Analysis of the spread of COVID-19 in Morocco based on a SEIR epidemic model

Abstract Fractional calculus has been widely used in mathematical modeling of evolutionary systems with memory effect on dynamics. The main interest of this work is, through a statistical approach, to attest how the hysteresis phenomenon, which describes the memory effect present in biological systems, can be treated by fractional calculus, and to analyze the contribution of the historical values of a function in the evaluation of fractional operators according their order. In order to illustrate the efficiency of this non-integer order calculus, we consider the SIR (Susceptible-Infected-Recovered) compartmental model which is widely used in epidemiology. We employ SIR models to model the dynamics, with and without memory, of the spread of Covid-19 in some countries.

Download Full-text

The Memory Effect on Fractional Calculus: An Application in the Spread of Covid-19

10.21203/rs.3.rs-41084/v3 ◽

2021 ◽

Author(s):

Laécio Carvalho de Barros ◽

Michele Martins Lopes ◽

Francielle Santo Pedro Simões ◽

Estevão Esmi ◽

José Paulo Carvalho dos Santos ◽

...

Keyword(s):

Mathematical Modeling ◽

Fractional Calculus ◽

Memory Effect ◽

Compartmental Model ◽

Statistical Approach ◽

Hysteresis Phenomenon ◽

Fractional Operators ◽

Main Interest ◽

Systems With Memory ◽

With Memory

Abstract Fractional calculus has been widely used in mathematical modeling of evolutionary systems with memory effect on dynamics. The main interest of this work is to attest, through a statistical approach, how the hysteresis phenomenon, which describes a type of memory effect present in biological systems, can be treated by fractional calculus. We also analyse the contribution of the historical values of a function in the evaluation of fractional operators according to their order. In order to illustrate the efficiency of this non-integer order calculus, we consider the SIR (Susceptible-Infected-Recovered) compartmental model which is widely used in epidemiology. We employ this compartmental model to study the dynamics of the spread of Covid-19 in some countries, one version with memory and one without memory.

Download Full-text

The Memory Effect on Fractional Calculus: An Application in the Spread of Covid-19

10.21203/rs.3.rs-41084/v2 ◽

2021 ◽

Author(s):

Laécio Carvalho de Barros ◽

Michele Martins Lopes ◽

Francielle Santo Pedro Simões ◽

Estevão Esmi ◽

José Paulo Carvalho dos Santos ◽

...

Keyword(s):

Mathematical Modeling ◽

Fractional Calculus ◽

Memory Effect ◽

Compartmental Model ◽

Statistical Approach ◽

Hysteresis Phenomenon ◽

Fractional Operators ◽

Main Interest ◽

Systems With Memory ◽

With Memory

Abstract Fractional calculus has been widely used in mathematical modeling of evolutionary systems with memory effect on dynamics. The main interest of this work is to attest, through a statistical approach, how the hysteresis phenomenon, which describes a type of memory effect present in biological systems, can be treated by fractional calculus. We also analyse the contribution of the historical values of a function in the evaluation of fractional operators according to their order. In order to illustrate the efficiency of this non-integer order calculus, we consider the SIR (Susceptible-Infected-Recovered) compartmental model which is widely used in epidemiology. We employ this compartmental model to study the dynamics of the spread of Covid-19 in some countries, one version with memory and one without memory.

Download Full-text

Fractional Linear Systems with Memory Deficiency and Their State-Space Integer-Order Approximation

Lecture Notes in Electrical Engineering - Non-Integer Order Calculus and its Applications ◽

10.1007/978-3-319-78458-8_15 ◽

2018 ◽

pp. 164-179 ◽

Cited By ~ 1

Author(s):

Stefan Domek

Keyword(s):

State Space ◽

Linear Systems ◽

Order Approximation ◽

Integer Order ◽

Systems With Memory ◽

With Memory

Download Full-text

Hydrodynamic Memory Effect on Stability, Bifurcation, and Chaos of Two-Point Mooring Systems

Journal of Ship Research ◽

10.5957/jsr.1997.41.1.26 ◽

1997 ◽

Vol 41 (01) ◽

pp. 26-44

Author(s):

Jin-Sug Chung ◽

Michael M. Bernitsas

Keyword(s):

Memory Effect ◽

Design Parameters ◽

Wave Loads ◽

Mooring Lines ◽

Stability Boundaries ◽

The Stability ◽

Systems With Memory ◽

Hydrodynamic Wave ◽

Nonlinear Elastic ◽

With Memory

The stability properties of two-point mooring systems governed by their slow horizontal motions are studied theoretically. The often-neglected memory effect due to hydrodynamic wave loads change—in some cases critically—the stability boundaries in the system design space. The third-order maneuvering equations and a nonlinear elastic spring model are used to describe the dynamics of the moored vessel and the mooring lines, respectively. The resulting model accurately represents a two-point mooring system and can be used for stability analysis in the sense of Lyapunov. The stability charts of mooring systems with memory effects exhibit considerable differences from systems without memory in local regions of bifurcation diagrams. Further, the pattern of these changes of stability boundaries varies with the hydrodynamic properties of the moored vessel and/or the environmental conditions. The findings of this study suggest that the number of influencing design parameters can be much more than the present stability theory of dynamical systems can handle. They prove, however, that neglecting the memory effect may result in selecting unsafe configurations of two-point mooring systems.

Download Full-text

Dynamic Game and Pricing for Data Sponsored 5G Systems With Memory Effect

IEEE Journal on Selected Areas in Communications ◽

10.1109/jsac.2020.2971811 ◽

2020 ◽

Vol 38 (4) ◽

pp. 750-765 ◽

Cited By ~ 1

Author(s):

Shaohan Feng ◽

Dusit Niyato ◽

Xiao Lu ◽

Ping Wang ◽

Dong In Kim

Keyword(s):

Memory Effect ◽

Dynamic Game ◽

5G Systems ◽

Systems With Memory ◽

With Memory

Download Full-text

Fractional Langevin Equation in Quantum Systems with Memory Effect

Applied Mathematics ◽

10.4236/am.2014.512167 ◽

2014 ◽

Vol 05 (12) ◽

pp. 1741-1749 ◽

Cited By ~ 3

Author(s):

Jing-Nuo Wu ◽

Hsin-Chien Huang ◽

Szu-Cheng Cheng ◽

Wen-Feng Hsieh

Keyword(s):

Memory Effect ◽

Langevin Equation ◽

Quantum Systems ◽

Fractional Langevin Equation ◽

Systems With Memory ◽

With Memory

Download Full-text

REVIEW OF SOME PROMISING FRACTIONAL PHYSICAL MODELS

International Journal of Modern Physics B ◽

10.1142/s0217979213300053 ◽

2013 ◽

Vol 27 (09) ◽

pp. 1330005 ◽

Cited By ~ 75

Author(s):

VASILY E. TARASOV

Keyword(s):

Fractional Calculus ◽

Power Law ◽

Particle Interaction ◽

Discrete Systems ◽

Physical Models ◽

Long Term Memory ◽

Fractional Dynamics ◽

Fractal Media ◽

Systems With Memory ◽

With Memory

Fractional dynamics is a field of study in physics and mechanics investigating the behavior of objects and systems that are characterized by power-law nonlocality, power-law long-term memory or fractal properties by using integrations and differentiation of non-integer orders, i.e., by methods in the fractional calculus. This paper is a review of physical models that look very promising for future development of fractional dynamics. We suggest a short introduction to fractional calculus as a theory of integration and differentiation of noninteger order. Some applications of integro-differentiations of fractional orders in physics are discussed. Models of discrete systems with memory, lattice with long-range inter-particle interaction, dynamics of fractal media are presented. Quantum analogs of fractional derivatives and model of open nano-system systems with memory are also discussed.

Download Full-text