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Published online by Cambridge University Press: 27 January 2009
This paper presents a theory of the competition of forces and the resolution of conflict over what system of government a country is to adopt. In scope it extends from the prospect of a novel system within a single state to the distribution of this system among all states; in method it considers political events as elements in a single continuous process, the culmination of which provides the resolution of the conflict. The process described in the paper — the sweep of a revolutionary ideology through resisting countries — is the analogue of the epidemic spread of a disease among a human population, a model which has been thoroughly studied.
1 Alternatively, our unit of measure could be individuals, who move from one category to another, en masse, along with the countries of which they are citizens.
2 The model is taken from Bailey, N. T. J., The Mathematical Theory of Epidemics (London: Charles Griffin, 1957)Google Scholar, chapter 2. Epidemic models appear in several works by social scientists; e.g. those of Bartholomew, J. D., Stochastic Models for Social Process (London: John Wiley, 1967)Google Scholar, Coleman, J. S., Introduction to Mathematical Sociology (London: Free Press of Glencoe, 1964)Google Scholar, and Rapoport, A., Fights, Games and Debates (Ann Arbor: University of Michigan Press, 1960)Google Scholar, chapter III.
3 In the analysis of the spread of contagious diseases through human populations, the basic model has been found to be inadequate in that it fails to depict that variations around the trend that may arise by chance. Biomathematicians therefore have devoted their efforts to developingprobabalistic descriptions of epidemic processes (Bartholomew, , Stochastic Models and M. S. Bartlett, Biomathematics: An Inaugural Lecture (Oxford: Clarendon Press, 1968)).Google Scholar The onlymodels that relax the assumptions of constant β and α are those of Gart, J. J., ‘Mathematical Analysis of an Epidemic with Two Kinds of Susceptibles’, Biometrics, 24 (1968), 557–66CrossRefGoogle ScholarPubMed, whodivides the unaffected portion of the population into two sub-portions, thouse with (constant) susceptibility β and those with (constant) susceptibility β': and of Rapoport (described by Bartholomew, Stochastic Models, chapter 8), who makes similar distinctions about the extent of mingling of different portions of the population.
4 The first formulation is incorporated in the model described by equations (1), (2a), (3) and (4a) in the appendix; the second in equations (1), (2b), (3) and (4b).
5 Carsten, F. L., The Rise of Fascism (London: B. T. Batsford, 1967)Google Scholar, and Nolte, Ernst, Three Faces of Fascism (London: Weidenfeld and Nicolson, 1965).Google Scholar