16 documents found, page 1 of 2

Exact solution for a discrete-time SIR model

We propose a nonstandard finite difference scheme for the Susceptible–Infected–Removed (SIR) continuous model. We prove that our discretized system is dynamically consistent with its continuous counterpart and we derive its exact solution. We end with the analysis of the long-term behavior of susceptible, infected and removed individuals, illustrating our results with examples. In contrast with the SIR discrete...

Stability analysis of Lotka-Volterra models: continuous, discrete and fractional

We consider a modified Lotka-Volterra model with a Michaelis-Menten type functional response with relevance to the bank system. We prove the model is well posed (non-negativity and boundedness of the solutions) and study the local stability using different methods. Firstly, we consider the continuous model. After, we investigate the dynamical consistency of two numerical schemes: Euler and Mickens. Finally, the...

A Lotka–Volterra-Type Model Analyzed Through Different Techniques

We consider a modified Lotka–Volterra model applied to the predator-prey system that can also be applied to other areas, for instance, the bank system. We show that the model is well-posed (nonnegativity of solutions and conservation law) and study the local stability using different methods. Firstly, we consider the continuous model, after which the numerical schemes of Euler and Mickens are investigated. Fina...

Discrete-Time System of an Intracellular Delayed HIV Model with CTL Immune Resp...

In [Math. Comput. Sci. 12 (2018), no. 2, 111--127], a delayed model describing the dynamics of the Human Immunodeficiency Virus (HIV) with Cytotoxic T Lymphocytes (CTL) immune response is investigated by Allali, Harroudi and Torres. Here, we propose a discrete-time version of that model, which includes four nonlinear difference equations describing the evolution of uninfected, infected, free HIV viruses, and CT...

Discrete-time system of an intracellular delayed HIV model with CTL immune resp...

In [Math. Comput. Sci. 12 (2018), no. 2, 111–127], a delayed model describing the dynamics of the Human Immunodeficiency Virus (HIV) with Cyto- toxic T Lymphocytes (CTL) immune response is investigated by Allali, Harroudi and Torres. Here, we propose a discrete-time version of that model, which includes four nonlinear difference equations describing the evolution of uninfected, infected, free HIV viruses, and C...

Might synthetic cannabinoids influence neural differentiation?

A Discrete-Time Compartmental Epidemiological Model for COVID-19 with a Case St...

Recently, a continuous-time compartmental mathematical model for the spread of the Coronavirus disease 2019 (COVID-19) was presented with Portugal as case study, from 2 March to 4 May 2020, and the local stability of the Disease Free Equilibrium (DFE) was analysed. Here, we propose an analogous discrete-time model and, using a suitable Lyapunov function, we prove the global stability of the DFE point. Using COV...

A dynamically-consistent nonstandard finite difference scheme for the SICA model

In this work, we derive a nonstandard finite difference scheme for the SICA (Susceptible-Infected-Chronic-AIDS) model and analyze the dynamical properties of the discretized system. We prove that the discretized model is dynamically consistent with the continuous, maintaining the essential properties of the standard SICA model, namely, the positivity and boundedness of the solutions, equilibrium points, and the...

A dynamically-consistent nonstandard finite difference scheme for the SICA model

In this work, we derive a nonstandard finite difference scheme for the SICA (Susceptible–Infected–Chronic–AIDS) model and analyze the dynamical properties of the discretized system. We prove that the discretized model is dynamically consistent with the continuous, maintaining the essential properties of the standard SICA model, namely, the positivity and boundedness of the solutions, equilibrium points, and the...

A discrete-time compartmental epidemiological model for COVID-19 with a case st...

Recently, a continuous-time compartmental mathematical model for the spread of the Coronavirus disease 2019 (COVID-19) was presented with Portugal as case study, from 2 March to 4 May 2020, and the local stability of the Disease Free Equilibrium (DFE) was analysed. Here, we propose an analogous discrete-time model and, using a suitable Lyapunov function, we prove the global stability of the DFE point. Using COV...