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Strain structure is of fundamental importance in the underlying dynamics of a number of pathogens. However, previous models have been too complex to accommodate many strains. This paper offers a solution to this problem, in the form of a simple model that is capable of capturing the dynamics of a large number of antigenic types that interact via host cross-immunity. We derive the structure of the model, which can manage the complexity of many strains by using a status-based formulation, assuming polarized immunity and cross-immunity act to reduced transmission probability. We then apply the model to address basic questions in strain dynamics, focusing particularly on the interpandemic dynamics of influenza. This model shows that strains have a tendency to “cluster.” For a long infectious period, relative to host lifetime, clusters may coexist. By contrast, a short infectious period leads to a single dominant cluster at any given time. We show how the speed of cluster replacement depends on the specificity of cross-immunity and on the underlying pathogen mutation rate.

This paper provides evidence for the involvement of immune mechanisms in conferring resistance to a spontaneous AKR leukemia. It is shown that genes in the B, J, or E subregions of the H-2 complex confer resistance to a spontaneously arisen, tissue culture-adapted AKR thymoma, BW5147. A direct correlation is demonstrated between survival to injected BW5147 cells and humoral responsiveness in various hybrids obtained from crosses of AKR mice and C57BL/10 or C3H/DiSn derived congeneic strains differing at H-2. Cellular immunity appears to play no role in resistance to the proliferation of tumor cells. It is further established that development of effective humoral immunity depends on B cells and Ly-1+, 2-, 3- helper T-cells bearing the I-Jk phenotype. These findings seem directly applicable to the spontaneous disease, and results of studies using transformed cells from an overtly leukemic AKR mouse parallel those obtained using BW1547 cells.