caa a22 4500 445330503 CHVBK 20180317142735.0 cr unu---uuuuu 170323e20110201xx s 000 0 eng 10.1007/s00285-010-0331-2 doi (NATIONALLICENCE)springer-10.1007/s00285-010-0331-2 Effective degree network disease models [Elektronische Daten] [Jennifer Lindquist, Junling Ma, P. van den Driessche, Frederick Willeboordse] An effective degree approach to modeling the spread of infectious diseases on a network is introduced and applied to a disease that confers no immunity (a Susceptible-Infectious-Susceptible model, abbreviated as SIS) and to a disease that confers permanent immunity (a Susceptible-Infectious-Recovered model, abbreviated as SIR). Each model is formulated as a large system of ordinary differential equations that keeps track of the number of susceptible and infectious neighbors of an individual. From numerical simulations, these effective degree models are found to be in excellent agreement with the corresponding stochastic processes of the network on a random graph, in that they capture the initial exponential growth rates, the endemic equilibrium of an invading disease for the SIS model, and the epidemic peak for the SIR model. For each of these effective degree models, a formula for the disease threshold condition is derived. The threshold parameter for the SIS model is shown to be larger than that derived from percolation theory for a model with the same disease and network parameters, and consequently a disease may be able to invade with lower transmission than predicted by percolation theory. For the SIR model, the threshold condition is equal to that predicted by percolation theory. Thus unlike the classical homogeneous mixing disease models, the SIS and SIR effective degree models have different disease threshold conditions. Springer-Verlag, 2010 Network nationallicence SIS disease model nationallicence SIR disease model nationallicence Basic reproduction number nationallicence Lindquist Jennifer Department of Mathematics and Statistics, University of Victoria, Victoria, BC, Canada aut Ma Junling Department of Mathematics and Statistics, University of Victoria, Victoria, BC, Canada aut van den Driessche P. Department of Mathematics and Statistics, University of Victoria, Victoria, BC, Canada aut Willeboordse Frederick Department of Physics, National University of Singapore, Singapore, Singapore aut Journal of Mathematical Biology Springer-Verlag 62/2(2011-02-01), 143-164 0303-6812 62:2<143 2011 62 285 https://doi.org/10.1007/s00285-010-0331-2 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00285-010-0331-2 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Lindquist Jennifer Department of Mathematics and Statistics, University of Victoria, Victoria, BC, Canada aut NATIONALLICENCE 700 1- Ma Junling Department of Mathematics and Statistics, University of Victoria, Victoria, BC, Canada aut NATIONALLICENCE 700 1- van den Driessche P. Department of Mathematics and Statistics, University of Victoria, Victoria, BC, Canada aut NATIONALLICENCE 700 1- Willeboordse Frederick Department of Physics, National University of Singapore, Singapore, Singapore aut NATIONALLICENCE 773 0- Journal of Mathematical Biology Springer-Verlag 62/2(2011-02-01), 143-164 0303-6812 62:2<143 2011 62 285 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer