We investigate two cases of a sharp change of incidencec functions on the dynamics of a susceptible-infective-susceptible epidemic model. In the first case, low population levels have mass action incidence, while high population levels have proportional incidence, the switch occurring when the total population reaches a certain threshold. Using a modified Dulac theorem, we prove that this syste...

Abstract—Stochastic User Equilibrium (SUE) model is a widely used traffic assignment model in transportation planning, which is regarded more advanced than Deterministic User Equilibrium (DUE) model. However, a problem exists that the performance of the SUE model depends on its error term parameter. The objective of this paper is to propose a systematic method of determining the appropriate err...

This paper examines a class of evolutionary models in which large shocks cause frequent movement between short-term "stable" equilibria. Mutations are rare in our model, but their effects are magnified by a "spread process" which causes a finite proportion of the population to initially adopt the entering strategy before the short-term selection dynamics takes effect. We examine the long run in...

This paper analyzes how capital structure and product market competition affect the firms’ choice between outsourcing with long term contracts and outsourcing to the spot market. When outsourcing to the spot market firms are exposed to price uncertainty, whereas a long term contract allows them to set in advance the outsourcing price. We show that, to the extent that leverage and uncertainty ca...

In this paper we study the zero reaction limit of the hyperbolic conservation law with stii source term @ t u + @ x f(u) = 1 u(1 ? u 2) : For the Cauchy problem to the above equation, we prove that as ! 0, its solution converges to piecewise constant (1) solution, where the two constants are the two stable local equilibrium. The constants are separated by either shocks that travel with speed 1 ...

In this paper we attempt to analyze the problem of centrally allocating tasks to selfinterested agents in environments characterized by high uncertainty. The analysis is based on equilibrium dynamics, taking into account the agents’ short-term and long-term considerations. The model reflects a rich realism by allowing both tasks and agents to dynamically arrive in the environment. This is corre...

The value of a gas fired power plant depends on the spark spread, defined as the difference between the unit price of electricity and the cost of gas. We model the spark spread using two-factor model, allowing mean-reversion in short-term variations and uncertainty in the equilibrium price to which prices revert. We analyze two types of gas plants. The first type is a base load plant, generatin...

This paper studies the equilibrium predatory practices that may arise when the borrowers have behavioral weaknesses. Rational lenders offer short term contracts that can be renewed at the cost of paying a penalty fee. We show how the optimal contracts depend on the degree of näıveté of the time inconsistent customers. Penalty fees have a dual role : they increase market share by providing a use...

The Poisson-Lévy excursion measure for the diffusion process with small noise satisfying the Itô equation dXε = b(Xε(t))dt + √ ε dB(t) is studied and the asymptotic behaviour in ε is investigated. The leading order term is obtained exactly and it is shown that at an equilibrium point there are only two possible forms for this term Lévy or Hawkes – Truman. We also compute the next to leading order.

A new economic model is presented. The Persistent Poverty Model shows one possibility of long term general equilibrium with unemployment. This model allows us to explain the NAIRU level and the poor results of conventional economic policies against poverty and long term unemployment. According to this theoretic model, an unconditional basic income policy would be able to reach both targets: pov...