A short note on analysis and application of a stochastic open-ended logistic growth model

Abstract

A minimal stochastic generalization of a deterministic open-ended logistic growth model is proposed for efficiently describing the biological growth of individual organisms under natural environment. The model is a system of stochastic differential equations. Its unique solvability in a strong sense is proven, and the behaviour of the solution is analysed. The presented model is then applied to the migratory fish Plecoglossus altivelis altivelis (P. altivelis, Ayu) having a one-year life history based on the data sets collected in 2017 and 2018.

A generalized Gompertz growth model with applications and related birth-death processes

“…In Table 14 the last column is dedicated to the asymptotic absorption probability (30). where φ a (t) is defined in (36) and…”

“…We recall the well-known approach based on diffusion processes for the stochastic model of tumor growth, such as that exploited in Albano and Giorno [1], Giorno et al [17], Giorno and Nobile [15], Hanson and Tier [19], Spina et al [29]. Other studies including Gompertz and logistic growth models based on stochastic diffusions can be found in Campillo et al [8], Himadri Ghosh and Prajneshu [21], and Yoshioka et al [36]. Recent advances involving fractional Gompertz growth models in biological contexts have been analyzed in Ascione and Pirozzi [4], Dewanji et al [11], Frunzo et al [14], and in Meoli et al [24].…”

A generalized Gompertz growth model with applications and related birth-death processes

“…Therefore, when A → 0 or b → 0 there is a good correspondence between the deterministic law (12) and the stochastic process with birth rates (38). Clearly, if A → 0 or b → 0, then λ(t) → 0.…”

“…For the birth process {X (t); t ≥ 0}, characterized by time-dependent birth rates (38) and initial state X (0) = y ∈ N, we can construct a customary event-based simulation procedure. Denoting by T k the k-th increment (birth) of the process, with T 0 = 0, for all k ∈ N one has P(T k+1 > t | T k = τ ) = e −(k+y)[Λ(t)−Λ(τ )] , t > τ ≥ 0,…”

“…We recall the well-known approach based on diffusion processes for the stochastic model of tumor growth, such as that exploited in Albano and Giorno [ 1 ], Giorno et al [ 18 ], Giorno and Nobile [ 16 ], Hanson and Tier [ 20 ], Spina et al [ 31 ]. Other studies including Gompertz and logistic growth models based on stochastic diffusions can be found in Campillo et al [ 8 ], Himadri Ghosh and Prajneshu [ 22 ], and Yoshioka et al [ 38 ]. Recent advances involving fractional Gompertz growth models in biological contexts have been analyzed in Ascione and Pirozzi [ 4 ], Dewanji et al [ 11 ], Frunzo et al [ 15 ], and in Meoli et al [ 25 ].…”