@misc{BestehornBestehornMichelitschetal., author = {Bestehorn, Michael and Bestehorn, Michael and Michelitsch, Thomas M. and Collet, Bernard A. and Riascos, Alejandro P. and Nowakowski, Andrzej. F.}, title = {Simple model of epidemic dynamics with memory effects}, series = {Physical Review E}, volume = {105}, journal = {Physical Review E}, number = {2}, issn = {2470-0045}, doi = {10.1103/PhysRevE.105.024205}, pages = {024205-1 -- 024205-10}, abstract = {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.}, language = {en} } @article{BestehornFantzFriedrichetal., author = {Bestehorn, Michael and Fantz, M. and Friedrich, R. and Haken, H. and P{\´e}rez-Garc{\´i}a, C.}, title = {Spiral Patterns in Thermal Convection}, language = {en} } @article{BestehornFantzFriedrichetal., author = {Bestehorn, Michael and Fantz, M. and Friedrich, R. and Haken, H.}, title = {Pattern formation in rotating B{\´e}nard convection}, language = {en} } @inproceedings{VaerenberghLegrosColinetetal., author = {Vaerenbergh, S. van and Legros, J. C. and Colinet, P. and Velarde, M. G. and Bestehorn, Michael and Lebon, G. and Thess, A. and Karcher, C.}, title = {Processes With Double Diffusive Instabilities Studied in Microgravity}, series = {The 2nd European Symposium on Utilisation of the International Space Station, 16 - 18 November 1998, ESTEC, Noordwijk, The Netherlands}, booktitle = {The 2nd European Symposium on Utilisation of the International Space Station, 16 - 18 November 1998, ESTEC, Noordwijk, The Netherlands}, publisher = {ESA Publ.}, address = {Noordwijk}, isbn = {92-9092-732-1}, pages = {241 -- 248}, language = {en} } @article{BestehornFantzFriedrichetal., author = {Bestehorn, Michael and Fantz, M. and Friedrich, R. and Haken, H.}, title = {Hexagonal and Spiral Patterns of Thermal Convection}, language = {en} } @article{BestehornNeufeldFriedrichetal., author = {Bestehorn, Michael and Neufeld, M. and Friedrich, R. and Haken, H.}, title = {Pattern formation in rotating B{\´e}nard convection}, language = {en} } @article{ThieleVelardeNeufferetal., author = {Thiele, Uwe and Velarde, M. G. and Neuffer, Kai and Bestehorn, Michael and Pomeau, Y.}, title = {Sliding drops in the diffusive interface model coupled to hydrodynamics}, series = {Physical Review E}, volume = {64}, journal = {Physical Review E}, number = {4}, issn = {1550-2376}, pages = {061601}, language = {en} } @article{ThieleNeufferBestehornetal., author = {Thiele, Uwe and Neuffer, Kai and Bestehorn, Michael and Pomeau, Y. and Velarde, M. G.}, title = {Sliding drops on an inclined plane}, series = {Colloids and Surfaces A}, volume = {206}, journal = {Colloids and Surfaces A}, number = {1-3}, pages = {87 -- 104}, language = {en} } @article{MillanRodriguezPerezGarciaBestehornetal., author = {Mill{\´a}n-Rodriguez, J. and P{\´e}rez-Garc{\´i}a, C. and Bestehorn, Michael and Fantz, M. and Friedrich, R.}, title = {Pattern Formation in Convection of Rotating Fluids with Broken Vertical Symmetry}, language = {en} } @article{MillanRodriguezBestehornPerezGarciaetal., author = {Mill{\´a}n-Rodriguez, J. and Bestehorn, Michael and P{\´e}rez-Garc{\´i}a, C. and Friedrich, R. and Neufeld, M.}, title = {Defects Motion in Rotating Fluids}, language = {en} } @article{MillanRodriguezBestehornPerezGarciaetal., author = {Mill{\´a}n-Rodriguez, J. and Bestehorn, Michael and P{\´e}rez-Garc{\´i}a, C. and Neufeld, M. and Friedrich, R.}, title = {Motion of Defects in Rotating Fluids}, language = {en} } @article{BestehornNeufeldFriedrichetal., author = {Bestehorn, Michael and Neufeld, M. and Friedrich, R. and Haken, H.}, title = {Comment on Spiral pattern formation in Rayleigh-B{\´e}nard Convection}, language = {en} }