In this paper, we study the question of existence and uniqueness of entropy solutions for a system of nonlinear partial differential equations with general anisotropic diffusivity and transport effects, supplemented with no-flux boundary conditions, modeling the spread of an epidemic disease through a heterogeneous habitat.
The calculus of looping sequences is a formalism for describing the evolution of biological systems by means of term rewriting rules. In this paper we enrich this calculus with a type discipline which preserves some biological properties depending on the minimum and the maximum number of elements of some type requested by the present elements. The type system enforces these properties and typed reductions guarantee that evolution preserves them. As an example, we model the hemoglobin structure and...
The calculus of looping sequences is a formalism for describing the evolution of biological systems by means of term rewriting rules. In this paper we enrich this calculus with a type discipline which preserves some biological properties depending on the minimum and the maximum number of elements of some type requested by the present elements. The type system enforces these properties and typed reductions guarantee that evolution preserves them. As an example, we model the hemoglobin structure...
We give a survey of results on global stability for deterministic compartmental epidemiological models. Using Lyapunov techniques we revisit a classical result, and give a simple proof. By the same methods we also give a new result on differential susceptibility and infectivity models with mass action and an arbitrary number of compartments. These models encompass the so-called differential infectivity and staged progression models. In the two cases we prove that if the basic reproduction ratio...
We present a unified mathematical approach to epidemiological models with parametric heterogeneity, i.e., to the models that describe individuals in the population as having specific parameter (trait) values that vary from one individuals to another. This is a natural framework to model, e.g., heterogeneity in susceptibility or infectivity of individuals. We review, along with the necessary theory, the results obtained using the discussed approach....
Basic models suitable to explain the epidemiology of dengue fever have previously shown the possibility of deterministically chaotic attractors, which might explain the observed fluctuations found in empiric outbreak data. However, the region of bifurcations and chaos require strong enhanced infectivity on secondary infection, motivated by experimental findings of antibody-dependent-enhancement. Including temporary cross-immunity in such models, which is common knowledge among field researchers...
Si considera l'equazione stocastica che modellizza la dinamica di popolazioni di due specie di tipo preda-predatore sotto perturbazioni stocastiche. Si dimostrano in primo luogo l'esistenza e l'unicità della soluzione dell'equazione; per questo è essenziale introdurre una funzione ausiliaria con cui si costruiscono soluzioni approssimate. Si dimostra inoltre che, se non sono presenti perturbazioni stocastiche dovute alla stocasticità demografica, ma solo perturbazioni stocastiche rappresentanti...
We discuss stochastic dynamics of finite populations of individuals playing symmetric games. We review recent results concerning the dependence of the long-run behavior of such systems on the number of players and the noise level. In the case of two-player games with two symmetric Nash equilibria, when the number of players increases, the population undergoes multiple transitions between its equilibria.
Space-time approximations of the FitzHugh–Nagumo system of coupled semi-linear parabolic PDEs are examined. The schemes under consideration are discontinuous in time but conforming in space and of arbitrary order. Stability estimates are presented in the natural energy norms and at arbitrary times, under minimal regularity assumptions. Space-time error estimates of arbitrary order are derived, provided that the natural parabolic regularity is present. Various physical parameters appearing in the...
Space-time approximations of the FitzHugh–Nagumo system of coupled semi-linear parabolic PDEs are examined. The schemes under consideration are discontinuous in time but conforming in space and of arbitrary order. Stability estimates are presented in the natural energy norms and at arbitrary times, under minimal regularity assumptions. Space-time error estimates of arbitrary order are derived, provided that the natural parabolic regularity is present....
A theorem on estimates of solutions of impulsive parabolic equations by means of solutions of impulsive ordinary differential equations is proved. An application to the population dynamics is given.