Global attractors of non-autonomous quasi-homogeneous dynamical systems.
Global dynamics of a HIV transmission model.
Global stability of dynamic systems of high order.
Global stability of sets for impulsive differential-difference equations by Lyapunov's direct method
Global stability of steady solutions for a model in virus dynamics
We consider a simple model for the immune system in which virus are able to undergo mutations and are in competition with leukocytes. These mutations are related to several other concepts which have been proposed in the literature like those of shape or of virulence – a continuous notion. For a given species, the system admits a globally attractive critical point. We prove that mutations do not affect this picture for small perturbations and under strong structural assumptions. Based on numerical...
Global Stability of Steady Solutions for a Model in Virus Dynamics
We consider a simple model for the immune system in which virus are able to undergo mutations and are in competition with leukocytes. These mutations are related to several other concepts which have been proposed in the literature like those of shape or of virulence – a continuous notion. For a given species, the system admits a globally attractive critical point. We prove that mutations do not affect this picture for small perturbations and under strong structural assumptions. Based on numerical...
Harvesting of a single-species system incorporating stage structure and toxicity.
Local and global properties of nonautonomous dynamical systems and their application to competition models.
Mathematical analysis of a within-host model of malaria with immune effectors and Holling type II functional response
In this paper, we consider a within-host model of malaria with Holling type II functional response. The model describes the dynamics of the blood-stage of parasites and their interaction with host cells, in particular red blood cells and immune effectors. First, we obtain equilibrium points of the system. The global stability of the disease-free equilibrium point is established when the basic reproduction ratio of infection is R₀< 1. Then the disease is controllable and dies out. In the absence...
Modeling HIV epidemic under contact tracing -- the Cuban case.
Modeling the role of constant and time varying recycling delay on an ecological food chain
We consider a mathematical model of nutrient-autotroph-herbivore interaction with nutrient recycling from both autotroph and herbivore. Local and global stability criteria of the model are studied in terms of system parameters. Next we incorporate the time required for recycling of nutrient from herbivore as a constant discrete time delay. The resulting DDE model is analyzed regarding stability and bifurcation aspects. Finally, we assume the recycling delay in the oscillatory form to model the...
Modelling immune response and drug therapy in human malaria infection.
Modelling Tuberculosis and Hepatitis B Co-infections
Tuberculosis (TB) is the leading cause of death among individuals infected with the hepatitis B virus (HBV). The study of the joint dynamics of HBV and TB present formidable mathematical challenges due to the fact that the models of transmission are quite distinct. We formulate and analyze a deterministic mathematical model which incorporates of the co-dynamics of hepatitis B and tuberculosis. Two sub-models, namely: HBV-only and TB-only sub-models...
Models of interactions between heterotrophic and autotrophic organisms
We present two simple models describing relations between heterotrophic and autotrophic organisms in the land and water environments. The models are based on the Dawidowicz & Zalasiński models but we assume the boundedness of the oxygen resources. We perform a basic mathematical analysis of the models. The results of the analysis are complemented by numerical illustrations.
On food chain in a chemostat with distinct removal rates.
On oscillatory pattern of malaria dynamics in a population with temporary immunity.
On stability and bifurcation of solutions of an SEIR epidemic model with vertical transmission.
On the Armellini-Tonelli-Sansone theorem.
On the asymptotic behavior of solutions of certain third-order nonlinear differential equations.
On the exponential stability of a certain Lurie system