Theoretical Studies of the Effects of Heterogeneity in the Parasite Population on the Transmission Dynamics of Malaria

Sunetra Gupta, Jonathan Swinton, Roy M. Anderson

Abstract

Periodicity in malaria transmission has generally been ascribed to seasonal fluctuations in mosquito population density or spatial heterogeneity with periodic migration. In this paper we demonstrate that simple models of strain heterogeneity can generate periodic behaviour as a consequence of the interaction between parasite strains and host immunological defences. As the degree of cross-immunity between strains increases, the system moves from a regime of independent strain transmission and coexistence, through increasingly coupled behaviour, to the displacement of the strain of lower transmissibility by the strain with a higher basic reproductive rate (R$_{0}$). Cross-immunity thus serves both to bring the strains into competition, and also to couple the dynamics. We find analytical and numerical results on strain coexistence to show how the range of possible outcomes may be read as an effect of the tension between these two effects of cross-protection.

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