The Influence of Cross-immunity on the Coexistence, Invasion and Evolution of Pathogen Strains

Adams, B. & Sasaki, A. ORCID: https://orcid.org/0000-0003-3582-5865 (2007). The Influence of Cross-immunity on the Coexistence, Invasion and Evolution of Pathogen Strains. IIASA Interim Report. IIASA, Laxenburg, Austria: IR-07-062

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Abstract

Several epidemic models with many co-circulating strains have shown that partial crossimmunity between otherwise identical strains of a pathogen can lead to three solutions: stable coexistence of all strains, stable coexistence of a subset of strains, coexistence of some or all strains in complex cycles. Here we step back to a three strain model to examine the mechanisms behind some of these solutions. Using a one-dimensional antigenic space, we consider a host population in which two strains are endemic and ask when it can be invaded by a third strain. If the function relating antigenic distance to cross-immunity is linear or a square-root this is always possible. If the function is parabolic it depends on the degree of antigenic similarity between strains and the basic reproductive number. We show that the differences between functional forms occur because their shape determines the importance of secondary infection. These results suggest that pathogens for which the relationship between antigenic distance and cross-immunity has a square-root form will exist as a cloud of strains without significant antigenic structuring. Conversely, pathogens for which the relationship is parabolic will exist in populations with strong antigenic structuring and the number of strains limited by the basic reproductive number. Furthermore, numerical simulation showssimulation shows that the maximum sustainable number of strains in such populations requires significant instantaneous changes in antigenic structure and cannot be achieved by a sequence of small point mutations alone.

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