Abstract
The epidemic spread of infectious diseases is ubiquitous and often has a considerable impact on public health and economic wealth. The large variability in the spatio-temporal patterns of epidemics prohibits simple interventions and requires a detailed analysis of each epidemic with respect to its infectious agent and the corresponding routes of transmission. To facilitate this analysis, we introduce a mathematical framework which links epidemic patterns to the topology and dynamics of the underlying transmission network. The evolution, both in disease prevalence and transmission network topology, is derived from a closed set of partial differential equations for infections without allowing for recovery. The predictions are in excellent agreement with complementarily conducted agent-based simulations. The capacity of this new method is demonstrated in several case studies on HIV epidemics in synthetic populations: it allows us to monitor the evolution of contact behavior among healthy and infected individuals and the contributions of different disease stages to the spreading of the epidemic. This gives both direction to and a test bed for targeted intervention strategies for epidemic control. In conclusion, this mathematical framework provides a capable toolbox for the analysis of epidemics from first principles. This allows for fast, in silico modeling - and manipulation - of epidemics and is especially powerful if complemented with adequate empirical data for parameterization.
Highlights
Despite huge efforts to improve public health, the spread of infectious diseases is still ubiquitous at the beginning of the 21st century, and there is considerable variability in epidemic patterns between locations
Because we focus on the interplay between transmission network topology and epidemics, we will restrict ourselves to diseases caused by agents that lead to either immunity or death in their host, i.e., in which infection can occur only once
It is important to assess changes in contact behavior throughout an epidemic; these may occur due to external factors, such as demographic change, or as a side effect of the epidemic itself, leading to an accumulation of individuals with risky behavior in the infected population
Summary
Despite huge efforts to improve public health, the spread of infectious diseases is still ubiquitous at the beginning of the 21st century, and there is considerable variability in epidemic patterns between locations. The recent influenza pandemic has been a global challenge, there have been differences in its timing in the northern and southern hemisphere due to seasonal effects [1,2]. Another prominent example for epidemic variability is the prevalence of sexually transmitted diseases (STDs), HIV infections. The spread of infectious diseases cannot be understood globally but understood only as the result of several local factors, such as climate and hygiene conditions, population density and structure, and cultural habits and mobility. A major remaining challenge in modern epidemiology is to link the variability of transmission networks to the corresponding emergent epidemics
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