Methods for studying stability of systems with linear delay.
Misbehaviour of Solutions of the Differential Equation y' = f(x,y) + ... when the Right Hand Side id Discontinuous.
Modeling Adaptive Behavior in Influenza Transmission
Contact behavior plays an important role in influenza transmission. In the progression of influenza spread, human population reduces mobility to decrease infection risks. In this paper, a mathematical model is proposed to include adaptive mobility. It is shown that the mobility response does not affect the basic reproduction number that characterizes the invasion threshold, but reduces dramatically infection peaks, or removes the peaks. Numerical...
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 the hepatitis C with different types of virus genome.
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...
Modelling tumour-immunity interactions with different stimulation functions
Tumour immunotherapy is aimed at the stimulation of the otherwise inactive immune system to remove, or at least to restrict, the growth of the original tumour and its metastases. The tumour-immune system interactions involve the stimulation of the immune response by tumour antigens, but also the tumour induced death of lymphocytes. A system of two non-linear ordinary differential equations was used to describe the dynamic process of interaction between the immune system and the tumour. Three different...
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.
Modifying some foliated dynamical systems to guide their trajectories to specified sub-manifolds
We show that dynamical systems in inverse problems are sometimes foliated if the embedding dimension is greater than the dimension of the manifold on which the system resides. Under this condition, we end up reaching different leaves of the foliation if we start from different initial conditions. For some of these cases we have found a method by which we can asymptotically guide the system to a specific leaf even if we start from an initial condition which corresponds to some other leaf. We demonstrate...
Monotonic asymptotic stability of a class of solutions along the coordinates
Monotonicity properties of oscillatory solutions of differential equation
We obtain monotonicity results concerning the oscillatory solutions of the differential equation . The obtained results generalize the results given by the first author in [1] (1976). We also give some results concerning a special case of the above differential equation.
Multi-type synchronization of impulsive coupled oscillators via topology degree
The existence of synchronization is an important issue in complex dynamical networks. In this paper, we study the synchronization of impulsive coupled oscillator networks with the aid of rotating periodic solutions of impulsive system. The type of synchronization is closely related to the rotating matrix, which gives an insight for finding various types of synchronization in a united way. We transform the synchronization of impulsive coupled oscillators into the existence of rotating periodic solutions...
Necessary and sufficient conditions for stability of Volterra integro-dynamic equation on time scales
In this research we establish necessary and sufficient conditions for the stability of the zero solution of scalar Volterra integro-dynamic equation on general time scales. Our approach is based on the construction of suitable Lyapunov functionals. We will compare our findings with known results and provides application to quantum calculus.
New approach to asymptotic stability: Time-varying nonlinear systems.
New Computational Tools for Modeling Chronic Myelogenous Leukemia
In this paper, we consider a system of nonlinear delay-differential equations (DDEs) which models the dynamics of the interaction between chronic myelogenous leukemia (CML), imatinib, and the anti-leukemia immune response. Because of the chaotic nature of the dynamics and the sparse nature of experimental data, we look for ways to use computation to analyze the model without employing direct numerical simulation. In particular, we develop several tools using Lyapunov-Krasovskii analysis that allow...
New results on asymptotic behavior of solutions of certain third-order nonlinear differential equations
New results on stability of periodic solution for CNNs with proportional delays and operator
The problems related to periodic solutions of cellular neural networks (CNNs) involving operator and proportional delays are considered. We shall present Topology degree theory and differential inequality technique for obtaining the existence of periodic solution to the considered neural networks. Furthermore, Laypunov functional method is used for studying global asymptotic stability of periodic solutions to the above system.
Nonautonomous attractors of skew-product flows with digitized driving systems.