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Optimal Treatment of an SIS Disease with Two Strains

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  • Telalagic, S.

Abstract

This paper explores optimal treatment of an SIS (Susceptible-Infected-Susceptible) disease that has two strains with di¤erent infectivities. When we assume that neither eradication nor full infection are possible, it is shown that there are two categories of equilibria. First, there are two continua of interior equilibria characterised by a fixed, positive total level of infection, where both strands of the disease prevail. It is hypothesised that a Skiba curve of indi¤erence lies between them. Second, there are two sets of equilibria where one strand of the disease is eradicated asymptotically. The feasibility of equilibria depends on parameter assumptions; a combination of low natural rate of recovery and large di¤erence between infectivities leaves only a small proportion of equilibria as feasible. Simulations exploring the relationship between cost and optimal policy are carried out. There exists a parameter range such that, counter-intuitively, it is optimal to allow the high-infectivity strain of the disease to prevail, while asymptotically eradicating the low-infectivity strain. Within this parameter range, there is added benefit from policy flexibility. At higher costs, simulations of the interior equilibria demonstrate the existence of a Skiba curve. The curve delineates two regions, each of which has a clear optimal policy.

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Bibliographic Info

Paper provided by Faculty of Economics, University of Cambridge in its series Cambridge Working Papers in Economics with number 1229.

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Date of creation: 30 May 2012
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Handle: RePEc:cam:camdae:1229

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Web page: http://www.econ.cam.ac.uk/index.htm

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Keywords: Epidemiological modelling; Optimal control; Simulations;

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  12. Toxvaerd, Flavio, 2010. "Recurrent Infection and Externalities in Prevention," CEPR Discussion Papers 8112, C.E.P.R. Discussion Papers.
  13. Wagener, F. O. O., 2003. "Skiba points and heteroclinic bifurcations, with applications to the shallow lake system," Journal of Economic Dynamics and Control, Elsevier, vol. 27(9), pages 1533-1561, July.
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