A predator–prey model with additive Allee effect and intraspecific competition on predator involving Atangana–Baleanu–Caputo derivative

Anggriani, Nursanti; Panigoro, Hasan S.; Rahmi, Emli; Peter, Olumuyiwa James; Jose, Sayooj Aby

doi:10.1016/j.rinp.2023.106489

Cited by 9 publications

(2 citation statements)

References 45 publications

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“…In our study, the number of infected individuals in the population is described using a finite birth process M(t) (see, for instance, Bailey [1,8], Cox and Miller [3], and Taylor and Karlin [4]). Recent developments in mathematical modeling, with applications in the transmission of infection in population dynamics, are investigated and analyzed in studies by Anggriani et al [9], Joseph et al [10], and Jose et al [11,12].…”

Section: Introductionmentioning

confidence: 99%

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: Introductionmentioning

confidence: 99%

Time-Inhomogeneous Finite Birth Processes with Applications in Epidemic Models

Giorno,

Nobile

2023

Mathematics

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“…Some related studies [21,22] gave us a deeper understanding of migration patterns. Furthermore, many scholars use fractional order differential equations to establish corresponding mathematical models, which further promotes the development of population models [23,24].…”

Section: Introductionmentioning

confidence: 99%

Survival Analysis of a Predator–Prey Model with Seasonal Migration of Prey Populations between Breeding and Non-Breeding Regions

Dai,

Jiao,

Jiao

et al. 2023

Mathematics

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In this paper, we establish and study a novel predator–prey model that incorporates: (i) the migration of prey between breeding and non-breeding regions; (ii) the refuge effect of prey; and (iii) the reduction in prey pulse birth rate, in the form of a fear effect, in the presence of predators. Applying the Floquet theory and the comparison theorem of impulsive differential equations, we obtain the sufficient conditions for the stability of the prey-extinction periodic solution and the permanence of the system. Furthermore, we also study the case where the prey population does not migrate. Sufficient conditions for the stability of the prey-extinction periodic solution and the permanence are also established, and the threshold for extinction and permanence of the prey population is obtained. Finally, some numerical simulations are provided to verify the theoretical results. These results provide a theoretical foundation for the conservation of biodiversity.

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