Disease extinction and persistence in a discrete-time sis epidemic model with vaccination and varying population size

Farnoosh, Rahman; Parsamanesh, Mahmood

doi:10.2298/fil1715735f

Cited by 12 publications

(6 citation statements)

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“…where b i , i = 1, 2, 3, are as in (13) and η = I e N e . By solving this problem we see that maximum value is negative and thus…”

Section: Stability Of the Endemic Equilibriummentioning

confidence: 99%

“…The probably most wellknown epidemic model, the SIS model, has been formulated in discrete formulation and analyzed in many works [9,10]. Among them some models include vaccination as a efficient strategy to control and eliminate the disease [11][12][13][14][15]. These models consider the vaccinated individuals as a separate component in the model.…”

Section: Introductionmentioning

confidence: 99%

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Stability of the equilibria in a discrete-time sivs epidemic model with standard incidence

Parsamanesh

Mehrshad

2019

Filomat

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A discrete-time SIS epidemic model with vaccination is presented and studied. The model includes deaths due to disease and the total population size is variable. First, existence and positivity of the solutions are discussed and equilibria of the model and basic reproduction number are obtained. Next, the stability of the equilibria is studied and conditions of stability are obtained in terms of the basic reproduction number R 0. Also, occurrence of the fold bifurcation, the flip bifurcation, and the Neimark-Sacker bifurcation is investigated at equilibria. In addition, obtained results are numerically discussed and some diagrams for bifurcations, Lyapunov exponents, and solutions of the model are presented.

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“…where b i , i = 1, 2, 3, are as in (13) and η = I e N e . By solving this problem we see that maximum value is negative and thus…”

Section: Stability Of the Endemic Equilibriummentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Stability of the equilibria in a discrete-time sivs epidemic model with standard incidence

Parsamanesh

Mehrshad

2019

Filomat

Self Cite

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“…Brauer et al [ 5 ] introduced a discrete-epidemic framework and highlight, emphasizing the final size of the epidemic, the similarities between single-outbreak comparable classical continuous-time epidemic models, and the discrete-time models. Farnoosh and Parsamanesh [ 6 ] investigated the stability and bifurcation in a discrete SIS model with bilinear incidence. The vaccination program implements not only on susceptible individuals but also on newcomers to the population.…”

Section: Introductionmentioning

confidence: 99%

Stability and bifurcations in a discrete-time epidemic model with vaccination and vital dynamics

2020

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Background The spread of infectious diseases is so important that changes the demography of the population. Therefore, prevention and intervention measures are essential to control and eliminate the disease. Among the drug and non-drug interventions, vaccination is a powerful strategy to preserve the population from infection. Mathematical models are useful to study the behavior of an infection when it enters a population and to investigate under which conditions it will be wiped out or continued. Results A discrete-time SIS epidemic model is introduced that includes a vaccination program. Some basic properties of this model are obtained; such as the equilibria and the basic reproduction number $$\mathcal {R}_0$$ R 0 . Then the stability of the equilibria is given in terms of $$\mathcal {R}_0$$ R 0 , and the bifurcations of the model are studied. By applying the forward Euler method on the continuous version of the model, a discretized model is obtained and analyzed. Conclusion It is proven that the disease-free equilibrium and endemic equilibrium are stable if $$\mathcal {R}_0<1$$ R 0 < 1 and $$\mathcal {R}_0>1$$ R 0 > 1 , respectively. Also, the disease-free equilibrium is globally stable when $$\mathcal {R}_0\le 1$$ R 0 ≤ 1 . The system has a transcritical bifurcation when $$\mathcal {R}_0=1$$ R 0 = 1 and it might also have period-doubling bifurcation. The sufficient conditions for the stability of equilibria in the discretized model are established. The numerical discussions verify the theoretical results.

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“…For the purpose of considering the effect of vaccination as an efficient strategy to control and eliminate infections, it is possible to add a compartment for the vaccinated individuals to the SIS model and obtain the SIS epidemic model with vaccination, namely SIVS epidemic model [8,14]. These models may be deterministic [4] or stochastic [5], with constant [11] or variable [14] population size, and with standard [10] or bilinear [4,5] incidence rate. In this paper, we consider a discrete-time SIVS epidemic model with standard incidence.…”

Section: Introductionmentioning

confidence: 99%

Stability and Bifurcations in a Discrete-Time Epidemic Model with Vaccination and Vital Dynamics

Parsamanesh

Erfanian

Mehrshad

2020

Preprint

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BackgroundThe spread of infectious diseases is such important that changes the demography of the population. Therefore, prevention and intervention measures are essential to control and eliminate the disease. Among the drug and non-drug interventions, vaccination is a powerful strategy to preserve the population from infection. Mathematical models are useful to study the behavior of an infection when it enters a population and investigate under which conditions it will be wiped out or continued.ResultsA discrete-time SIS epidemic model is introduced that includes a vaccination program. Some basic properties of this model are obtained; such as the equilibria and the basic reproduction number $\mathcal{R}_0$ . Then the stability of the equilibria is given in terms of $\mathcal{R}_0$ , and moreover, the bifurcations of the model are studied. By applying the forward Euler method on the continuous version of model, a discretized model is obtained and analyzed. ConclusionIt is proved that the disease-free equilibrium and endemic equilibrium are stable if $\mathcal{R}_0<1$ and $\mathcal{R}_0>1$ , respectively. The system has a transcritical bifurcation when $\mathcal{R}_0=1$ and it might also have period-doubling bifurcation. The sufficient conditions for the stability of equilibria in the discretized model are established. The numerical discussions verify the theoretical results.

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Disease extinction and persistence in a discrete-time sis epidemic model with vaccination and varying population size

Cited by 12 publications

References 13 publications

Stability of the equilibria in a discrete-time sivs epidemic model with standard incidence

Stability of the equilibria in a discrete-time sivs epidemic model with standard incidence

Stability and bifurcations in a discrete-time epidemic model with vaccination and vital dynamics

Stability and Bifurcations in a Discrete-Time Epidemic Model with Vaccination and Vital Dynamics

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