Study of a general growth model

Albano, Giuseppina; Giorno, Virginia; Román-Román, Patricia; Torres-Ruiz, Francisco

doi:10.1016/j.cnsns.2021.106100

Cited by 10 publications

(10 citation statements)

References 18 publications

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“…with the initial condition lim t↓t 0 p j,n (t|t 0 ) = δ j,n , where δ j,n is the Kronecker delta function. For the TNH finite birth process M(t), with birth intensity functions (18), one has ∑ N n=j p j,n (t|t 0 ) = 1. Moreover, from the first equation in (19), one obtains the following:…”

Section: The Stochastic Finite Birth Processmentioning

confidence: 99%

“…Proposition 2. Let j, n and N be fixed parameters, with j ≤ n ≤ N. For the TNH finite birth process M(t), with intensity functions defined in (18), this results in the following:…”

Section: The Stochastic Finite Birth Processmentioning

confidence: 99%

“…For the process M(t), with birth intensity functions (18), the r-th FPT conditional moment is as follows:…”

Section: First-passage Timementioning

confidence: 99%

“…The stochastic process M(t), with intensities functions λ n (t) = λ(t)(N − n)ξ n , given in (18), includes the TNH flexible birth process characterized by…”

Section: Stochastic Flexible Finite Birth Processmentioning

confidence: 99%

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Time-Inhomogeneous Finite Birth Processes with Applications in Epidemic Models

Giorno,

Nobile

2023

Mathematics

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We consider the evolution of a finite population constituted by susceptible and infectious individuals and compare several time-inhomogeneous deterministic models with their stochastic counterpart based on finite birth processes. For these processes, we determine the explicit expressions of the transition probabilities and of the first-passage time densities. For time-homogeneous finite birth processes, the behavior of the mean and the variance of the first-passage time density is also analyzed. Moreover, the approximate duration until the entire population is infected is obtained for a large population size.

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Section: The Stochastic Finite Birth Processmentioning

confidence: 99%

“…Proposition 2. Let j, n and N be fixed parameters, with j ≤ n ≤ N. For the TNH finite birth process M(t), with intensity functions defined in (18), this results in the following:…”

Section: The Stochastic Finite Birth Processmentioning

confidence: 99%

“…For the process M(t), with birth intensity functions (18), the r-th FPT conditional moment is as follows:…”

Section: First-passage Timementioning

confidence: 99%

“…The stochastic process M(t), with intensities functions λ n (t) = λ(t)(N − n)ξ n , given in (18), includes the TNH flexible birth process characterized by…”

Section: Stochastic Flexible Finite Birth Processmentioning

confidence: 99%

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Time-Inhomogeneous Finite Birth Processes with Applications in Epidemic Models

Giorno,

Nobile

2023

Mathematics

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“…For example, see [3,31]. The Richards model [2,17,25,44], shown below, is a generalization of the logistic model.…”

Section: Introduction Studies Have Investigated the Properties Of The...mentioning

confidence: 99%

Approximate solutions of generalized logistic equation

Onitsuka

2024

DCDS-B

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This study investigates the behavior of the approximate solutions of the generalized logistic equation y ′ = y (1 − y α ), where α > 0. Based on the concept of Ulam stability, a concrete estimate of the amplitude of the difference between the approximate solution and the exact solution is obtained using the comparison principle and some sharp inequalities. The obtained results can be applied to the nonautonomous Richards model C ′ = r(t)C 1 − C α K .

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Modeling the random spreading of fake news through a two‐dimensional time‐inhomogeneous birth‐death process

Di Crescenzo,

Paraggio

2024

Math Methods in App Sciences

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We consider a two‐dimensional time‐inhomogeneous birth‐death process to model the time‐evolution of fake news in a population. The two components of the process represent, respectively: (i) the number of individuals (say spreaders) who know the rumor and intend to spread it and (ii) the number of individuals (say inactives) who have forgotten the rumor previously received. We employ the probability generating function‐based approach to obtain the moments and the covariance of the two‐dimensional process. We also analyze a new adimensional index to study the correlation between the two components. Some special cases are considered in which both the expected numbers of spreaders and inactives are equal to suitable sigmoidal curves, which are often adopted in modeling growth phenomena. Finally, we provide an application based on real data related to the diffusion of fake news, in which the optimal choice of the sigmoidal curve that fit the datasets is based on the minimization of the mean square error and of the relative absolute error.

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Study of a general growth model

Cited by 10 publications

References 18 publications

Time-Inhomogeneous Finite Birth Processes with Applications in Epidemic Models

Time-Inhomogeneous Finite Birth Processes with Applications in Epidemic Models

Approximate solutions of generalized logistic equation

Modeling the random spreading of fake news through a two‐dimensional time‐inhomogeneous birth‐death process

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