Saddle point approximations in n-type epidemics and contact birth processes

L ∞ - convergence of saddle - point approximations for second order problems

Saddle Point Formulation of the Quasistatic Contact Problems with Friction

The paper is concerned with the numerical solution of the quasi-variational inequality modelling a contact problem with Coulomb friction. After discretization of the problem by mixed finite elements and with Lagrangian formulation of the problem by choosing appropriate multipliers, the duality approach is improved by splitting the normal and tangential stresses. The novelty of our approach in t...

SADDLE POINT VARIATIONAL METHOD FOR DIRAC CONFINEMENT

A saddle point variational (SPV ) method was applied to the Dirac equation as an example of a fully relativistic equation with both negative and positive energy solutions. The effect of the negative energy states was mitigated by maximizing the energy with respect to a relevant parameter while at the same time minimizing it with respect to another parameter in the wave function. The Cornell pot...

On expected durations of birth-death processes, with applications to branching processes and SIS epidemics

We study continuous-time birth-death type processes, where individuals have independent and identically distributed lifetimes, according to a random variable Q, with E[Q] = 1, and where the birth rate if the population is currently in state (has size) n is α(n). We focus on two important examples, namely α(n) = λn being a branching process, and α(n) = λn(N −n)/N which corresponds to an SIS (sus...

Correcting mean-field approximations for birth-death-movement processes.

On the microscale, migration, proliferation and death are crucial in the development, homeostasis and repair of an organism; on the macroscale, such effects are important in the sustainability of a population in its environment. Dependent on the relative rates of migration, proliferation and death, spatial heterogeneity may arise within an initially uniform field; this leads to the formation of...