Final-size solutions for SIRI models with vaccination
by Maria A. Gutierrez and Julia R. Gog
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This work extends the deterministic SIR epidemic model to allow reinfections of individuals in the recovered compartment. Hosts with prior immunity, elicited from vaccination or a past infection, are less susceptible to the disease. We interpret partial host immunity as either all-or-none or leaky. For both interpretations, we find final-size solutions for the cumulative number of reinfections and primary infections across a transient epidemic wave. These analytical expressions depend on the vaccination coverage of the host population, the vaccine efficacy on naive hosts, the relative susceptibility to reinfection, and the basic reproduction number (R0). If R0 is above a reinfection threshold, the leaky model has an endemic equilibrium.
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