Periodic orbits for periodic eco-epidemiological systems with infected prey

Jesus, Lopo F. de; Silva, César M.; Vilarinho, Helder

doi:10.14232/ejqtde.2020.1.54

Cited by 5 publications

(4 citation statements)

References 16 publications

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“…for all sufficiently large t. Notice that, for a general G, if g does not depend on I, we have g(S, I, P) ≥ g(s * (t)+𝜖, 0, 𝑦 * (t)−𝜖) and we still obtain inequality (11).…”

Section: Resultsmentioning

confidence: 86%

“…[1][2][3][4][5][6][7] To make models more realistic, it is important, in many situations, to consider time varying parameters. Several nonautonomous eco-epidemiological systems have been proposed and studied in the literature, starting with the case of periodic parameters, 2,[8][9][10][11][12][13] an important case since it is well known in epidemiology that some parameters, for instance incidence rates, are seldom subject to periodic seasonal fluctuations.…”

Section: Introductionmentioning

confidence: 99%

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An eco‐epidemiological model with general functional response of predator to prey

Jesus

Silva

Vilarinho

2022

Math Methods in App Sciences

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Funding informationL. de Jesus, C. M. Silva and H. Vilarinho were partially supported by FCT through CMA-UBI (project UIDB/00212/2020). L. F. de Jesus was also supported by INAGBE. The authors are listed in alphabetical order of the surname and contributed equally.We consider a nonautonomous eco-epidemiological model with general functions for predation on infected and uninfected preys as well as general functions associated to the vital dynamics of the susceptible prey and predator populations. We obtain persistence and extinction results for the infected prey based on assumptions on auxiliary systems constructed from the disease-free system. We moreover consider an iterative process that can improve the extinction results. We apply our results to general eco-epidemiological models that include several examples existent in the literature.

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“…for all sufficiently large t. Notice that, for a general G, if g does not depend on I, we have g(S, I, P) ≥ g(s * (t)+𝜖, 0, 𝑦 * (t)−𝜖) and we still obtain inequality (11).…”

Section: Resultsmentioning

confidence: 86%

Section: Introductionmentioning

confidence: 99%

An eco‐epidemiological model with general functional response of predator to prey

Jesus

Silva

Vilarinho

2022

Math Methods in App Sciences

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“…It can be of interest to give some considerations which are based on known general results of the qualitative theory of differential equations which indicate that there is a unique global asymptotically stable attractor which is always one of the equilibrium points [43][44][45]. The global attractor is the disease-free equilibrium if the reproduction number is less than or equal to one and the endemic equilibrium point if such a parameter exceeds unity.…”

Section: Remarkmentioning

confidence: 99%

On an SEIR Epidemic Model with Vaccination of Newborns and Periodic Impulsive Vaccination with Eventual On-Line Adapted Vaccination Strategies to the Varying Levels of the Susceptible Subpopulation

2020

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This paper investigates a susceptible-exposed-infectious-recovered (SEIR) epidemic model with demography under two vaccination effort strategies. Firstly, the model is investigated under vaccination of newborns, which is fact in a direct action on the recruitment level of the model. Secondly, it is investigated under a periodic impulsive vaccination on the susceptible in the sense that the vaccination impulses are concentrated in practice in very short time intervals around a set of impulsive time instants subject to constant inter-vaccination periods. Both strategies can be adapted, if desired, to the time-varying levels of susceptible in the sense that the control efforts be increased as those susceptible levels increase. The model is discussed in terms of suitable properties like the positivity of the solutions, the existence and allocation of equilibrium points, and stability concerns related to the values of the basic reproduction number. It is proven that the basic reproduction number lies below unity, so that the disease-free equilibrium point is asymptotically stable for larger values of the disease transmission rates under vaccination controls compared to the case of absence of vaccination. It is also proven that the endemic equilibrium point is not reachable if the disease-free one is stable and that the disease-free equilibrium point is unstable if the reproduction number exceeds unity while the endemic equilibrium point is stable. Several numerical results are investigated for both vaccination rules with the option of adapting through ime the corresponding efforts to the levels of susceptibility. Such simulation examples are performed under parameterizations related to the current SARS-COVID 19 pandemic.

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“…Typically, the functional response of the predator to prey is given by some particular function. In this paper we take as reference the model proposed in [19,20] that generalizes the one in [21] by considering general functions corresponding to the predation of uninfected and infected prey. Besides the population compartments, given by S, I and P that correspond, respectively, to the susceptible prey, infected prey and predator, we may understood Λ and µ as the (random) recruitment rate and the natural death rate of prey population, respectively, β as the incidence rate of the disease, η as the predation rate of infected prey, c as the death rate in the infective class, γ as the rate converting susceptible prey into predator (biomass transfer), r as the rate of converting infected prey into predator, f (S, I, P ) is the predation of susceptible prey and g(S, I, P ) is the predation of infected prey.…”

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confidence: 99%

Random perturbations of an eco-epidemiological model

Jesus¹,

Silva²,

Vilarinho³

2022

DCDS-B

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We consider random perturbations of a general eco-epidemiological model. We prove the existence of a global random attractor, the persistence of susceptibles preys and provide conditions for the simultaneous extinction of infectives and predators. We also discuss the dynamics of the corresponding random epidemiological SI and predator-prey models. We obtain for this cases a global random attractor, prove the prevalence of susceptibles/preys and provide conditions for the extinctions of infectives/predators.

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Periodic orbits for periodic eco-epidemiological systems with infected prey

Cited by 5 publications

References 16 publications

An eco‐epidemiological model with general functional response of predator to prey

An eco‐epidemiological model with general functional response of predator to prey

On an SEIR Epidemic Model with Vaccination of Newborns and Periodic Impulsive Vaccination with Eventual On-Line Adapted Vaccination Strategies to the Varying Levels of the Susceptible Subpopulation

Random perturbations of an eco-epidemiological model

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