Exact solution to a dynamic SIR model

Exact solution of a stochastic SIR model

Abstract The susceptible-infectious-recovered (SIR) model describes the evolution of three species of individuals which are subject to an infection and recovery mechanism. A susceptible S can become infectious with an infection rate β by an infectious Itype provided that both are in contact. The Itype may recover with a rate γ and from then on stay immune. Due to the coupling between the differ...

An Exact Elastodynamic Solution for Func-tionally Graded Thick-Walled Cylinders Subjected to Dynamic Pressures

In the present paper, an exact solution for transient response of an infinitely long functionally graded thick-walled cylinder subjected to dynamic pressures at the boundary surfaces is presented for arbitrary initial conditions. The cylinder is assumed to have a plane-strain condition and the dynamic pressures are assumed to be imposed uniformly and axis...

An Exact Solution to a Three Dimensional Ising Model

A high temperature expansion is employed to map some complex anisotropic nonhermitian three dimensional Ising models with algebraic long range interactions into a solvable two dimensional variant. Some solutions are presented. This framework further allows for some very simple general observations. It will be seen that the absence of a “phase interference” effect plays an important role in high...

Exact Solution of a Model of Localization

The exact solution is presented for the "susceptibility," χ (the number of sites covered by the maximally extended eigenfunction), for the zero-energy solutions of a hopping model on a randomly dilute Cayley tree. If p is the concentration, then χ~(p*−p)−1 with p*~pce1/ξ1, where pc is the critical percolation concentration and ξ1 the one-dimensional localization length. This result is argued to...

An exact Solution for a Finite Solution Server Model