Maia Martcheva

DYNAMICS OF TWO-STRAIN INFLUENZA WITH ISOLATION AND PARTIAL CROSS-IMMUNITY ∗

The time evolution of the influenza A virus is linked to a nonfixed landscape driven by interactions between hosts and competing influenza strains. Herd-immunity, cross-immunity, and age-structure are among the factors that have been shown to support strain coexistence and/or disease oscillations. In this study, we put two influenza strains under various levels of (interference) competition. We establish that cross-immunity and host isolation lead to periodic epidemic outbreaks (sustained oscillations) in this multistrain system. We compute the isolation reproductive number for each strain (

Gender-structured population modeling : mathematical methods, numerics, and simulations

\Re_i

Vaccine-induced pathogen strain replacement: what are the mechanisms?

) independently, as well as for the full system (

Vaccination strategies and backward bifurcation in an age-since-infection structured model.

\Re_q

Diseases with chronic stage in a population with varying size.

), and show that when

The role of coinfection in multidisease dynamics

\Re_q < 1

A non-autonomous multi-strain SIS epidemic model.

, both strains die out. Subthreshold coexistence driven by cross-immunity is possible even when the isolation reproductive number of one strain is below 1. Conditions that guarantee a winning type or coexistence are established in general. Oscillatory coexistence is established via Hopf bifurcation theory and confirmed via n...

A cost-based comparison of quarantine strategies for new emerging diseases

Preface 1. Historical perspective of mathematical demography 2. Gender structure and the problem of modeling marriages 3. Well-posedness of the Fredrickson-Hoppensteadt two-sex model 4. Numerical methods 5. Age profiles and exponential growth Appendix Bibliography Index.

Exponential growth in age-structured two-sex populations.

Host immune systems impose natural selection on pathogen populations, which respond by evolving different antigenic signatures. Like many evolutionary processes, pathogen evolution reflects an interaction between different levels of selection; pathogens can win in between-strain competition by taking over individual hosts (within-host level) or by infecting more hosts (population level). Vaccination, which intensifies and modifies selection by protecting hosts against one or more pathogen strains, can drive the emergence of new dominant pathogen strains—a phenomenon called vaccine-induced pathogen strain replacement. Here, we review reports of increased incidence of subdominant variants after vaccination campaigns and extend the current model for pathogen strain replacement, which assumes that pathogen strain replacement occurs only through the differential effectiveness of vaccines against different pathogen strains. Based on a recent theoretical study, we suggest a broader range of possible mechanisms, some of which allow pathogen strain replacement even when vaccines are perfect—that is, they protect all vaccinated individuals completely against all pathogen strains. We draw an analogy with ecological and evolutionary explanations for competitive dominance and coexistence that allow for tradeoffs between different competitive and life-history traits.

MODELING SEASONALITY IN AVIAN INFLUENZA H5N1

We consider models for a disease with acute and chronic infective stages, and variable infectivity and recovery rates, within the context of a vaccination campaign. Models for SIRS and SIS disease cycles exhibit backward bifurcations under certain conditions, which complicate the criteria for success of the vaccination campaign by making it possible to have stable endemic states when R(0)<1. We also show the extent to which the forms of the infectivity and recovery functions affect the possibility of backward bifurcations. SIR and SI models examined do not exhibit this behavior.