Human mobility networks and persistence of rapidly mutating pathogens

Rapidly mutating pathogens may be able to persist in the population and reach an endemic equilibrium by escaping hosts' acquired immunity. For such diseases, multiple biological, environmental and population-level mechanisms determine the dynamics of the outbreak, including pathogen's epidemiological traits (e.g. transmissibility, infectious period and duration of immunity), seasonality, interaction with other circulating strains and hosts' mixing and spatial fragmentation. Here, we study a susceptible-infected-recovered-susceptible model on a metapopulation where individuals are distributed in subpopulations connected via a network of mobility flows. Through extensive numerical simulations, we explore the phase space of pathogen's persistence and map the dynamical regimes of the pathogen following emergence. Our results show that spatial fragmentation and mobility play a key role in the persistence of the disease whose maximum is reached at intermediate mobility values. We describe the occurrence of different phenomena including local extinction and emergence of epidemic waves, and assess the conditions for large scale spreading. Findings are highlighted in reference to previous works and to real scenarios. Our work uncovers the crucial role of hosts' mobility on the ecological dynamics of rapidly mutating pathogens, opening the path for further studies on disease ecology in the presence of a complex and heterogeneous environment.Comment: 29 pages, 7 figures. Submitted for publicatio

Dynamical patterns of epidemic outbreaks in complex heterogeneous networks

We present a thorough inspection of the dynamical behavior of epidemic phenomena in populations with complex and heterogeneous connectivity patterns. We show that the growth of the epidemic prevalence is virtually instantaneous in all networks characterized by diverging degree fluctuations, independently of the structure of the connectivity correlation functions characterizing the population network. By means of analytical and numerical results, we show that the outbreak time evolution follows a precise hierarchical dynamics. Once reached the most highly connected hubs, the infection pervades the network in a progressive cascade across smaller degree classes. Finally, we show the influence of the initial conditions and the relevance of statistical results in single case studies concerning heterogeneous networks. The emerging theoretical framework appears of general interest in view of the recently observed abundance of natural networks with complex topological features and might provide useful insights for the development of adaptive strategies aimed at epidemic containment.Comment: 13 pages, 11 figure

Selected topics on reaction-diffusion-advection models from spatial ecology

We discuss the effects of movement and spatial heterogeneity on population dynamics via reaction-diffusion-advection models, focusing on the persistence, competition, and evolution of organisms in spatially heterogeneous environments. Topics include Lokta-Volterra competition models, river models, evolution of biased movement, phytoplankton growth, and spatial spread of epidemic disease. Open problems and conjectures are presented

Characterising two-pathogen competition in spatially structured environments

Different pathogens spreading in the same host population often generate complex co-circulation dynamics because of the many possible interactions between the pathogens and the host immune system, the host life cycle, and the space structure of the population. Here we focus on the competition between two acute infections and we address the role of host mobility and cross-immunity in shaping possible dominance/co-dominance regimes. Host mobility is modelled as a network of traveling flows connecting nodes of a metapopulation, and the two-pathogen dynamics is simulated with a stochastic mechanistic approach. Results depict a complex scenario where, according to the relation among the epidemiological parameters of the two pathogens, mobility can either be non-influential for the competition dynamics or play a critical role in selecting the dominant pathogen. The characterisation of the parameter space can be explained in terms of the trade-off between pathogen's spreading velocity and its ability to diffuse in a sparse environment. Variations in the cross-immunity level induce a transition between presence and absence of competition. The present study disentangles the role of the relevant biological and ecological factors in the competition dynamics, and provides relevant insights into the spatial ecology of infectious diseases.Comment: 30 pages, 6 figures, 1 table. Final version accepted for publication in Scientific Report

Age-structured models and optimal control in mathematical equidemiology: a survey

In this chapter we shall discuss the use of both optimal control theory and age-structured epidemic models in mathematical epidemiology. We use a very broad definition of optimal control, for example mathematical models for control by vaccination, as well as applications of optimal control theory. This is a wide area and we have had to be selective. In terms of applications a lot of the models which we present are applicable to the spread of common childhood diseases as that is an area in which age-structured models have been shown to fit data well and are most commonly applied in practice. This is because vaccination programs are often age-dependent targeting children of a given age and so they need age-structured models. The first section of this chapter discusses age-structured epidemic models including the question of optimal vaccination in them. 2 Then we move on to the optimal control in “stage-structured” (rather than age-structured) epidemic models, in which the individuals are grouped into susceptible, infected, and so on, depending on their relation to the epidemic. This gives a survey of how the ideas of optimal control theory, in particular the Maximum Principle and dynamic programming have been applied in the past to determine optimal control strategies for an epidemic, for example by immunization or removal of infected individuals. We finish this section with a few papers which apply optimal control theory to drug epidemics. We next survey some articles which give applications of optimal control to age-structured epidemic models. Much of this work concerns the existence and structure of optimal age-dependent vaccination strategies for common childhood diseases but we cover some other applications too. This is followed by a short section on spatial models used to determine optimal epidemic control policies. A brief summary and discussion conclude