We develop a mathematical model that describes the tumour–immune interaction and the effect on it of pulsed immunotherapy, based on the administration of adoptive cellular immunotherapy (ACI) combined with interleukin-2 (IL-2). The stability conditions for the tumour-free periodic solution are...

The standard footloose capital (FC) model, as well as the discrete time version, assumes that all capital units are internationally mobile between two regions. In this paper, we assume that in one of the two regions some of the blueprints/capital units may be immobile because their utilization...

This paper concludes the study of transition paths in the continuous-time recombinant endogenous growth model by providing numerical methods to estimate the threshold initial value of capital (a Skiba-type point) above which the economy takes off toward sustained growth in the long run, while it...

We consider a network of interacting agents and we model the process of choice on the adoption of a given innovative product by means of statistical-mechanics tools. The modelization allows us to focus on the effects of direct interactions among agents in establishing the success or failure of...

The method investigated in this paper is concerned with the multivariate global optimization with box constraints. A new quadratic lower bound in a branch and bound framework is proposed. For a continuous, twice differentiable function f, the new lower bound is given by a difference of the...

Cournot oligopolies are examined with two kinds of output adjustment costs, which model the use of contingent work force and additional investments. The best responses of the firms are first determined and the partial adjustment toward best responses is assumed in formulating a dynamic model....

We present a simple financial market model with interacting chartists and fundamentalists. Since some speculators only become active when a certain misalignment level has been crossed, the model dynamics is driven by a discontinuous piecewise linear map. Recent mathematical techniques allow a...

There are very few optimal fourth order methods for solving nonlinear algebraic equations having roots of multiplicity m. In a previous paper we have compared 5 such methods, two of which require the evaluation of the (m−1)th root. We have used the basin of attraction idea to recommend the...

Due to errors in measurements and inherent variability in the quantities of interest, models based on random differential equations give more realistic results than their deterministic counterpart. The generalized polynomial chaos (gPC) is a powerful technique used to approximate the solution of...

We study global dynamics of the New Economic Geography model which describes spatial distribution of industrial activity in the long run across three identical regions depending on the balancing of agglomeration and dispersion forces. It is defined by a two-dimensional piecewise smooth map...