On the estimation of averages over infinite intervals with an application to average persistence in population models.
On the global dynamics of the cancer AIDS-related mathematical model
In this paper we examine some features of the global dynamics of the four-dimensional system created by Lou, Ruggeri and Ma in 2007 which describes the behavior of the AIDS-related cancer dynamic model in vivo. We give upper and lower ultimate bounds for concentrations of cell populations and the free HIV-1 involved in this model. We show for this dynamics that there is a positively invariant polytope and we find a few surfaces containing omega-limit sets for positive half trajectories in the positive...
On the linearized stability of age-structured multispecies populations.
On the semigroups of age-size dependent population dynamcis with spatial diffusion.
On the speed of coming down from infinity for -coalescent processes.
On the study of chemostat model with pulsed input in a polluted environment.
On the theory of remediability
Suppose and are two families of semigroups on a Banach space X (not necessarily of class C₀) such that for some initial datum u₀, G₁(t)u₀ tends towards an undesirable state u*. After remedying by means of an operator ρ we continue the evolution of the state by applying G₂(t) and after time 2t we retrieve a prosperous state u given by u = G₂(t)ρG₁(t)u₀. Here we are concerned with various properties of the semigroup (t): ρ → G₂(t)ρG₁(t). We define (X) to be the space of remedial operators for...
On the Weak Solutions of the McKendrick Equation: Existence of Demography Cycles
We develop the qualitative theory of the solutions of the McKendrick partial differential equation of population dynamics. We calculate explicitly the weak solutions of the McKendrick equation and of the Lotka renewal integral equation with time and age dependent birth rate. Mortality modulus is considered age dependent. We show the existence of demography cycles. For a population with only one reproductive age class, independently of the stability of the weak solutions and after a transient time,...
On the well posedness and refined estimates for the global attractor of the TYC model.
Optimal campaign in the smoking dynamics.
Optimal control for a nonlinear age-structured population dynamics model.
Optimal control for a nonlinear population dynamics problem.
Optimal Screening in Structured SIR Epidemics
We present a model for describing the spread of an infectious disease with public screening measures to control the spread. We want to address the problem of determining an optimal screening strategy for a disease characterized by appreciable duration of the infectiveness period and by variability of the transmission risk. The specific disease we have in mind is the HIV infection. However the model will apply to a disease for which class-age structure...
Oscillation and global attractivity in a discrete survival red blood cells model
We consider the discrete survival red blood cells model (*) , where δₙ and Pₙ are positive sequences. In the autonomous case we show that (*) has a unique positive steady state N*, we establish some sufficient conditions for oscillation of all positive solutions about N*, and when k = 1 we give a sufficient condition for N* to be globally asymptotically stable. In the nonatonomous case, assuming that there exists a positive solution Nₙ*, we present necessary and sufficient conditions for oscillation...
Oscillation and stability of nonlinear discrete models exhibiting the Allee effect