Threshold behaviour of a SIR epidemic model with age structure and immigration

Franceschetti, A; Pugliese, Andrea

doi:10.1007/s00285-007-0143-1

Cited by 49 publications

(37 citation statements)

References 23 publications

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“…where the fraction of recovered is obtained from R(z, t) = 1 − S(z, t) − I(z, t). We refer to [26,25,21,27] for analytical results concerning model (2) and (3) in a deterministic setting.…”

Section: A Socially Structured Compartmental Model With Uncertaintymentioning

confidence: 99%

Modelling lockdown measures in epidemic outbreaks using selective socio-economic containment with uncertainty

Albi

Pareschi

Zanella

2020

Preprint

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After an initial phase characterized by the introduction of timely and drastic containment measures aimed at stopping the epidemic contagion from SARS-CoV2, many governments are preparing to relax such measures in the face of a severe economic crisis caused by lockdowns. Assessing the impact of such openings in relation to the risk of a resumption of the spread of the disease is an extremely difficult problem due to the many unknowns concerning the actual number of people infected, the actual reproduction number and infection fatality rate of the disease. In this work, starting from a compartmental model with a social structure, we derive models with multiple feedback controls depending on the social activities that allow to assess the impact of a selective relaxation of the containment measures in the presence of uncertain

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Section: A Socially Structured Compartmental Model With Uncertaintymentioning

confidence: 99%

Modelling lockdown measures in epidemic outbreaks using selective socio-economic containment with uncertainty

Albi

Pareschi

Zanella

2020

Preprint

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“…The previous model can be extended to include vital dynamics [23], delays equations [24], age structured population, migration [25], and diffusion. In any case, all these generalizations only introduce some slight changes on the steady states of the system, or in the case of spatially extended models, travelling waves [26].…”

Section: The Sir Modelmentioning

confidence: 99%

Invited review: Epidemics on social networks

Kuperman

2013

Pap. Phys.

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Since its rst formulations almost a century ago, mathematical models for disease spreading contributed to understand, evaluate and control the epidemic processes. They promoted a dramatic change in how epidemiologists thought of the propagation of infectious diseases. In the last decade, when the traditional epidemiological models seemed to be exhausted, new types of models were developed. These new models incorporated concepts from graph theory to describe and model the underlying social structure. Many of these works merely produced a more detailed extension of the previous results, but some others triggered a completely new paradigm in the mathematical study of epidemic processes. In this review, we will introduce the basic concepts of epidemiology, epidemic modeling and networks, to nally provide a brief description of the most relevant results in the eld.

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“…Therefore, the fact that the length of the period of infectivity is α is expressed by the condition lim a→α a 0 q(t − a + s, s, x)ds = +∞, uniformly for (t, x) ∈ (0, T ) × V. (1.8) Age-structured epidemics models of various kind, without spatial heterogeneity, are analyzed since many years: see e.g. [4,7,15,17,18]. If diffusion is taken into consideration epidemic models with age structure are studied in [5], where existence of periodic solutions is investigated in the case V = R n and with a time periodic forcing, in [12] and [13], where existence of traveling wave solutions is investigated in the scalar case and in [19], where approximate solutions using Galerkin methods are considered.…”

Section: The Modelmentioning

confidence: 99%

Mathematical analysis for an epidemic model with spatial and age structure

Blasio

2010

J. Evol. Equ.

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A system of parabolic-hyperbolic equations with a non-local boundary condition, arising in mathematical theory of epidemics, is analyzed. For such a system, well-posedness as well as Sobolev regularity with respect to the space variables is proved. Asymptotic behavior of the solutions is also investigated. The modelLet V ⊂ R n be an open and bounded set with regular boundary and let denote the Laplace operator in V . This paper deals with the following problem: givenwhere D ν denotes the exterior normal derivative on . Here, m, q : (0, T ) × (0, α) × V → R + and v : (0, T ) × V → R + are measurable functions satisfying suitable assumptions, which will be specified in Sect. 2. Furthermore, δ S , δ i and δ R are positive constants, denoting the diffusion coefficients. Problems of this kind occur in the study of some mathematical models of epidemics, the so-called SIR models, where S and R specify the space structure at time t of susceptible (not infected) population and removed (permanently immune) population, (2000): Primary 35K70; Secondary 35K90, 92A15 Mathematics Subject Classification

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Threshold behaviour of a SIR epidemic model with age structure and immigration

Cited by 49 publications

References 23 publications

Modelling lockdown measures in epidemic outbreaks using selective socio-economic containment with uncertainty

Modelling lockdown measures in epidemic outbreaks using selective socio-economic containment with uncertainty

Invited review: Epidemics on social networks

Mathematical analysis for an epidemic model with spatial and age structure

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