Mathematical Structures of Epidemic Systems

Capasso, Vincenzo

doi:10.1007/978-3-540-70514-7

Cited by 403 publications

(359 citation statements)

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“…As a consequence, due to the contradiction, (17) cannot have solution with non-negative real part, and the equilibrium is locally stable. The proof on global stability is essentially based method of contracting rectangles (in our case: intervals) [6,22], and in it we shall use the function g(z) = B ψ (μ)P (z). Since p(C) is decreasing, it is p(C(t)) ≤ p(0) and as a consequence:…”

Section: A2 Main Propositionsmentioning

confidence: 99%

“…We feel this case is fundamentally more appropriate in the developed world than the alternative hypothesis that demand is driven by the disease incidence, especially for those common vaccine preventable infections which currently have very low or even zero incidence. To this aim we study the dynamics of vaccine uptake for a homogeneously mixing vaccine preventable SIR disease [6] with vital dynamics and vaccination by a perfect vaccine under the following circumstances: a) vaccination is voluntary; b) the vaccine has a constant probability to generate severe, non-lethal, side effects; c) the perceived risk of suffering serious disease following infection is steadily low, so that the vaccine demand is essentially related, through a decreasing function, to the perceived risk M of suffering a vaccine associated side effect; d) the perceived risk M is evaluated from publicly available information on current, past, or even future (through expectations) trends of side effects caused, or attributed, to the vaccine. In particular, in order to evaluate the risk of VSE, parents are assumed to use the public information on the current, or past, reported incidence of VSE, or the prevalence of those who suffered side effects.…”

Section: Introductionmentioning

confidence: 99%

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Vaccine demand driven by vaccine side effects: Dynamic implications for SIR diseases

d’Onofrio

Manfredi²

2010

Journal of Theoretical Biology

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Section: A2 Main Propositionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Vaccine demand driven by vaccine side effects: Dynamic implications for SIR diseases

d’Onofrio

Manfredi²

2010

Journal of Theoretical Biology

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“…The most virulent strain can takeover hosts already infected with the less virulent strain. Under these assumptions a globally stable equilibrium is possible where both strains may coexist [3]. The stability of the positive equilibrium i~ only guaranteed for certain range of values of superinfection.…”

Section: Superinfection and Coexistencementioning

confidence: 99%

Competitive exclusion in a vector-host model for the dengue fever

Feng

Hernández²

1997

Journal of Mathematical Biology

306

189

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In this work we study a system of differential equations that models the population dynamics of an SIR vector transmitted disease with two pathogen strains. This model arose from our study of the population dynamics of dengue fever. The dengue virus presents four serotypes each of which induces host immunity but only certain degree of crossimmunity to the other different serotypes. The model studied here has been constructed as a paradigm for the study of the epidemiological trends in the disease and for the theoretical study of conditions that permit coexistence in competing strains. Dengue is mainly an epidemic disease in the Americas and this model is geared to generalize this type of dynamics. In the model two different strains of virus are considered with temporary cross-immunity. The model shows the existence of an unstable endemic state ('saddle' point). The nature of this equilibrium produces a transient behavior characterized as a quasi-steady state of long duration during which both dengue serotypes co-circulate. Conditions for asymptotic stability of the equilibria are discussed together with numerical simulations. We argue that the existence of competitive exclusion in this system is due to the interplay between the host superinfection process and the frequency-dependent (vector to host) contact rates.

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“…Furthermore, epidemic systems have also been used in non-medical areas to study processes that follow an epidemiological behaviour. Here, we have analysed a S IS model [18] composed by a susceptible population, denoted by S (t), and an infected population, denoted by I(t), as shown in Figure 4. Two different cases for the S IS model will be studied depending on whether death by the disease is considered in the system or not.…”

Section: Non-linear Epidemiological S Is Modelmentioning

confidence: 99%

Guaranteed computation methods for compartmental in-series models under uncertainty

Pereda

Romero‐Vivó

Ricarte

et al. 2013

Computers & Mathematics with Applications

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The pattern of some real phenomenona can be described by compartmental in-series models. Nevertheless, most of these processes are characterized by their variability, which produces that the exact values of the model parameters are uncertain, although they can be bounded by intervals.The aim of this paper is to compute tight solution envelopes that guarantee the inclusion of all possible behaviours of such processes. Current methods, such as monotonicity analysis, enable us to obtain guaranteed solution envelopes. However, if the model includes non-monotone compartments or parameters, the computation of solution envelopes may produce a significant overestimation.Our proposal consists in performing a change of variables in which the output is unaltered, and the model obtained is monotone with respect to the uncertain parameters. The monotonicity of the new system allows us to compute the output bounds for the original system without overestimation. These model transformations have been developed for linear and non-linear systems. Furthermore, if the conditions are not completely satisfied, a novel method to compute tight solution envelopes is proposed. The methods exposed in this paper have been applied to compute tight solution envelopes for two different models: a linear system for glucose modelling and a non-linear system for an epidemiological model.

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Mathematical Structures of Epidemic Systems

Cited by 403 publications

References 0 publications

Vaccine demand driven by vaccine side effects: Dynamic implications for SIR diseases

Vaccine demand driven by vaccine side effects: Dynamic implications for SIR diseases

Competitive exclusion in a vector-host model for the dengue fever

Guaranteed computation methods for compartmental in-series models under uncertainty

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