Comparative dynamics of monovalent and bivalent vaccination for immunologically unrelated pathogens

Multivalent vaccines are designed to immunize against two or more pathogens in a single dose vaccination. A challenge for wide spread use of these vaccines is their lower protection efficacy compared to monovalent vaccines that immunize individuals against a single pathogen. We sought, for the first time, to evaluate the outcomes of bivalent and monovalent vaccines in terms of the reduction in the number of infections over time. For this evaluation, we developed epidemiological models governing the transmission dynamics of two immunologically unrelated pathogens, where immunity conferred by vaccination or natural infection of one pathogen does not provide any cross-protection against the other pathogen. We assumed that a monovalent vaccine provides full, but temporary, protection against a particular pathogen. While protecting against both pathogens requires two pathogen-specific monovalent vaccines, a single dose of the bivalent vaccine provides partial protection against both pathogens. We analyzed the two models to investigate the impact of vaccination. In addition to examining global behaviors and disease persistence of the models, we performed simulations to show the existence of a biologically feasible region for the bivalent vaccine to outperform monovalent vaccines for prevention of disease transmission using a lower number of vaccines

A spatial model for conflict incorporating within- and between-actor effects

The application of ecological models to human conflict scenarios has given rise to a number of models which describe antagonistic relationships between adversaries. Recent work demonstrates that the spatial disaggregation of such models is not only well-motivated but also gives rise to interesting dynamic behaviour, particularly with respect to the spatial distribution of resources. One feature which is largely absent from previous models, however, is the ability of an adversary to coordinate activity across its various locations. Most immediately, this corresponds to the notion of `support' - the reallocation of resources from one site to another according to need - which plays an important role in real-world conflict. In this paper, we generalise a spatially-disaggregated form of the classic Richardson model of conflict escalation by adding a cross-location interaction term for the within-adversary dynamics at each location. We explore the model analytically, giving conditions for the stability of the balanced equilibrium state. We then also carry out a number of numerical simulations which correspond to stylised real-world conflict scenarios. Potential further applications of the model, and its implications for policy, are then discussed

A monotonic relationship between the variability of the infectious period and final size in pairwise epidemic modelling

For a recently derived pairwise model of network epidemics with non-Markovian recovery, we prove that under some mild technical conditions on the distribution of the infectious periods, smaller variance in the recovery time leads to higher reproduction number, and consequently to a larger epidemic outbreak, when the mean infectious period is fixed. We discuss how this result is related to various stochastic orderings of the distributions of infectious periods. The results are illustrated by a number of explicit stochastic simulations, suggesting that their validity goes beyond regular networks

Optimal temporary vaccination strategies for epidemic outbreaks

We propose temporary vaccination strategies in the SIR disease outbreak model, where vaccination starts when the infection level reaches a threshold, and continues until susceptibles drop below a level such that the number of infected hosts is decreasing without further intervention. Costs are assigned to vaccination and disease burden, and we investigate which one of this two parameter family of VUHIA (vaccinate until herd immunity achieved) strategies gives the minimal cost. When the cost of vaccination is very small compared to the cost of disease burden, the optimal strategy is to start vaccination as early as possible and as high rate as possible. When vaccination is very expensive, the minimal cost is attained without vaccination. However, when these costs are of similar magnitudes, we uncover some counter-intuitive phenomena, namely the total cost can be a non-monotone function of the vaccination rate and the threshold value. We also show that for different basic reproduction numbers, the corresponding optimal strategies can be very different