Memory effects on epidemic evolution: The susceptible-infected-recovered epidemic model

Abstract

Memory has a great impact on the evolution of every process related to human societies. Among them, the evolution of an epidemic is directly related to the individuals' experiences. Indeed, any real epidemic process is clearly sustained by a non-Markovian dynamics: memory effects play an essential role in the spreading of diseases. Including memory effects in the susceptible-infected-recovered (SIR) epidemic model seems very appropriate for such an investigation. Thus, the memory prone SIR model dynamics is investigated using fractional derivatives. The decay of long-range memory, taken as a power-law function, is directly controlled by the order of the fractional derivatives in the corresponding nonlinear fractional differential evolution equations. Here we assume "fully mixed" approximation and show that the epidemic threshold is shifted to higher values than those for the memoryless system, depending on this memory "length" decay exponent. We also consider the SIR model on structured networks and study the effect of topology on threshold points in a non-Markovian dynamics. Furthermore, the lack of access to the precise information about the initial conditions or the past events plays a very relevant role in the correct estimation or prediction of the epidemic evolution. Such a "constraint" is analyzed and discussed.

Dynamical phase diagrams of a love capacity constrained prey–predator model

“…In order to achieve a deeper understanding it can be fruitful to reconsider these constraints in future research. It seems that it would be useful also to think about the evolution of love under "external fields", and about the dynamics of the system over time, allowing for memory effects [16][17][18].…”

Analysis of Fractional Order Mathematical Model of Hematopoietic Stem Cell Gene-Based Therapy

“…The distance of memory effect indicates the history of disease spread. Thus, memory effects on the spread of an infectious disease can be investigated using fractional derivatives [8][9][10][11][12][13].…”

A Fractional-Order Model for HIV Dynamics in a Two-Sex Population

“…Thus, memory effects on the spread of infectious diseases can be investigated using fractional derivatives. Fractional derivatives have been used in the literature to observe the effect of memory on a system dynamics by replacing the ordinary derivative order with the fractional derivative order [12][13][14][15]. Sardar et al [13] formulated the dengue model with memory in the transmission process by using fractional differential operator and order of the fractional derivative as an index of memory.…”

“…They also performed a local stability analysis on the fractional-order framework of HIV disease spread and bifurcation behavior of the system. In 2017, Saeedian et al [14] studied the evolution of the SIR epidemic model, considering memory effects. Using the fractional calculus technique, the authors in [14] show that the dynamics of such a system depend on the strength of memory effects, controlled by the order of fractional derivatives.…”

“…In 2017, Saeedian et al [14] studied the evolution of the SIR epidemic model, considering memory effects. Using the fractional calculus technique, the authors in [14] show that the dynamics of such a system depend on the strength of memory effects, controlled by the order of fractional derivatives. In 2017, Pinto and Carvalho [15] derived a fractional-order model for the dynamics of the coinfection of HIV and TB in the presence of TB resistant strains.…”