Stochastic dynamics of predator-prey interactions

Singh, Abhyudai

doi:10.1371/journal.pone.0255880

Cited by 15 publications

(4 citation statements)

References 84 publications

(37 reference statements)

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“…For simplicity one may assume that beta 𝛽 is a reproduction factor of predators. By excluding the validity practice for 𝛿 = 0 where the system (4) will be reduced to a system (6).…”

Section: Note (2)mentioning

confidence: 99%

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Probabilistic Population Modeling with Interactions between Species

Ahangar

2023

JAMCS

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World Health Organization(WHO) instigates a continuous alertness and preparation to contain re-emergence of other variants of corona viruses. In the same vein, public welfare managements in allocating health related resources require predictive decision making, made possible through the assessment of existing health challenges. Therefore it is imperative to carryout an efficiency analysis to prioritize and determine an optimal control strategy that curtailed the transmission of COVID19 in Akwa Ibom state. In this paper, a deterministic epidemic model has been formulated using principles of Mathematical modelling of infectious diseases. This is a nonlinear system of differential equations coupled with three (3) time-varying control functionals. The control functionals are exible educational programmes, vaccination and treatment of COVID-19. The usual fuzzy-like characterization of infection severity (0 ≤ R0;Rc ≤ 1) and ( R0;Rc > 1) were achieved using the Next Generation Matrix Operator. An optimality system was derived using Pontryagin's Maximum principle, with some propositions on controllability criteria. Some forward-backward numerical solutions was executed in maple16 using validated datasets published by the Nigeria Centre for Disease Control(NCDC), peculiar to Akwa Ibom State. The efficiency analysis predicted that Strategy I (a combination of educational intervention programmes and vaccinations of the exposed and susceptible individual) as the most efficacious and optimal control strategy. Comparatively, Strategy I with 96% efficiency on reducing the infected sub-population is more effective than Strategy IV (a combination of the three control states) with efficiency index of 91%. A continuous vaccination and educational awareness programme has been recommended for community health practitioners, and compliance to these policies by the citizens can eradicate the dreaded pandemic with minimal intervention cost in the state.

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“…For simplicity one may assume that beta 𝛽 is a reproduction factor of predators. By excluding the validity practice for 𝛿 = 0 where the system (4) will be reduced to a system (6).…”

Section: Note (2)mentioning

confidence: 99%

“…In a modeling approach, we may assume x(t) and y(t) follow the logistical growth in the absence predator-prey interaction [3][4][5][6]. The mathematical model of the population in continuous deterministic case would be in the following form: are two carrying capacities of two species.…”

Section: Introduction To Deterministic Interactionsmentioning

confidence: 99%

Probabilistic Population Modeling with Interactions between Species

Ahangar

2023

JAMCS

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“…It will also be important to explicitly consider parasitoid extinction in stochastic formulations of these models with both environment fluctuations in parameters, such as the host reproduction R, and demographic stochasticity. Given the nonlinearities present in these models, the analysis will depend on both stochastic simulations and several closure schemes developed for analyzing population dynamic models [60]- [66]. Finally, it will be important to expand this analysis to Type II and Type III functional responses, which would require semi-discrete formulations that mechanistically capture the continuous changes in population densities during the host's vulnerable stage [17], [67], [68].…”

Section: Conculsionmentioning

confidence: 99%

Linking parasitoid-driven host density suppression with density-dependence in host growth

Singh

2023

Preprint

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Leveraging the discrete-time formalism of the Nicholson-Bailey model, we investigate the ecological population dynamics of host-parasitoid interactions with an arbitrary form of density-dependence in the host growth rate, andmap out regimes allowing stable coexistence of the consumer (parasitoid) and the resource (host). If the parasitoid-free host population dynamics is stable, we provide sufficient conditions that ensure stability is maintained with the inclusion of the parasitoid irrespective of the level of parasitism. When parasitoids parasitize hosts at a constant rate, high parasitism levels are shown to always destabilize the population dynamics. This results in a limit of host suppression that we quantify using the ratio of host density (just before stability is lost for high parasitism levels) and the host's parasitoid-free carrying capacity. We systematically examine this limit for different types of intrinsic self-limitations in host growth. Our analysis shows that for both Ricker and Beverton-Holt-type host population dynamics, this parasitoid-driven host suppression limit is $33\%$ for slow-growing hosts and $10-20\%$ for fast-growing hosts. Moreover, our results reveal that these limits can be much higher for Hill-type density-dependence in host growth rate. In summary, this contribution characterizes the impact of coupling different forms of intrinsic host population dynamics with and without additional stabilizing factors (such as a fraction of hosts protected from parasitism). These results have important implications for using parasitoids as natural enemies against arthropod pest populations, and the success of such biological control is inherently tied to the form of self-limitation in host growth.

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“…There is a long-standing tradition of modeling host-parasitoid population dynamics using discrete-time models [1][2][3][4][5][6]. This is primarily motivated by populations living in the temperate regions of the world where annual insect life stages are synchronized by season and reproduction occurs at specific times in the year.…”

Section: Introductionmentioning

confidence: 99%

Fundamental limits of parasitoid-driven host population suppression: Implications for biological control

Singh

2023

PLoS ONE

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Parasitoid wasps are increasingly being used to control insect pest populations, where the pest is the host species parasitized by the wasp. Here we use the discrete-time formalism of the Nicholson-Bailey model to investigate a fundamental question—are there limits to parasitoid-driven suppression of the host population density while still ensuring a stable coexistence of both species? Our model formulation imposes an intrinsic self-limitation in the host’s growth resulting in a carrying capacity in the absence of the parasitoid. Different versions of the model are considered with parasitism occurring at a developmental stage that is before, during, or after the growth-limiting stage. For example, the host’s growth limitation may occur at its larval stage due to intraspecific competition, while the wasps attack either the host egg, larval or pupal stage. For slow-growing hosts, models with parasitism occurring at different life stages are identical in terms of their host suppression dynamics but have contrasting differences for fast-growing hosts. In the latter case, our analysis reveals that wasp parasitism occurring after host growth limitation yields the lowest pest population density conditioned on stable host-parasitoid coexistence. For ecologically relevant parameter regimes we estimate this host suppression to be roughly 10-20% of the parasitoid-free carrying capacity. We further expand the models to consider a fraction of hosts protected from parasitism (i.e., a host refuge). Our results show that for a given host reproduction rate there exists a critical value of protected host fraction beyond which, the system dynamics are stable even for high levels of parasitism that drive the host to arbitrary low population densities. In summary, our systematic analysis sheds key insights into the combined effects of density-dependence in host growth and parasitism refuge in stabilizing the host-parasitoid population dynamics with important implications for biological control.

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Stochastic dynamics of predator-prey interactions

Cited by 15 publications

References 84 publications

Probabilistic Population Modeling with Interactions between Species

Probabilistic Population Modeling with Interactions between Species

Linking parasitoid-driven host density suppression with density-dependence in host growth

Fundamental limits of parasitoid-driven host population suppression: Implications for biological control

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