TY - GEN A1 - Bestehorn, Michael A1 - Bestehorn, Michael A1 - Michelitsch, Thomas M. A1 - Collet, Bernard A. A1 - Riascos, Alejandro P. A1 - Nowakowski, Andrzej. F. T1 - Simple model of epidemic dynamics with memory effects T2 - Physical Review E N2 - We introduce a compartment model with memory for the dynamics of epidemic spreading in a constant population of individuals. Each individual is in one of the states S=susceptible, I=infected, or R=recovered (SIR model). In state R an individual is assumed to stay immune within a finite-time interval. In the first part, we introduce a random lifetime or duration of immunity which is drawn from a certain probability density function. Once the time of immunity is elapsed an individual makes an instantaneous transition to the susceptible state. By introducing a random duration of immunity a memory effect is introduced into the process which crucially determines the epidemic dynamics. In the second part, we investigate the influence of the memory effect on the space-time dynamics of the epidemic spreading by implementing this approach into computer simulations and employ a multiple random walker's model. If a susceptible walker meets an infectious one on the same site, then the susceptible one gets infected with a certain probability. The computer experiments allow us to identify relevant parameters for spread or extinction of an epidemic. In both parts, the finite duration of immunity causes persistent oscillations in the number of infected individuals with ongoing epidemic activity preventing the system from relaxation to a steady state solution. Such oscillatory behavior is supported by real-life observations and not captured by the classical standard SIR model. KW - Bifurcations KW - Diseases KW - Dynamics of networks KW - Patterns in complex systems KW - Nonlinear Dynamics KW - Interdisciplinary Physics KW - Biological Physics Y1 - 2022 UR - https://journals.aps.org/pre/abstract/10.1103/PhysRevE.105.024205 U6 - https://doi.org/10.1103/PhysRevE.105.024205 SN - 2470-0045 VL - 105 IS - 2 SP - 024205-1 EP - 024205-10 ER - TY - JOUR A1 - Bestehorn, Michael A1 - Fantz, M. A1 - Friedrich, R. A1 - Haken, H. A1 - Pérez-García, C. T1 - Spiral Patterns in Thermal Convection KW - 2D Order Parameter Models Y1 - 1992 ER - TY - JOUR A1 - Bestehorn, Michael A1 - Fantz, M. A1 - Friedrich, R. A1 - Haken, H. T1 - Pattern formation in rotating Bénard convection KW - 2D Order Parameter Models Y1 - 1992 ER - TY - CHAP A1 - Vaerenbergh, S. van A1 - Legros, J. C. A1 - Colinet, P. A1 - Velarde, M. G. A1 - Bestehorn, Michael A1 - Lebon, G. A1 - Thess, A. A1 - Karcher, C. T1 - Processes With Double Diffusive Instabilities Studied in Microgravity T2 - The 2nd European Symposium on Utilisation of the International Space Station, 16 - 18 November 1998, ESTEC, Noordwijk, The Netherlands Y1 - 1999 SN - 92-9092-732-1 SP - 241 EP - 248 PB - ESA Publ. CY - Noordwijk ER - TY - JOUR A1 - Bestehorn, Michael A1 - Fantz, M. A1 - Friedrich, R. A1 - Haken, H. T1 - Hexagonal and Spiral Patterns of Thermal Convection KW - 2D Order Parameter Models Y1 - 1993 ER - TY - JOUR A1 - Bestehorn, Michael A1 - Neufeld, M. A1 - Friedrich, R. A1 - Haken, H. T1 - Pattern formation in rotating Bénard convection KW - 2D Order Parameter Models Y1 - 1994 ER - TY - JOUR A1 - Thiele, Uwe A1 - Velarde, M. G. A1 - Neuffer, Kai A1 - Bestehorn, Michael A1 - Pomeau, Y. T1 - Sliding drops in the diffusive interface model coupled to hydrodynamics JF - Physical Review E Y1 - 2001 SN - 1550-2376 VL - 64 IS - 4 SP - 061601 ER - TY - JOUR A1 - Thiele, Uwe A1 - Neuffer, Kai A1 - Bestehorn, Michael A1 - Pomeau, Y. A1 - Velarde, M. G. T1 - Sliding drops on an inclined plane JF - Colloids and Surfaces A Y1 - 2002 UR - 0927-7757 VL - 206 IS - 1-3 SP - 87 EP - 104 ER - TY - JOUR A1 - Millán-Rodriguez, J. A1 - Pérez-García, C. A1 - Bestehorn, Michael A1 - Fantz, M. A1 - Friedrich, R. T1 - Pattern Formation in Convection of Rotating Fluids with Broken Vertical Symmetry Y1 - 1992 ER - TY - JOUR A1 - Millán-Rodriguez, J. A1 - Bestehorn, Michael A1 - Pérez-García, C. A1 - Friedrich, R. A1 - Neufeld, M. T1 - Defects Motion in Rotating Fluids Y1 - 1995 ER - TY - JOUR A1 - Millán-Rodriguez, J. A1 - Bestehorn, Michael A1 - Pérez-García, C. A1 - Neufeld, M. A1 - Friedrich, R. T1 - Motion of Defects in Rotating Fluids Y1 - 1994 ER - TY - JOUR A1 - Bestehorn, Michael A1 - Neufeld, M. A1 - Friedrich, R. A1 - Haken, H. T1 - Comment on Spiral pattern formation in Rayleigh-Bénard Convection Y1 - 1994 ER -