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A Cost-Effectiveness-Assessing Model of Vaccination for Varicella and Zoster

M. Comba, S. Martorano-Raimundo, E. Venturino (2012)

Mathematical Modelling of Natural Phenomena

A decision analytical model is presented and analysed to assess the effectiveness and cost-effectiveness of routine vaccination against varicella and herpes-zoster, or shingles. These diseases have as common aetiological agent the varicella-zoster virus (VZV). Zoster can more likely occur in aged people with declining cell-mediated immunity. The general concern is that universal varicella vaccination might lead to more cases of zoster: with more...

A discrete predator-prey system with age-structure for predator and natural barriers for prey

Sanyi Tang, Lansun Chen (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We analyze a two species discrete predator-prey model in which the prey disperses between two patches of a heterogeneous environment with barriers and the mature predator disperses between the patches with no barrier. By using the discrete dynamical system generated by a monotone, concave maps for subcommunity of prey, we obtain the subcommunity of prey exists an equilibrium which attracts all positive solutions, and using the stability trichotomy results on the monotone and continuous operator,...

A discrete predator-prey system with age-structure for predator and natural barriers for prey

Sanyi Tang, Lansun Chen (2001)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We analyze a two species discrete predator-prey model in which the prey disperses between two patches of a heterogeneous environment with barriers and the mature predator disperses between the patches with no barrier. By using the discrete dynamical system generated by a monotone, concave maps for subcommunity of prey, we obtain the subcommunity of prey exists an equilibrium which attracts all positive solutions, and using the stability trichotomy results on the monotone and continuous operator,...

A first order partial differential equation with an integral boundary condition

Gabriella Di Blasio, Mimmo Iannelli, Eugenio Sinestrari (1981)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

In questo lavoro si considera un’equazione alle derivate parziali del primo ordine con una condizione sulla frontiera di tipo integrale. Si studia resistenza, l'unicità e il comportamento asintotico delle soluzioni.

A game-theoretic model of social adaptation in an infinite population

A. Wieczorek, A. Wiszniewska (1999)

Applicationes Mathematicae

The paper deals with the question of existence and properties of equilibrated distributions of individual characteristics in an infinite population. General game-theoretic methods are applied and special attention is focused on the case of fitness functions depending only on the distance of an individual characteristic from a reference point and from the mean characteristics. Iterative procedures leading to equilibrated distributions are also considered.

A linear scheme to approximate nonlinear cross-diffusion systems*

Hideki Murakawa (2011)

ESAIM: Mathematical Modelling and Numerical Analysis

This paper proposes a linear discrete-time scheme for general nonlinear cross-diffusion systems. The scheme can be regarded as an extension of a linear scheme based on the nonlinear Chernoff formula for the degenerate parabolic equations, which proposed by Berger et al. [RAIRO Anal. Numer.13 (1979) 297–312]. We analyze stability and convergence of the linear scheme. To this end, we apply the theory of reaction-diffusion system approximation. After discretizing the scheme in space, we obtain a versatile,...

A linear scheme to approximate nonlinear cross-diffusion systems*

Hideki Murakawa (2011)

ESAIM: Mathematical Modelling and Numerical Analysis

This paper proposes a linear discrete-time scheme for general nonlinear cross-diffusion systems. The scheme can be regarded as an extension of a linear scheme based on the nonlinear Chernoff formula for the degenerate parabolic equations, which proposed by Berger et al. [RAIRO Anal. Numer.13 (1979) 297–312]. We analyze stability and convergence of the linear scheme. To this end, we apply the theory of reaction-diffusion system approximation. After discretizing the scheme in space, we obtain a versatile,...

A method for treating a class of non­linear diffusion problems

Stavros Busenberg, Mimmo Iannelli (1982)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Si presenta un metodo di soluzione di una classe di problemi di diffusione nonlineare che hanno origine dalla teoria delle popolazioni con struttura di età.

A Minimal Model of Pursuit-Evasion in a Predator-Prey System

Y. Tyutyunov, L. Titova, R. Arditi (2010)

Mathematical Modelling of Natural Phenomena

A conceptual minimal model demonstrating spatially heterogeneous wave regimes interpreted as pursuit-evasion in predator-prey system is constructed and investigated. The model is based on the earlier proposed hypothesis that taxis accelerations of prey and predators are proportional to the density gradient of another population playing a role of taxis stimulus. Considering acceleration rather than immediate velocity allows obtaining realistic solutions even while ignoring variations of total...

A new application of the homotopy analysis method in solving the fractional Volterra's population system

Mehdi Ghasemi, Mojtaba Fardi, Reza Khoshsiar Ghaziani (2014)

Applications of Mathematics

This paper considers a Volterra's population system of fractional order and describes a bi-parametric homotopy analysis method for solving this system. The homotopy method offers a possibility to increase the convergence region of the series solution. Two examples are presented to illustrate the convergence and accuracy of the method to the solution. Further, we define the averaged residual error to show that the obtained results have reasonable accuracy.

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