A Mathematical Model for early HBV and -HDV Kinetics during Anti-HDV Treatment.

Hepatitis delta virus (HDV) is an infectious subviral agent that can only propagate in people infected with hepatitis B virus (HBV). HDV/HBV infection is considered to be the most severe form of chronic viral hepatitis. In this contribution, a mathematical model for the interplay between HDV and HBV under anti-HDV treatment is presented. Previous models were not designed to account for the observation that HBV rises when HDV declines with HDV-specific therapy. In the simple model presented here, HDV and HBV kinetics are coupled, giving rise to an improved viral kinetic model that simulates the early interplay of HDV and HBV during anti-HDV therapy.

Effects of distribution of infection rate on epidemic models.

A goal of many epidemic models is to compute the outcome of the epidemics from the observed infected early dynamics. However, often, the total number of infected individuals at the end of the epidemics is much lower than predicted from the early dynamics. This discrepancy is argued to result from human intervention or nonlinear dynamics not incorporated in standard models. We show that when variability in infection rates is included in standard susciptible-infected-susceptible (SIS) and susceptible-infected-recovered (SIR) models the total number of infected individuals in the late dynamics can be orders lower than predicted from the early dynamics. This discrepancy holds for SIS and SIR models, where the assumption that all individuals have the same sensitivity is eliminated. In contrast with network models, fixed partnerships are not assumed. We derive a moment closure scheme capturing the distribution of sensitivities. We find that the shape of the sensitivity distribution does not affect R_{0} or the number of infected individuals in the early phases of the epidemics. However, a wide distribution of sensitivities reduces the total number of removed individuals in the SIR model and the steady-state infected fraction in the SIS model. The difference between the early and late dynamics implies that in order to extrapolate the expected effect of the epidemics from the initial phase of the epidemics, the rate of change in the average infectivity should be computed. These results are supported by a comparison of the theoretical model to the Ebola epidemics and by numerical simulation.

A vaccination model for a multi-city system.

A modelling approach is used for studying the effects of population vaccination on the epidemic dynamics of a set of n cities interconnected by a complex transportation network. The model is based on a sophisticated mover-stayer formulation of inter-city population migration, upon which is included the classical SIS dynamics of disease transmission which operates within each city. Our analysis studies the stability properties of the Disease-Free Equilibrium (DFE) of the full n-city system in terms of the reproductive number R(0). Should vaccination reduce R(0) below unity, the disease will be eradicated in all n-cities. We determine the precise conditions for which this occurs, and show that disease eradication by vaccination depend on the transportation structure of the migration network in a very direct manner. Several concrete examples are presented and discussed, and some counter-intuitive results found.