Rumours, Epidemics, and Processes of Mass Action: Synthesis and Analysis

Mathematical and Computer Modelling

Volumn 38, Issue 11-13, 2003, Pages 1157-1167

  Dickinson, R E ^a,b   Pearce, C E M ^a  

^a UNIVERSITY OF ADELAIDE   (Australia)

^b DEFENCE SCIENCE AND TECHNOLOGY ORGANISATION   (Australia)

Author keywords

Block matrix methods; Epidemics; Kolmogorov equations; Rumours; Transient processes

Indexed keywords

EID: 0344303631     PISSN: 08957177     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0895-7177(03)90116-6     Document Type: Conference Paper

References (22)

1. A. Rapoport, Spread of information through a population with socio-structural bias: I. Assumption of transitivity, Bull. Math. Biophys. 15, 523-533, (1953).
2. A. Rapoport, Spread of information through a population with socio-structural bias: I. Various models with partial transitivity, Bull. Math. Biophys. 15, 535-546, (1953).
3. H.D. Landahl, On the spread of information with time and distance, Bull. Math. Biophys. 15, 367-381, (1953).
4. H.G. Landau and A. Rapoport, Contribution to the mathematical theory of contagion and spread of information: I. Spread through a thoroughly mixed population, Bull. Math. Biophys. 15, 173-183, (1953).
5. D.J. Daley and D.G. Kendall, Stochastic rumours, J. Inst. Math. Applic. 1, 42-55, (1965).
6. D.P. Maki and M. Thompson, Mathematical Models and Applications, Prentice-Hall, Englewood Cliffs, NJ, (1973).
7. J.C. Frauenthal, Mathematical Modeling in Epidemiology, Springer-Verlag, Heidelberg, (1980).
8. A. Sudbury, The proportion of the population never hearing a rumour, J. Appl. Prob. 22, 443-446, (1985).
9. R. Watson, On the size of a rumour, Stoch. Proc. and Applic. 27, 141-149, (1988).
10. C. Lefèvre and P. Picard, Distribution of the final extent of a rumour process, J. Appl. Prob. 31, 244-249, (1994).
11. C.E.M. Pearce, The exact solution of the general stochastic rumour, Mathl. Comput. Modelling 31 (10-12), 289-298, (2000).
12. V. Siskind, A solution of the general stochastic epidemic, Biometrika 52, 613-616, (1965).
13. J. Gani, On a partial differential equation of epidemic theory. I, Biometrika 52, 617-622, (1965).
14. th Berkeley Symp. on Math. Stat. and Prob., Volume 4, (Edited by L.M. Le Cam and J. Neyman), pp. 271-279, Univ. of Calif. Press, Berkeley, CA, (1967).
15. M.F. Neuts and J.-M. Li, An algorithmic study of S-I-R stochastic epidemic models, In Athens Conference on Applied Probability and Time Series, Volume 1, (Edited by C.C. Heyde, Yu.V. Prohorov, R. Pyke and S.T. Rachev), pp. 295-306, Springer-Verlag, Heidelberg, (1996).
16. G.K. Osei and J.W. Thompson, The supersession of one rumour by another, J. Appl. Prob. 14, 127-134, (1977).
17. Karmeshu and R.K. Pathria, Stochastic evolution of competing social groups, J. Math. Sociology 7, 47-58, (1980).
18. G.W. Allport, The Psychology of Rumor, Russell and Russell, New York, (1965).
19. E. Taylor, Strategy of Terror, Houghton Mifflin, Boston, MA, (1940).
20. C.E.M. Pearce, The determinant of a triangular-block matrix, SIAM Review 39, 519-520, (1997).
21. J. Gani, The Maki-Thompson rumour model: A detailed analysis, (preprint).
22. A. Rapoport and L.J. Rebhun, On the mathematical theory of rumour spread, Bull. Math. Biophys. 14, 375-383, (1952).