Disease transmission models with biased partnership selection Original Research Article

In multi-group epidemiological models with nonrandom mixing between people in the different groups, often artificial constraints have to be imposed in order to satisfy the balance conditions. We present and analyze simple selective mixing models governed by systems of ordinary differential equations, where the balance conditions are automatically satisfied as a natural consequence of the equations. These models can be applied in situations where biased partnership formations among people in different risk, social, economic, ethnic, or geographic groups must be accounted to accurately predict the epidemic. Because in these models the actual number of partners an individual has depends upon the distribution of the population, the threshold conditions are a sensitive function of this distribution. We formulate threshold conditions for the model and analyze the sensitivity of these conditions to different population distributions, to changes in transmission rates and to the biasing in the partnership selection. These conditions were determined by either explicitly defining a Liapunov function or by using the eigenvalues of the Jacobian matrix to calculate a reproductive number. We present numerical examples to illustrate how the reproductive number depends upon the variations in the population and transmission parameters.