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Published in final edited form as: Biometrics. 2013 Feb 4;69(1):235–244. doi: 10.1111/j.1541-0420.2012.01826.x

1A. Model A of colonisation. The model has two strains and four states of colonisation. The states are uncolonised (0), colonised with strain 1, colonised with strain 2, and colonised with both strains (1 and 2). The model is governed by eight transition hazards, which fulfil conditions (A1) and (A2) if q_{1, 12}/q_{2, 12} = q_{0, 2}/q_{0, 1}. In the text, this model is considered for an arbitrary number of strains, separately for the vaccinated (T) and control (C) individuals. 1B. Model B of colonisation. The model has two strains and three states of colonisation. The states are uncolonised (0), colonised with strain 1, and colonised with strain 2. The model is governed by six transition hazards, which fulfil conditions (B1) and (B2) if q_{1, 2}/q_{2, 1} = q_{0, 2}/q_{0, 1}. In the aggregated model, states 0, 1 and 2 correspond to aggregated states , and (see Section 5).

Inline graphic — 1A. Model A of colonisation. The model has two strains and four states of colonisation. The states are uncolonised (0), colonised with strain 1, colonised with strain 2, and colonised with both strains (1 and 2). The model is governed by eight transition hazards, which fulfil conditions (A1) and (A2) if q_{1, 12}/q_{2, 12} = q_{0, 2}/q_{0, 1}. In the text, this model is considered for an arbitrary number of strains, separately for the vaccinated (T) and control (C) individuals. 1B. Model B of colonisation. The model has two strains and three states of colonisation. The states are uncolonised (0), colonised with strain 1, and colonised with strain 2. The model is governed by six transition hazards, which fulfil conditions (B1) and (B2) if q_{1, 2}/q_{2, 1} = q_{0, 2}/q_{0, 1}. In the aggregated model, states 0, 1 and 2 correspond to aggregated states , and (see Section 5).