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The exact solution of the general stochastic rumour. (English) Zbl 1043.92526
Summary: A characterization is given of the complete time-dependent evolution of a general stochastic rumour which includes the two Daley-Kendall models and the Maki-Thompson model as special cases.

60K99Special processes
Full Text: DOI
[1] Dietz, K.: Epidemics and rumours: A survey. J. roy. Statist. soc. Ser. A 130, 505-528 (1967)
[2] Bartholomew, D. J.: Stochastic models for social processes. (1973) · Zbl 0278.60058
[3] Bailey, N. T. J: The mathematical theory of infectious diseases. (1975) · Zbl 0334.92024
[4] Mollison, D.: Spatial contact models for ecological and epidemic spread. J. roy. Statist. soc. Ser. B 39, 283-326 (1977) · Zbl 0374.60110
[5] Bailey, N. T. J: The mathematical theory of epidemics. (1957) · Zbl 0090.35202
[6] Frauenthal, J. C.: Mathematical modelling in epidemiology. (1980) · Zbl 0442.92021
[7] Lauwerier, H. A.: Mathematical models of epidemics. Mathematical centre tracts 138 (1981) · Zbl 0466.92022
[8] Becker, N. G.: Analysis of infectious disease data. (1989)
[9] Gabriel, J. -P; Lefèvre, C.; Picard, P.: Stochastic processes in epidemic theory. Lecture notes in biomathematics 86 (1990)
[10] Daley, D. J.; Kendall, D. G.: Stochastic rumours. J. inst. Math. applic. 1, 42-55 (1965)
[11] Siskind, V.: A solution of the general stochastic epidemic. Biometrika 52, 613-616 (1965) · Zbl 0134.37909
[12] Gani, J.: On a partial differential equation of epidemic theory I. Biometrika 52, 617-622 (1965) · Zbl 0134.38001
[13] Gani, J.: On the general stochastic epidemic. Proc. 5th Berkeley symp. On math. Stat. and prob. 4, 271-279 (1967)
[14] Rapoport, A.; Rebhun, L. J.: On the mathematical theory of rumour spread. Bull. math. Biophys. 14, 375-383 (1952)
[15] Rapoport, A.: Spread of information through a population with socio-structural bias: I. Assumption of transitivity. Bull. math. Biophys. 15, 523-533 (1953)
[16] Rapoport, A.: Spread of information through a population with socio-structural bias: I. Various models with partial transitivity. Bull. math. Biophys. 15, 535-546 (1953)
[17] Landau, H. G.; Rapoport, A.: 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)
[18] Landahl, H. D.: On the spread of information with time and distance. Bull. math. Biophys. 15, 367-381 (1953)
[19] Daley, D. J.: Concerning the spread of news in a population of individuals who never forget. Bull. math. Biophys. 29, 373-376 (1967)
[20] Barbour, A. D.: The principle of the diffusion of arbitrary constants. J. appl. Prob. 9, 519-541 (1972) · Zbl 0241.60070
[21] Watson, R.: On the size of a rumour. Stoch. proc. And applic. 27, 141-149 (1988) · Zbl 0643.60055
[22] Pittel, B.: On a daley-Kendall model of random rumours. J. appl. Prob. 27, 14-27 (1990) · Zbl 0698.60061
[23] Dunstan, R.: The rumour process. J. appl. Prob. 19, 759-766 (1982) · Zbl 0502.92020
[24] Cane, V. R.: A note on the size of epidemics and the number of people hearing a rumour. J. roy. Statist. soc. Ser. B 28, 487-490 (1966) · Zbl 0171.19101
[25] Maki, D. P.; Thompson, M.: Mathematical models and applications. (1973)
[26] Sudbury, A.: The proportion of the population never hearing a rumour. J. appl. Prob. 22, 443-446 (1985) · Zbl 0578.92025
[27] Lefèvre, C.; Picard, P.: Distribution of the final extent of a rumour process. J. appl. Prob. 31, 244-249 (1994) · Zbl 0796.60098
[28] Roughan, M.; Pope, K.: The determinant of a triangular-block matrix. SIAM review 38, 513-514 (1996)