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Dynamics of Targeted Treatment

An SIS epidemiological household model is studied to understand the dynamics of targeted treatment. The household model splits the population into households, which may, for example, represent patches within a landscape or dorms within a school. Interactions between households typically occur at a much lower rate than intra-household interactions. In an agricultural setting, households are crop fields that can be infected with insect pests. Plants will recover when insecticide is applied and the insects on them are killed. Rather than using a fixed per-capita recovery or treatment rate, an individual's treatment rate will be a function of the infection level in that individual's household. This allows for targeted treatment directed towards households with larger infections. A model is developed and a moment-closure approximation approach is used to truncate the resulting infinite system of differential equations. Numerical results from the truncated system are computed and compared to stochastic simulations. It was found that targeted treatment does not change the endemic equilibrium when the population-wide treatment rate is controlled. Surprisingly, targeted treatment decreases the amount of time it takes to reach the steady state, which could be detrimental during an epidemic.

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Issac J. Michaud, University of Maine
Samuel F. Potter, University of Arizona
David Murillo, Arizona State Univeristy
David E. Hiebeler, University of Maine
Young S. Lee, Manchester College
Tae S. Do, Kwandong University
Faina Berezovskaya, Howard University