We present a Lax–Friedrichs-type algorithm to numerically integrate a class of nonlocal and nonlinear systems of conservation laws in several space dimensions. The convergence of the approximate ...solutions is proved, also providing the existence of a solution in a slightly more general setting than in other results in the current literature. An application to a crowd dynamics model is considered.
Full text
Available for:
BFBNIB, INZLJ, NMLJ, NUK, PNG, SAZU, UL, UM, UPUK, ZRSKP
We present a modeling framework based on a structured SIR model where different vaccination strategies can be tested and compared. Vaccinations can be dosed at prescribed ages or at prescribed times ...to prescribed portions of the susceptible population. Different choices of these prescriptions lead to entirely different evolutions of the disease. Once suitable "costs" are introduced, it is natural to seek, correspondingly, the "best" vaccination strategies. Rigorous results ensure the Lipschitz continuous dependence of various reasonable costs on the control parameters, thus ensuring the existence of optimal controls and suggesting their search, for instance, by means of the steepest descent method.
Consider a Conservation Law and a Hamilton-Jacobi equation with a flux/Hamiltonian depending also on the space variable. We characterize first the attainable set of the two equations and, second, the ...set of initial data evolving at a prescribed time into a prescribed profile. An explicit example then shows the deep differences between the cases of x-independent and x-dependent fluxes/Hamiltonians.
Full text
Available for:
BFBNIB, GIS, IJS, KISLJ, NUK, PNG, UL, UM, UPUK
We present an analytic framework where biological pest control can be simulated. Control is enforced through the choice of a time and space dependent function representing the deployment of a species ...of predators that feed on pests. A sample of different strategies aimed at reducing the presence of pests is considered, evaluated and compared. The strategies explicitly taken into account range, for instance, from the uniform deployment of predators on all the available area over a short/long time interval, to the alternated insertion of predators in different specific regions, to the release of predators in suitably selected regions. The effect of each strategy is measured through a suitably defined cost, essentially representing the total amount of prey present over a given time interval over all the considered region, but the variation in time of the total amount of pests is also evaluated. The analytic framework is provided by an integro-differential hyperbolic-parabolic system of partial differential equations. While prey diffuse according to the usual Laplace operator, predators hunt for prey, moving at finite speed towards regions of higher prey density.
SIR
models, also with age structure, can be used to describe the evolution of an infectious disease. A vaccination campaign influences this dynamics immunizing part of the susceptible individuals, ...essentially turning them into recovered individuals. We assume that vaccinations are dosed at prescribed times or ages which introduce discontinuities in the evolution of the
S
and
R
populations. It is then natural to seek the
“best”
vaccination strategies in terms of costs and/or effectiveness. This paper provides the basic well posedness and stability results on the
SIR
model with vaccination campaigns, thus ensuring the existence of optimal dosing strategies.
Full text
Available for:
CEKLJ, DOBA, EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, IZUM, KILJ, KISLJ, MFDPS, NLZOH, NUK, ODKLJ, OILJ, PILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, UILJ, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
We present an epidemic model capable of describing key features of the Covid-19 pandemic. While capturing several qualitative properties of the virus spreading, it allows to compute the basic ...reproduction number, the number of deaths due to the virus and various other statistics. Numerical integrations are used to illustrate the adherence of the evolutions described by the model to specific well known real features of the present pandemic. In particular, this model is consistent with the well known relevance of quarantine, shows the dramatic role of care houses and accounts for the increase in the death toll when spatial movements are not constrained.
We propose a framework for the description of the effects of vaccinations on the spreading of an epidemic disease. Different vaccines can be dosed, each providing different immunization times and ...immunization levels. Differences due to individuals’ ages are accounted for through the introduction of either a continuous age structure or a discrete set of age classes. Extensions to gender differences or to distinguish fragile individuals can also be considered. Within this setting, vaccination strategies can be simulated, tested and compared, as is explicitly described through numerical integrations.
Full text
Available for:
EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, KILJ, KISLJ, MFDPS, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
A large class of biological models leads to initial boundary value problems for nonhomogeneous balance laws, possibly with nonlocal boundary conditions. Here, for these equations, a general well ...posedness result is proved, a full set of stability estimates is provided, and sample control problems are tackled.
Full text
Available for:
FZAB, GIS, IJS, KILJ, NLZOH, NUK, OILJ, SAZU, SBCE, SBMB, UL, UM, UPUK
We prove the stability with respect to the flux of solutions to initial – boundary value problems for scalar non autonomous conservation laws in one space dimension. Key estimates are obtained ...through a careful construction of the solutions.
We develop a time and space‐dependent predator—prey model. The predators' equation is a nonlocal hyperbolic balance law, while the diffusion of prey obeys a parabolic equation, so that predators ...“hunt” for prey, while prey diffuse. A control term allows to describe the use of predators as parasitoids to limit the growth of prey–parasites. The general well‐posedness and stability results here obtained ensure the existence of optimal pest control strategies, as discussed through some numerical integrations. The specific example we have in mind is that of Trichopria drosophilæ used to fight against the spreading of Drosophila suzukii.
Full text
Available for:
DOBA, FZAB, GIS, IJS, IZUM, KILJ, NLZOH, NUK, ODKLJ, OILJ, PILJ, PNG, SAZU, SBCE, SBMB, UILJ, UKNU, UL, UM, UPUK
PDF
