Qualitative Effects of Monovalent Vaccination Against Rotavirus: A Comparison of North America and South America.

Rotavirus is the most common cause of severe gastroenteritis in young children worldwide. The introduction of vaccination programs has led to a significant reduction in number of hospitalizations due to rotavirus in North and South American countries. Little work has been done, however, to examine the differential impact of vaccination as a function of strain distribution and strain-specific vaccine efficacy. We developed a two-strain epidemiological model of rotavirus transmission, and used it to examine the effects of a monovalent vaccine (Rotarix) on the qualitative behaviors of infection levels in a population. For contrast, we parameterized our model with strain distribution data from North America and from South America. In all cases, the introduction of the vaccine led to significant decreases in the prevalence of primary infection due to both strains for a decade or more, after which the overall prevalence recovers to near pre-vaccination levels. The prevalence of G1P[8] is significantly higher in North America (73 % of all rotavirus infections) compared to that in South America (34 %). Our model predicts that the introduction of Rotarix might result in major strain replacement in regions such as North America where the prevalence of G1P[8] is relatively high, due to higher efficacy of Rotarix against infection caused by G1P[8], while regions with lower prevalence of G1P[8], such as South America, are not susceptible to major strain replacement.

Synchrony, waves and ripple in spatially coupled Kuramoto oscillators with Mexican hat connectivity.

Spatiotemporal waves of synchronized activity are known to arise in oscillatory neural networks with lateral inhibitory coupling. How such patterns respond to dynamic changes in coupling strength is largely unexplored. The present study uses analysis and simulation to investigate the evolution of wave patterns when the strength of lateral inhibition is varied dynamically. Neural synchronization was modeled by a spatial ring of Kuramoto oscillators with Mexican hat lateral coupling. Broad bands of coexisting stable wave solutions were observed at all levels of inhibition. The stability of these waves was formally analyzed in both the infinite ring and the finite ring. The broad range of multi-stability predicted hysteresis in transitions between neighboring wave solutions when inhibition is slowly varied. Numerical simulation confirmed the predicted transitions when inhibition was ramped down from a high initial value. However, non-wave solutions emerged from the uniform solution when inhibition was ramped upward from zero. These solutions correspond to spatially periodic deviations of phase that we call ripple states. Numerical continuation showed that stable ripple states emerge from synchrony via a supercritical pitchfork bifurcation. The normal form of this bifurcation was derived analytically, and its predictions compared against the numerical results. Ripple states were also found to bifurcate from wave solutions, but these were locally unstable. Simulation also confirmed the existence of hysteresis and ripple states in two spatial dimensions. Our findings show that spatial synchronization patterns can remain structurally stable despite substantial changes in network connectivity.