{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,28]],"date-time":"2025-03-28T06:00:34Z","timestamp":1743141634078,"version":"3.40.3"},"publisher-location":"Berlin, Heidelberg","reference-count":40,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783642114557"},{"type":"electronic","value":"9783642114564"}],"license":[{"start":{"date-parts":[[2011,1,1]],"date-time":"2011-01-01T00:00:00Z","timestamp":1293840000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2011,1,1]],"date-time":"2011-01-01T00:00:00Z","timestamp":1293840000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2011]]},"DOI":"10.1007\/978-3-642-11456-4_12","type":"book-chapter","created":{"date-parts":[[2011,3,28]],"date-time":"2011-03-28T12:32:26Z","timestamp":1301315546000},"page":"183-191","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Dynamics and Biological Thresholds"],"prefix":"10.1007","author":[{"given":"N. J.","family":"Burroughs","sequence":"first","affiliation":[]},{"given":"M.","family":"Ferreira","sequence":"additional","affiliation":[]},{"given":"J.","family":"Martins","sequence":"additional","affiliation":[]},{"given":"B. M. P. M.","family":"Oliveira","sequence":"additional","affiliation":[]},{"given":"Alberto A.","family":"Pinto","sequence":"additional","affiliation":[]},{"given":"N.","family":"Stollenwerk","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2011,1,20]]},"reference":[{"key":"12_CR1_12","volume-title":"The Elements of Stochastic Processes with Applications to the Natural Sciences","author":"NTJ Bailey","year":"1964","unstructured":"Bailey, N.T.J.: The Elements of Stochastic Processes with Applications to the Natural Sciences. Wiley, New York (1964)"},{"key":"12_CR2_12","doi-asserted-by":"publisher","first-page":"343","DOI":"10.1016\/S0022-5193(87)80121-2","volume":"124","author":"RJ Boer","year":"1987","unstructured":"Boer, R.J., Hogeweg, P.: Immunological discrimination between self and non-self by precursor depletion and memory accumulation. J. Theor. Biol. 124, 343 (1987)","journal-title":"J. Theor. Biol."},{"key":"12_CR3_12","volume-title":"Pinto","author":"NJ Burroughs","year":"2010","unstructured":"Burroughs, N.J., Oliveira, B.M.P.M., Pinto, A.A.: Autoimmunity arising from bystander proliferation of T cells in an immune response model. Math. Comput. Model. (2010)"},{"key":"12_CR4_12","doi-asserted-by":"publisher","first-page":"134","DOI":"10.1016\/j.jtbi.2005.11.010","volume":"241","author":"NJ Burroughs","year":"2006","unstructured":"Burroughs, N.J., Oliveira, B.M.P.M., Pinto, A.A.: Regulatory T cell adjustment of quorum growth thresholds and the control of local immune responses. J. Theor. Biol. 241, 134\u2013141 (2006)","journal-title":"J. Theor. Biol."},{"key":"12_CR5_12","unstructured":"Burroughs, N.J., Oliveira, B.M.P.M., Pinto, A.A., Ferreira, M.: A transcritical bifurcation in an immune response model. J. Differ. Eqn. Appl. (to appear)"},{"key":"12_CR6_12","unstructured":"Burroughs, N.J., Oliveira, B.M.P.M., Pinto, A.A., Ferreira, M.: Immune responses Dynamics. Math. Comput. Model (2010)"},{"key":"12_CR7_12","doi-asserted-by":"publisher","first-page":"714","DOI":"10.1016\/j.mcm.2007.06.007","volume":"47","author":"NJ Burroughs","year":"2008","unstructured":"Burroughs, N.J., Oliveira, B.M.P.M., Pinto, A.A., Sequeira, H.J.T.: Sensibility of the quorum growth thresholds controlling local immune responses. Math. Comput. Model. 47, 714\u2013725 (2008)","journal-title":"Math. Comput. Model."},{"key":"12_CR8_12","doi-asserted-by":"crossref","unstructured":"Dammer, S.M., Hinrichsen, H.: Spreading with immunization in high dimensions. J. Stat. Mech. (2004)","DOI":"10.1088\/1742-5468\/2004\/07\/P07011"},{"key":"12_CR9_12","doi-asserted-by":"crossref","unstructured":"Furtado, Glaucia C., Curotto de Lafaille, Maria A., Kutchukhidze, Nino L., Juan, J.: IInterleukin 2 signaling is required for CD4\u2009+\u2009 regulatory T cell function. J. Exp. Med. 6, 851\u2013857 (2002)","DOI":"10.1084\/jem.20020190"},{"key":"12_CR10_12","doi-asserted-by":"publisher","first-page":"2488","DOI":"10.1103\/PhysRevE.55.2488","volume":"55","author":"P Grassberger","year":"1997","unstructured":"Grassberger, P., Chat\u00e9, H., Rousseau, G.: Spreading in media with long-time memory. Phys. Rev. E 55, 2488\u20132495 (1997)","journal-title":"Phys. Rev. E"},{"key":"12_CR11_12","doi-asserted-by":"publisher","first-page":"267","DOI":"10.1016\/j.immuni.2004.07.009","volume":"21","author":"C-S Hsieh","year":"2004","unstructured":"Hsieh, C.-S., Liang, Y., Tyznik, A.J., Self, S.G., Liggitt, D., Rudensky, A.Y.: Recognition of the peripheral self by naturally arising CD25\u2009+\u2009 CD4\u2009+\u2009 T cell receptors. Immunity 21, 267\u2013277 (2004)","journal-title":"Immunity"},{"key":"12_CR12_12","doi-asserted-by":"publisher","first-page":"036114","DOI":"10.1103\/PhysRevE.70.036114","volume":"70","author":"J Joo","year":"2004","unstructured":"Joo, J., Lebowitz, J.L.: Pair approximation of the stochastic susceptible-infected-recovered-susceptible epidemic model on the hypercubic lattice. Phys. Rev. E 70, 036114 (2004)","journal-title":"Phys. Rev. E"},{"key":"12_CR13_12","doi-asserted-by":"publisher","first-page":"685","DOI":"10.2307\/3214374","volume":"26","author":"R Kryscio","year":"1989","unstructured":"Kryscio, R., Lefevre, C.: On the extinction of the S-I-S stochastic logistic epidemic. J. Appl. Prob. 26, 685\u2013694 (1989)","journal-title":"J. Appl. Prob."},{"key":"12_CR14_12","doi-asserted-by":"crossref","unstructured":"Leon, K., Faro, J., Lage, A., Carneiro, J.: Inverse correlation between the incidences of autoimmune disease and infection predicted by a model of T cell mediated tolerance. J. Autoimmun. 31\u201342 (2004)","DOI":"10.1016\/j.jaut.2003.10.002"},{"key":"12_CR15_12","doi-asserted-by":"publisher","first-page":"107","DOI":"10.1016\/S0022-5193(03)00226-1","volume":"225","author":"K Leon","year":"2003","unstructured":"Leon, K., Lage, A., Carneiro, J.: Tolerance and immunity in a mathematical model of T-cell mediated suppression. J. Theor. Biol. 225, 107\u2013126 (2003)","journal-title":"J. Theor. Biol."},{"key":"12_CR16_12","doi-asserted-by":"publisher","first-page":"231","DOI":"10.1006\/jtbi.2000.2169","volume":"207","author":"K Leon","year":"2000","unstructured":"Leon, K., Perez, R., Lage, A., Carneiro, J.: Modelling T-cell-mediated suppression dependent on interactions in multicellular conjugates. J. Theor. Biol. 207, 231\u2013254 (2000)","journal-title":"J. Theor. Biol."},{"key":"12_CR17_12","unstructured":"Martins, J., Aguiar, M., Pinto, A.A., Stollenwerk, N.: On the series expansion of the spatial SIS evolution operator. J. Differ. Eqn. Appl. 1\u201313 (2010)"},{"issue":"5","key":"12_CR18_12","doi-asserted-by":"publisher","first-page":"479","DOI":"10.1080\/17513750802601058","volume":"3","author":"J Martins","year":"2009","unstructured":"Martins, J., Pinto, A.A., Stollenwerk, N.: A scaling analysis in the SIRI epidemiological model. J. Biol. Dyn. 3(5), 479\u2013496 (2009)","journal-title":"J. Biol. Dyn."},{"key":"12_CR19_12","unstructured":"Martins, J., Pinto, A.A., Stollenwerk, N.: Stationarity in moment closure and quasi-stationarity of the SIS model. (submitted)"},{"key":"12_CR20_12","doi-asserted-by":"crossref","first-page":"2480","DOI":"10.1002\/eji.200425274","volume":"34","author":"S. Maurus de la Rosa","year":"2004","unstructured":"Maurus de la Rosa, S., Rutz, S., Dorninger, H., Scheffold, A.: Interleukin-2 is essential for CD4\u2009+\u2009CD25\u2009+\u2009 regulatory T cells function. Eur. J. Immunol. 34, 2480\u20132488 (2004)","journal-title":"Eur. J. Immunol."},{"key":"12_CR21_12","unstructured":"Mudur, G.S.: Maths for movies, medicine & markets. The Telegraph Calcutta, India, 20\/09\/2010"},{"key":"12_CR22_12","doi-asserted-by":"publisher","first-page":"21","DOI":"10.1016\/S0025-5564(98)10059-7","volume":"156","author":"I N\u00e5sell","year":"1999","unstructured":"N\u00e5sell, I.: On the quasi-stationary distribution of the stochastic logistic epidemic. Math. Biosci. 156, 21\u201340 (1999)","journal-title":"Math. Biosci."},{"key":"12_CR23_12","doi-asserted-by":"publisher","first-page":"895","DOI":"10.2307\/1428186","volume":"28","author":"I N\u00e5sell","year":"1996","unstructured":"N\u00e5sell, I.: The quasi-stationary distribution of the closed endemic SIS model. Adv. Appl. Prob. 28, 895\u2013932 (1996)","journal-title":"Adv. Appl. Prob."},{"key":"12_CR24_12","doi-asserted-by":"crossref","unstructured":"Nagata, S.: Fas ligand-induced apoptosis. Annu. Rev. Genet. 29\u201355 (1999)","DOI":"10.1146\/annurev.genet.33.1.29"},{"key":"12_CR25_12","doi-asserted-by":"crossref","unstructured":"Pinto, A.A., Aguiar, M., Martins, J., Stollenwerk, N.: Dynamics of Epidemiological Models. Acta Biotheor. 1\u201315 (2010)","DOI":"10.1007\/s10441-010-9116-7"},{"key":"12_CR26_12","unstructured":"Pinto, A.A., Burroughs, N.J., Ferreira, M., Oliveira, B.M.P.M.: Dynamics of Immunological Models. Acta Biotheor. (to appear)"},{"key":"12_CR27_12","doi-asserted-by":"crossref","unstructured":"Pinto, A.A., Martins, J., Stollenwerk, N.: The higher moments dynamic on SIS model. Numerical Analysis and Applied Mathematics. In: Simos, T.E., et al. (eds.) AIP Conference Proceedings, vol.\u20091168, pp.\u20091527\u20131530 (2009)","DOI":"10.1063\/1.3241390"},{"key":"12_CR28_12","volume-title":"Advanced Ecological Theory, pp. 100\u2013142","author":"DA Rand","year":"1999","unstructured":"Rand, D.A.: Correlation equations and pair approximations for spatial ecologies. In: Jacqueline McGlade (ed.) Advanced Ecological Theory, pp.\u2009100\u2013142. Blackwell Science, Oxford, London, Edinburgh, Paris (1999)"},{"key":"12_CR29_12","doi-asserted-by":"crossref","unstructured":"Rogers, Paul R., Dubey, Caroline, Swain and Susan L.: Qualitative changes accompany memory t cell generation: faster, more effective responses at lower doses of antigen. J. Immunol. 164, 2338\u20132346 (2000)","DOI":"10.4049\/jimmunol.164.5.2338"},{"key":"12_CR30_12","doi-asserted-by":"publisher","first-page":"531","DOI":"10.1146\/annurev.immunol.21.120601.141122","volume":"22","author":"S Sakaguchi","year":"2004","unstructured":"Sakaguchi, S.: Naturally arising CD4\u2009+\u2009 regulatory T cells for immunological self-tolerance and negative control of immune responses. Annu. Rev. Immunol. 22, 531\u2013562 (2004)","journal-title":"Annu. Rev. Immunol."},{"key":"12_CR31_12","doi-asserted-by":"publisher","first-page":"58","DOI":"10.1034\/j.1600-065X.2001.1820104.x","volume":"182","author":"EM Shevach","year":"2001","unstructured":"Shevach, E.M., McHugh, R.S., Piccirillo, C.A., Thornton, A.M.: Control of T-cell activation by CD4(\u2009+\u2009) CD25(\u2009+\u2009) suppressor T cells. Immunol. Rev. 182, 58\u201367 (2001)","journal-title":"Immunol. Rev."},{"key":"12_CR32_12","doi-asserted-by":"publisher","first-page":"426","DOI":"10.1038\/80868","volume":"1","author":"KS Schluns","year":"2000","unstructured":"Schluns, K.S., Kieper, W.C., Jameson, S.C., Lefrancois, L.: Interleukin-7 mediates the homeostasis of naive and memory CD8 T cells. Nat. Immunol. 1, 426\u2013432 (2000)","journal-title":"Nat. Immunol."},{"key":"12_CR33_12","first-page":"1","volume":"1","author":"N Stollenwerk","year":"2008","unstructured":"Stollenwerk, N., Aguiar, M.: The SIRI stochastic model with creation and annihilation operators. Quant. Methods 1, 1\u201310 (2008)","journal-title":"Quant. Methods"},{"key":"12_CR34_12","doi-asserted-by":"publisher","first-page":"379","DOI":"10.1016\/j.physleta.2007.06.040","volume":"371","author":"N Stollenwerk","year":"2007","unstructured":"Stollenwerk, N., Martins, J., Pinto, A.A.: The phase transition lines in pair approximation for the basic reinfection model SIRI. Phys. Lett. A 371, 379\u2013388 (2007)","journal-title":"Phys. Lett. A"},{"key":"12_CR35_12","doi-asserted-by":"crossref","unstructured":"Stollenwerk, N., van Noort, S., Martins, J., Aguiar, M., Hilker, F., Pinto, A.A., Gomes, G.: A spatially stochastic epidemic model with partial immunization shows in mean field approximation the reinfection threshold. J. Biol. Dyn. 1\u201317 (2010)","DOI":"10.1080\/17513758.2010.487159"},{"key":"12_CR36_12","doi-asserted-by":"crossref","first-page":"4285","DOI":"10.4049\/jimmunol.172.7.4285","volume":"172","author":"C Tanchot","year":"2004","unstructured":"Tanchot, C., Vasseur, F., Pontoux, C., Garcia, C., Sarukhan, A.: Immune regulation by self-reactive T cells is antigen specific. J. Immunol. 172, 4285\u20134291 (2004)","journal-title":"J. Immunol."},{"key":"12_CR37_12","doi-asserted-by":"crossref","first-page":"6519","DOI":"10.4049\/jimmunol.172.11.6519","volume":"172","author":"AM Thornton","year":"2004","unstructured":"Thornton, A.M., Donovan, E.E., Piccirillo, C.A., Shevach, E.M.: Cutting edge: IL-2 is critically required for the in vitro activation of CD4(\u2009+\u2009)CD25(\u2009+\u2009) T cell suppressor function. J. Immunol. 172, 6519\u20136523 (2004)","journal-title":"J. Immunol."},{"key":"12_CR38_12","doi-asserted-by":"publisher","first-page":"287","DOI":"10.1084\/jem.188.2.287","volume":"188","author":"AM Thornton","year":"1998","unstructured":"Thornton, A.M., Shevach, E.M.: CD4\u2009+\u2009CD25\u2009+\u2009 immunoregulatory T cells suppress polyclonal T cell activation in vitro by inhibiting interleukine 2 production. J. Exp. Med. 188, 287\u2013296 (1998)","journal-title":"J. Exp. Med."},{"key":"12_CR39_12","doi-asserted-by":"crossref","first-page":"183","DOI":"10.4049\/jimmunol.164.1.183","volume":"164","author":"AM Thornton","year":"2000","unstructured":"Thornton, A.M., Shevach, E.M.: Suppressor effector function of CD4\u2009+\u2009CD25\u2009+\u2009 immunoregulatory T cells is antigen nonspecific. J. Immunol. 164, 183\u2013190 (2000)","journal-title":"J. Immunol."},{"key":"12_CR40_12","volume-title":"Stochastic processes in physics and chemistry","author":"NG van Kampen","year":"1981","unstructured":"van Kampen, N.G.: Stochastic processes in physics and chemistry. North-Holland, Amsterdam (1981)"}],"container-title":["Springer Proceedings in Mathematics","Dynamics, Games and Science I"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-642-11456-4_12","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,1,27]],"date-time":"2023-01-27T21:40:45Z","timestamp":1674855645000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-642-11456-4_12"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011]]},"ISBN":["9783642114557","9783642114564"],"references-count":40,"URL":"https:\/\/doi.org\/10.1007\/978-3-642-11456-4_12","relation":{},"ISSN":["2190-5614","2190-5622"],"issn-type":[{"type":"print","value":"2190-5614"},{"type":"electronic","value":"2190-5622"}],"subject":[],"published":{"date-parts":[[2011]]},"assertion":[{"value":"20 January 2011","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}}]}}