scholarly journals A Discrete-Time Compartmental Epidemiological Model for COVID-19 with a Case Study for Portugal

Axioms ◽  
2021 ◽  
Vol 10 (4) ◽  
pp. 314
Author(s):  
Sandra Vaz ◽  
Delfim F. M. Torres
Keyword(s):  
Mathematical Model ◽  
Discrete Time ◽  
Continuous Time ◽  
Local Stability ◽  
Real Data ◽  
Time Model ◽  
Discrete Time Model ◽  
Theoretical Results ◽  
Disease Free

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 COVID-19 real data, we show, through numerical simulations, the consistence of the obtained theoretical results.

Birth and death processes with random environments in continuous time

1981 ◽  
Vol 18 (01) ◽  
pp. 19-30 ◽  
Author(s):  
Robert Cogburn ◽  
William C. Torrez
Keyword(s):  
Discrete Time ◽  
Random Environment ◽  
Continuous Time ◽  
Death Process ◽  
Random Environments ◽  
Birth And Death Process ◽  
Time Model ◽  
Birth And Death Processes ◽  
Discrete Time Model ◽  
Extinction Probabilities

A generalization to continuous time is given for a discrete-time model of a birth and death process in a random environment. Some important properties of this process in the continuous-time setting are stated and proved including instability and extinction conditions, and when suitable absorbing barriers have been defined, methods are given for the calculation of extinction probabilities and the expected duration of the process.

scholarly journals Extreme stability and almost periodicity in continuous and discrete neuronal models with finite delays

2002 ◽  
Vol 44 (2) ◽  
pp. 261-282 ◽  
Author(s):  
S. Mohamad ◽  
K. Gopalsamy
Keyword(s):  
Discrete Time ◽  
Continuous Time ◽  
Model Neuron ◽  
Sufficient Conditions ◽  
External Stimulus ◽  
Input Stimulus ◽  
Time System ◽  
Time Model ◽  
Discrete Time Model ◽  
Continuous Time System

We consider the dynamical characteristics of a continuous-time isolated Hopfield-type neuron subjected to an almost periodic external stimulus. The model neuron is assumed to be dissipative having finite time delays in the process of encoding the external input stimulus and recalling the encoded pattern associated with the external stimulus. By using non-autonomous Halanay-type inequalities we obtain sufficient conditions for the hetero-associative stable encoding of temporally non-uniform stimuli. A brief study of a discrete-time model derived from the continuous-time system is given. It is shown that the discrete-time model preserves the stability conditions of the continuous-time system.

On Zeros of Discrete-Time Models for Collocated Mass-Damper-Spring Systems

2004 ◽  
Vol 126 (1) ◽  
pp. 205-210 ◽  
Author(s):  
Mitsuaki Ishitobi ◽  
Shan Liang
Keyword(s):  
Discrete Time ◽  
Continuous Time ◽  
Sampling Period ◽  
Sufficient Condition ◽  
Time System ◽  
Time Model ◽  
Discrete Time Model ◽  
Mass Damper ◽  
Approximate Expressions ◽  
Continuous Time System

When a continuous-time system is discretized using the zero-order hold, there is no simple relation which shows how the zeros of the continuous-time system are transformed by sampling. In this paper, for a discrete-time model of a collocated mass-damper-spring system, the asymptotic behavior of the zeros is analyzed with respect to the sampling period and the linear approximate expressions are given. In addition, the linear approximate expressions lead to a sufficient condition for all the zeros of the discrete-time model to lie inside the unit circle for sufficiently small sampling periods. The sufficient condition is satisfied when a damping matrix is positive definite. Moreover, an example is shown to illustrate the validity of the linear approximations. Finally, a comment for a noncollocated system is presented.

MAPPING DISCRETE-TIME MODELS FOR DESCRIPTOR-SYSTEMS WITH CONSISTENT INITIAL CONDITIONS

2016 ◽  
Vol 40 (1) ◽  
pp. 59-77 ◽  
Author(s):  
Shin Kawai ◽  
Noriyuki Hori
Keyword(s):  
Discrete Time ◽  
Continuous Time ◽  
Initial Conditions ◽  
Descriptor Systems ◽  
Descriptor System ◽  
Initial Time ◽  
Design Parameters ◽  
Time Model ◽  
Discrete Time Model ◽  
Sinusoidal Input

Discretization of a regular continuous-time descriptor-system, whose initial condition is consistent with its input, is considered using a general mapping method presented in our previous paper. The proposed mapping discrete-time model is shown to be a proper discretization under the definition explained in the paper. This assures that the response of the mapping model approaches that of the continuous-time descriptor system as the sampling period approaches zero. The consistency of initial conditions for the discrete-time model is also studied and the long-standing issue of ambiguities surrounding irregularities of discrete-time responses at the initial time are clarified with a simple solution. A proper range of design parameters are investigated and their suitable choices suggested. To illustrate the use of the proposed method, a simple circuit that cannot be expressed in the ordinary state-space form is considered. Its responses to a sinusoidal input when started from the consistent and inconsistent initial conditions are simulated to show that the irregularities at the initial time can be overcome easily. The proposed technique provides a convenient simulation and design environment for handling discrete-time systems in a unified manner with consistency and ease.

DISCRETE AND CONTINUOUS TIME POPULATION MODELS, A COMPARISON CONCERNING PROLIFERATION BY FISSION

1995 ◽  
Vol 03 (02) ◽  
pp. 543-558 ◽  
Author(s):  
B.W. KOOI ◽  
M.P. BOER
Keyword(s):  
Discrete Time ◽  
Continuous Time ◽  
Matrix Theory ◽  
Dimensional Torus ◽  
Continuous Time Model ◽  
Time Model ◽  
Discrete Time Model ◽  
Fixed Part ◽  
Number Of Individuals ◽  
Insight Into

We present two approaches, discrete time and continuous time models, for individuals which propagate through binary fission. The volumes of the two daughters are a fixed part of that of the mother, not necessarily the half, and their growth rates may differ. The discrete time approach gives more insight into the results obtained with the continuous time model. We define classes in the continuous time model such that the total number of individuals in these classes at specific moments in time is equal to the unknown number in a discrete time model. Then the discrete time model is homologous to the continuous one in the sense of having the same solutions at specific moments. Population matrix theory applies when the ratio of the inter-division times of the two daughters is rational. There is inter-class convergence but no intra-class convergence. The latter feature implies that there is no convergence of the size distribution in the continuous time model either. When the ratio is irrational the continuous time model holds and there is convergence but the rate of convergence can become infinitesimally small. This phenomenon is linked with quasi-periodicity on a 2-dimensional torus.

Birth and death processes with random environments in continuous time

1981 ◽  
Vol 18 (1) ◽  
pp. 19-30 ◽  
Author(s):  
Robert Cogburn ◽  
William C. Torrez
Keyword(s):  
Discrete Time ◽  
Random Environment ◽  
Continuous Time ◽  
Death Process ◽  
Random Environments ◽  
Birth And Death Process ◽  
Time Model ◽  
Birth And Death Processes ◽  
Discrete Time Model ◽  
Extinction Probabilities

A generalization to continuous time is given for a discrete-time model of a birth and death process in a random environment. Some important properties of this process in the continuous-time setting are stated and proved including instability and extinction conditions, and when suitable absorbing barriers have been defined, methods are given for the calculation of extinction probabilities and the expected duration of the process.

Fractional-Order Calculus in Antimicrobial Resistance and Waning Vaccination

2020 ◽  
pp. 1-20
Author(s):  
E. Ahmed ◽  
Ahmed Ezzat Mohamed Matouk
Keyword(s):  
Antimicrobial Resistance ◽  
Fractional Order ◽  
Discrete Time ◽  
Local Stability ◽  
Chaotic Attractors ◽  
Time Model ◽  
Fractional Order Calculus ◽  
Discrete Time Model ◽  
Dynamical Behaviors ◽  
Numerical Tools

In this chapter, a simple model for competition between drug resistant and drug sensitive bacteria is given. So, a model of antimicrobial resistance (AMR) and waning vaccination is presented. The model's steady states are obtained. The conditions of local stability of the equilibria are also derived via the fractional Routh-Hurwitz criterion. A discretization scheme has also been applied to the proposed fractional-order model to enhance the model's adequacy and accuracy of describing natural phenomena. So, dynamical behaviors of the resulting discrete-time model are studied such as local stability, existence of Neimark-Sacker, and flip bifurcations. Furthermore, existence of chaos in the discrete-time model is proved using the theorem given by Marotto. Chaotic attractors and routes to chaos are also depicted via various numerical tools.

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