passage times have been considered.

Determination of the Transition Regime Collision Kernel from Mean First Passage Times

2011 ◽  
Vol 45 (12) ◽  
pp. 1499-1509 ◽  
Author(s):  
Ranganathan Gopalakrishnan ◽  
Christopher J. Hogan
Keyword(s):  
First Passage Times ◽  
Collision Kernel ◽  
Transition Regime ◽  
First Passage ◽  
Mean First Passage Times ◽  
Passage Times

On first passage times of sticky reflecting diffusion processes with double exponential jumps

2020 ◽  
Vol 57 (1) ◽  
pp. 221-236 ◽  
Author(s):  
Shiyu Song ◽  
Yongjin Wang
Keyword(s):  
Diffusion Processes ◽  
First Passage Time ◽  
Passage Time ◽  
Explicit Solutions ◽  
First Passage ◽  
Uhlenbeck Process ◽  
Double Exponential ◽  
Upper Level ◽  
First Passage Problem ◽  
Passage Times

AbstractWe explore the first passage problem for sticky reflecting diffusion processes with double exponential jumps. The joint Laplace transform of the first passage time to an upper level and the corresponding overshoot is studied. In particular, explicit solutions are presented when the diffusion part is driven by a drifted Brownian motion and by an Ornstein–Uhlenbeck process.

A note on first passage times in birth and death and nonnegative diffusion processes

1983 ◽  
Vol 30 (2) ◽  
pp. 283-285 ◽  
Author(s):  
Cyrus Derman ◽  
Sheldon M. Ross ◽  
Zvi Schechner
Keyword(s):  
Diffusion Processes ◽  
First Passage Times ◽  
First Passage ◽  
Passage Times

An improved technique for the simulation of first passage times for diffusion processes

1999 ◽  
Vol 28 (4) ◽  
pp. 1135-1163 ◽  
Author(s):  
Maria Teresa Giraudo ◽  
Laura Sacerdote
Keyword(s):  
Diffusion Processes ◽  
First Passage Times ◽  
First Passage ◽  
Improved Technique ◽  
Passage Times

More general problems on first-passage times for diffusion processes: A new version of the fptdApprox R package

2014 ◽  
Vol 244 ◽  
pp. 432-446 ◽  
Author(s):  
P. Román-Román ◽  
J.J. Serrano-Pérez ◽  
F. Torres-Ruiz
Keyword(s):  
Diffusion Processes ◽  
R Package ◽  
First Passage Times ◽  
First Passage ◽  
Passage Times

First-passage percolation on the square lattice, II

1977 ◽  
Vol 9 (2) ◽  
pp. 283-295 ◽  
Author(s):  
John C. Wierman
Keyword(s):  
Sufficient Conditions ◽  
Initial Result ◽  
First Passage Times ◽  
Square Lattice ◽  
Maximum Height ◽  
First Passage Percolation ◽  
First Passage ◽  
Necessary And Sufficient ◽  
Passage Times

Several problems are considered in the theory of first-passage percolation on the two-dimensional integer lattice. The results include: (i) necessary and sufficient conditions for the existence of moments of first-passage times; (ii) determination of an upper bound for the time constant; (iii) an initial result concerning the maximum height of routes for first-passage times; (iv) ergodic theorems for a class of reach processes.

First passage times of a jump diffusion process

2003 ◽  
Vol 35 (2) ◽  
pp. 504-531 ◽  
Author(s):  
S. G. Kou ◽  
Hui Wang
Keyword(s):  
Diffusion Process ◽  
Diffusion Processes ◽  
Jump Diffusion ◽  
First Passage Times ◽  
First Passage ◽  
Jump Diffusion Processes ◽  
Lookback Options ◽  
Double Exponential ◽  
Jump Diffusion Process ◽  
Passage Times

This paper studies the first passage times to flat boundaries for a double exponential jump diffusion process, which consists of a continuous part driven by a Brownian motion and a jump part with jump sizes having a double exponential distribution. Explicit solutions of the Laplace transforms, of both the distribution of the first passage times and the joint distribution of the process and its running maxima, are obtained. Because of the overshoot problems associated with general jump diffusion processes, the double exponential jump diffusion process offers a rare case in which analytical solutions for the first passage times are feasible. In addition, it leads to several interesting probabilistic results. Numerical examples are also given. The finance applications include pricing barrier and lookback options.

A Note on First Passage Times in Birth and Death and Nonnegative Diffusion Processes.

1979 ◽  
Author(s):  
Cyrus Derman ◽  
Sheldon M. Ross ◽  
Zvi Schechner
Keyword(s):  
Diffusion Processes ◽  
First Passage Times ◽  
First Passage ◽  
Passage Times
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