Perspectives on the role of mobility, behavior, and time scales in the spread of diseases.

The dynamics, control, and evolution of communicable and vector-borne diseases are intimately connected to the joint dynamics of epidemiological, behavioral, and mobility processes that operate across multiple spatial, temporal, and organizational scales. The identification of a theoretical explanatory framework that accounts for the pattern regularity exhibited by a large number of host-parasite systems, including those sustained by host-vector epidemiological dynamics, is but one of the challenges facing the coevolving fields of computational, evolutionary, and theoretical epidemiology. Host-parasite epidemiological patterns, including epidemic outbreaks and endemic recurrent dynamics, are characteristic to well-identified regions of the world; the result of processes and constraints such as strain competition, host and vector mobility, and population structure operating over multiple scales in response to recurrent disturbances (like El Niño) and climatological and environmental perturbations over thousands of years. It is therefore important to identify and quantify the processes responsible for observed epidemiological macroscopic patterns: the result of individual interactions in changing social and ecological landscapes. In this perspective, we touch on some of the issues calling for the identification of an encompassing theoretical explanatory framework by identifying some of the limitations of existing theory, in the context of particular epidemiological systems. Fostering the reenergizing of research that aims at disentangling the role of epidemiological and socioeconomic forces on disease dynamics, better understood as complex adaptive systems, is a key aim of this perspective.

The social benefits of private infectious disease-risk mitigation.

Does society benefit from private measures to mitigate infectious disease risks? Since mitigation reduces both peak prevalence and the number of people who fall ill, the answer might appear to be yes. But mitigation also prolongs epidemics and therefore the time susceptible people engage in activities to avoid infection. These avoidance activities come at a cost-in lost production or consumption, for example. Whether private mitigation yields net social benefits depends on the social weight given to the costs of illness and illness avoidance, now and into the future. We show that, for a large class of infectious diseases, private risk mitigation is socially beneficial. However, in cases where society discounts the future at either very low or very high rates relative to private individuals, or where it places a low weight on the private cost of illness, the social cost of illness under proportionate mixing (doing nothing) may be lower than the social cost of illness under preferential mixing (avoiding infectious individuals). That is, under some circumstances, society would prefer shorter, more intense epidemics without avoidance costs over longer, less intense epidemics with avoidance costs. A sobering (although not surprising) implication of this is that poorer societies should be expected to promote less private disease-risk mitigation than richer societies.

Disease risk mitigation: the equivalence of two selective mixing strategies on aggregate contact patterns and resulting epidemic spread.

The personal choices affecting the transmission of infectious diseases include the number of contacts an individual makes, and the risk-characteristics of those contacts. We consider whether these different choices have distinct implications for the course of an epidemic. We also consider whether choosing contact mitigation (how much to mix) and affinity mitigation (with whom to mix) strategies together has different epidemiological effects than choosing each separately. We use a set of differential equation compartmental models of the spread of disease, coupled with a model of selective mixing. We assess the consequences of varying contact or affinity mitigation as a response to disease risk. We do this by comparing disease incidence and dynamics under varying contact volume, contact type, and both combined across several different disease models. Specifically, we construct a change of variables that allows one to transition from contact mitigation to affinity mitigation, and vice versa. In the absence of asymptomatic infection we find no difference in the epidemiological impacts of the two forms of disease risk mitigation. Furthermore, since models that include both mitigation strategies are underdetermined, varying both results in no outcome that could not be reached by choosing either separately. Which strategy is actually chosen then depends not on their epidemiological consequences, but on the relative cost of reducing contact volume versus altering contact type. Although there is no fundamental epidemiological difference between the two forms of mitigation, the social cost of alternative strategies can be very different. From a social perspective, therefore, whether one strategy should be promoted over another depends on economic not epidemiological factors.

SIR DYNAMICS WITH ECONOMICALLY DRIVEN CONTACT RATES.

The susceptible-infected-recovered (SIR) model has greatly evidenced epidemiology despite its apparent simplicity. Most applications of the SIR framework use a form of nonlinear incidence to describe the number of new cases per instant. We adapt theorems to analyze the stability of SIR models with a generalized nonlinear incidence structure. These theorems are then applied to the case of standard incidence and incidence resulting from adaptive behavioral response based on epidemiological-economic theory. When adaptive behavior is included in the SIR model multiple equilibria and oscillatory epidemiological dynamics can occur over a greater parameter space. Our analysis, based on the epidemiological-economic incidence, provides new insights into epidemics as complex adaptive systems, highlights important nonlinearities that lead to complex behavior, and provides mechanistic motivation for a shift away from standard incidence, and outlines important areas of research related to the complex-adaptive dynamics of epidemics.

Static behavioral effects on gonorrhea transmission dynamics in a MSM population.

An SIS/SAS model of gonorrhea transmission in a population of highly active men-having-sex-with-men (MSM) is presented in this paper to study the impact of safe behavior on the dynamics of gonorrhea prevalence. Safe behaviors may fall into two categories-prevention and self-awareness. Prevention will be modeled via consistent condom use and self-awareness via STD testing frequency. Stability conditions for the disease free equilibrium and endemic equilibrium are determined along with a complete analysis of global dynamics. The control reproductive number is used as a means for measuring the effect of changes to model parameters on the prevalence of the disease. We also find that appropriate intervention would be in the form of a multifaceted approach at overall risk reduction rather than tackling one specific control individually.

Notes from the heterogeneous: a few observations on the implications and necessity of affinity.

The problem of who is mixing with whom is of great theoretical importance in the context of heterosexual mixing. In this article, we publish for the first time, data from a study carried out in 1989 that had the goal of estimating who is mixing with whom, in heterosexually active college populations in the presence of co-factors like drinking. The gathering of these data and the challenges involved in modelling the interaction between and among heterosexually active populations of individuals are highlighted in this manuscript. The modelling is based on the assumptions that at least two processes are involved: individual affinities or preferences determine 'what we want' while mixing patterns describe 'what we get'. We revisit past results on the role of affinity/preference on observed mixing patterns in one- and two-sex mixing populations. Some new results for homosexually active populations are presented. The study of mixing is but the means to an end and consequently, we also look at the role of affinity on epidemics as filtered by observed mixing patterns. It would not be surprising to observe that highly distinct preference or mixing structures may actually lead to quite similar epidemic patterns.

The effect of static and dynamic spatially structured disturbances on a locally dispersing population.

Previous models of locally dispersing populations have shown that in the presence of spatially structured fixed habitat heterogeneity, increasing local spatial autocorrelation in habitat generally has a beneficial effect on such populations, increasing equilibrium population density. It has also been shown that with large-scale disturbance events which simultaneously affect contiguous blocks of sites, increasing spatial autocorrelation in the disturbances has a harmful effect, decreasing equilibrium population density. Here, spatial population models are developed which include both of these spatially structured exogenous influences, to determine how they interact with each other and with the endogenously generated spatial structure produced by the population dynamics. The models show that when habitat is fragmented and disturbance occurs at large spatial scales, the population cannot persist no matter how large its birth rate, an effect not seen in previous simpler models of this type. The behavior of the model is also explored when the local autocorrelation of habitat heterogeneity and disturbance events are equal, i.e. the two effects occur at the same spatial scale. When this scale parameter is very small, habitat fragmentation prevents the population from persisting because sites attempting to reproduce will drop most of their offspring on unsuitable sites; when the parameter is very large, large-scale disturbance events drive the population to extinction. Population levels reach their maximum at intermediate values of the scale parameter, and the critical values in the model show that the population will persist most easily at these intermediate scales of spatial influences. The models are investigated via spatially explicit stochastic simulations, traditional (infinite-dispersal) and improved (local-dispersal) mean-field approximations, and pair approximations.