Persistence and extinction for stochastic delay differential model of prey predator system with hunting cooperation in predators

Rihan, Fathalla A.; Alsakaji, Hebatallah J.

doi:10.1186/s13662-020-02579-z

Cited by 25 publications

(10 citation statements)

References 40 publications

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“…Here R 0 = ξ η+α is known as the basic reproduction number of the deterministic model. In fact, there is an increasing indication that superior consistency with some phenomena can be contributed if the effects of environmental noises in the system are taken into account [34]. Epidemic model (1) assumes that the observed dynamics are driven exclusively by internal deterministic cases.…”

Section: Stochastic Sirc Epidemic Modelmentioning

confidence: 99%

Stochastic SIRC epidemic model with time-delay for COVID-19

2020

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Environmental factors, such as humidity, precipitation, and temperature, have significant impacts on the spread of the new strain coronavirus COVID-19 to humans. In this paper, we use a stochastic epidemic SIRC model, with cross-immune class and time-delay in transmission terms, for the spread of COVID-19. We analyze the model and prove the existence and uniqueness of positive global solution. We deduce the basic reproduction number ${\mathcal{R}}_{0}^{s}$ R 0 s for the stochastic model which is smaller than ${\mathcal{R}}_{0}$ R 0 of the corresponding deterministic model. Sufficient conditions that guarantee the existence of a unique ergodic stationary distribution, using the stochastic Lyapunov function, and conditions for the extinction of the disease are obtained. Our findings show that white noise plays an important part in controlling the spread of the disease; When the white noise is relatively large, the infectious diseases will become extinct; Re-infection and periodic outbreaks can occur due to the existence of feedback time-delay (or memory) in the transmission terms.

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Section: Stochastic Sirc Epidemic Modelmentioning

confidence: 99%

Stochastic SIRC epidemic model with time-delay for COVID-19

2020

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“…Based on the idea of the SIR framework, numerous types of mathematical models using compartmental approach have been developed in the meanwhile, all incorporating more structure and details of the transmission process and infectious disease dynamics [1,2,4]. Other authors use stochastic approach to models the dynamics and transmission of emergent and re-emergent infectious diseases [13,14]. In [13], the authors develop and study a stochastic approach to model the spread of COVID-19 epidemic by taking into account the cross immunity and time delay of transmission.…”

Section: Introduction and Mathematical Modelmentioning

confidence: 99%

SIARD model and effect of lockdown on the dynamics of COVID-19 disease with non total immunity

Aziz-Alaoui

Najm

Yafia

2021

Math. Model. Nat. Phenom.

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We propose a new compartmental mathematical model describing the transmission and the spreading of COVID-19 epidemic with a special focus on the non-total immunity. The model (called SIARD) is given by a system of differential equations which model the interactions between five populations “susceptible”, “reported infectious”, “unreported infectious”, “recovered with/without non total immunity” and “death”. Depending on the basic reproduction number, we prove that the total immunity induces local stability-instability of equilibria and the epidemic may disappear after a first epidemic wave and more epidemic waves may appear in the case of non-total immunity. Using the sensitivity analysis we identify the most sensitive parameters. Numerical simulations are carried out to illustrate our theoretical results. As an application, we found that our model fits well the Moroccan epidemic wave, and predicts more than one wave for French case.

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“…Thus, a qualitative analytical account to probe internal viral dynamics of SARS-CoV-2 virus with noise perturbations is yet under developmental stage and our research executions attempt to explore infection progression dynamics of SARS-CoV-2 virus with noise effects. Dynamical probes in model system inevitably evolving around their past states is widely acknowledged and concerning epidemiological studies, exquisite realistic dynamical expounds are achieved by executing analytical explorations inclusive of past states as time delay incorporation

in model systems, render interesting exemplifications as seen in the works of [34] , [35] , [36] .…”

Section: Introductionmentioning

confidence: 99%

Stochastic probical strategies in a delay virus infection model to combat COVID-19

Pitchaimani

Devi

2021

Chaos, Solitons & Fractals

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In disease model systems, random noises and time delay factors play key role in interpreting disease dynamics to comprehend deeper insights into the course of dynamics. An endeavor to forecast intercellular behavioral dynamics of SARS-CoV-2 virus via Infection model with responsive host immune mechanisms forms the crux of this research study. Incorporation of time delay factor into infection transmission rates in noisy system epitomizes spectacular view on internal viral dynamics and stability properties are rigorously analyzed around equilibrium steady states to probe feasible strategies in mitigating rapid spread. Efforts to perceive inocular view on infection dynamics are not limited to theoretical frontiers but are substantiated with empirically simulated outcomes and visualized as graphical upshots. Discussions on numerical investigations emphasized shorter incubation periods and vaccination at pertinent time intervals to restrain massive spread and exhibit total immunity against SARS-CoV-2 infections.

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Persistence and extinction for stochastic delay differential model of prey predator system with hunting cooperation in predators

Cited by 25 publications

References 40 publications

Stochastic SIRC epidemic model with time-delay for COVID-19

Stochastic SIRC epidemic model with time-delay for COVID-19

SIARD model and effect of lockdown on the dynamics of COVID-19 disease with non total immunity

Stochastic probical strategies in a delay virus infection model to combat COVID-19

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