Date: Tue, August 1, 17:00-
Place: Room Dw601, D Block, IIS, The University of Tokyo
Invited Speaker: Dr. Ben Adams (Kyushu University)

1. Phase structure in resonant solutions of a two strain SIR model

In seasonally forced SIR models subharmonic resonance may result in  
stable, deterministic solutions in which the epidemic period is  an  
integer multiple of the forcing period.  For models with two pathogen  
strains it is known that immunological cross-reaction affects the  
resonance period. This talk examines how it affects the phase  
relationship between epidemics of each strain. The solutions that  
occur at different intensities of  cross-reaction are classified.  
Solutions with both epidemics perfectly in phase occur over fairly  
wide ranges of cross-reaction intensity. Solutions with out of phase  
epidemics only occur for narrow ranges. To explain this a heuristic  
assessment of the stability restrictions for different solution  
structures is made. This indicates that in phase structures moderate  
the impact of changes in cross-reaction intensity while out of phase  
structures amplify it. Implications of the model for RSV and dengue  
will be discussed.

2. The influence of cross-immunity on the coexistence, invasion and  
evolution of pathogen strains

Several epidemic models with many co-circulating strains show that  
partial cross-immunity between otherwise identical strains of a  
pathogen can lead to three solutions: all strains stably coexisting,  
a subset of strains stably coexisting, all strains coexisting in  
complex cycles. This talk takes a step back to a three strain model  
to examine the mechanisms behind some of these solutions. The  
conditions under which a host population with two endemic strains can  
be invaded by a third strain are examined. The shape of the function  
relating antigenic distance to cross-immunity is important because it  
affects the significance of secondary infection. The basic  
reproductive number is important because it affects the size of the  
tertiary susceptible population. In agreement with the many-strain  
models this predicts that, depending on the shape of the cross- 
immunity function and the basic reproductive number, a pathogen will  
exist as a cloud of strains with no structure in antigenic space or  
as a small number of strains with strong structure in antigenic space.