The epidemic process as a system. The social regulators of the epidemic process

The article deals with the mechanisms of spontaneous (urbanization, the international migration of population, the anthropogenic transformation of nature) and goal-oriented regulatory action on the epidemic process. Social factors have been shown to transform into ecological ones with the subsequent transformation of information in the parasitic system and their reflection in the social subsystem as the indices of the risk of infection and its socio-economical importance. Using the processes of urbanization as an example, the present work demonstrates that the mechanism of transmission acts as a filter whose specific features are determined by a range of social factors playing the most important role in the regulation of the epidemic process on the socio-ecosystemic level of its organization.     

The epidemic process as a system. I. The structure of the epidemic process

A new epidemiological concept (socio-ecological) has been formulated on the basis of the principles of the theory of systems and the theory of information. In accordance with this concept, the epidemic process is organized on the same principle as living matter, and the stability of this process at all levels of its organization is ensured by the processes of self-regulation. The conditions of the life of human society have been shown to be organically incorporated into the structure of the epidemic process as a regulating subsystem on the socio-ecological level.     

The asymptotic speed of propagation of the deterministic non-reducible n-type epidemic

A model has been formulated in [7] to describe the spatial spread of an epidemic involving n types of individuals, when triggered by the introduction of infectives from outside. Wave solutions for such a model have been investigated in [5] and [8] and have been shown only to exist at certain speeds. This paper establishes that the asymptotic speed of propagation, as denned in Aronson and Weinberger [1, 2], of such an epidemic is in fact c₀, the minimum speed at which wave solutions exist. This extends the known result for the one-type and host-vector epidemics.     

The system of the epidemic process

An original social-ecological concept of the epidemic process has been constructed on the basis of using social ecology, systemic approach and the basic principles of cybernetics. According to this concept, the epidemic process is regarded as a biosocial, hierarchic, integral system providing for the reproduction of the species of human parasites. At a higher level of organization, the epidemic process is an epidemiological social-ecological system consisting of two interacting subsystems: the biological (epidemiological ecosystem) and the social (social and economic conditions of life of the society) subsystems where the biological subsystem plays the role of the governed object and the social acts as the internal regulator of these interactions. On the basis of this concept a rational structure of the system of epidemiological surveillance over infectious diseases has been proposed according to which each level of the structure of the epidemic process should be subject to adequate monitoring.     

Global asymptotic stability of a periodic solution to an epidemic model

In this paper a periodic delay differential equation with spatial spread is investigated. This equation can be used to model the growth of malaria which is transmitted by a mosquito. Using monotone techniques, it is shown that the following bifurcation holds: either the disease dies out or the density of infectious people tends to a spatially homogeneous, time periodic and positive solution.Research partially supported by NSF Grant MCS 810-4837     

The epidemic process in mumps infection

Manifestations of the epidemic process of a parotitis infection can be explained by the theory of the self regulation of parasitic systems. A characteristic feature of epidemic parotitis is the formation of epidemic foci in the absence of parotitis cases and without the penetration of the infective agent from the outside. The epidemic wave of parotitis infection decreases as the virulence of the infective agent attenuates due to its passage through persons gaining immunity in the course of the epidemic. The avirulent infective agent persists in the body of some immune carriers till a sufficient stratum of susceptible subjects accumulates in the chain of the agent circulation. The analysis points to the autonomous character of the epidemic process not only among the urban and rural population, but also among separate social and age groups of the population within one town or settlement. The findings evidence an independent formation of the epidemic variant of the infective agent in individual schools and preschool institutions.     

On a simple epidemic model with a heterogeneous infective population

This paper is concerned with a generalization of the simple epidemic model in which the infective population is partitioned intom classes, each of specific infectiousness. Attention is restricted, however, to the case where all the meeting rates between two individuals are equal to each other. Both deterministic and stochastic versions are examined. In either case the development in time of the epidemic process is investigated by exploiting a connection with the standard simple epidemic model. Finally, it is shown that the technique used also applies to a similar model for the spread of information.     

Analysis of a simple self-organizing process

This paper contains mathematical results relating to a recently discovered self-organizing process. In particular, an analysis of two partial processes is presented. In the first one, a set of numerical representations assumes the correct order, and in the second one the final map of the representations converges to its asymptotic form.     

A simple SIS epidemic model with a backward bifurcation

It is shown that an SIS epidemic model with a non-constant contact rate may have multiple stable equilibria, a backward bifurcation and hysteresis. The consequences for disease control are discussed. The model is based on a Volterra integral equation and allows for a distributed infective period. The analysis includes both local and global stability of equilibria.     

The mycobiota of landfill leachates in the pretreatment process in a sequencing batch reactor

The paper discusses the dynamics of the accumulation of microscopic fungi, depending on the sludge load (Bx), in activated sludge used for landfill leachate pretreatment. The propagule washout from the sludge into pretreated leachates is determined, including genera and species that may threaten environmental health. An increased accumulation of microscopic fungi in sludge flocs occurred at Bx=0.23−0.45 mg chemical oxygen demand (COD) mg⁻¹ d⁻¹. Microscopic fungi were eluted at the maximal Bx value tested of 1.64 mg COD mg⁻¹ d⁻¹. Both the activated sludge and the leachate runoff from the sequencing batch reactor (SBR) pose health risks to the environment due to the occurrence of fungi such as Aspergillus fumigatus, Purpureocillium lilacinum, Cyberlindnera jadinii (C. utilis), Geotrichum candidum and G. fragrans. Their count is sufficient to cause multi-organ infections in homeothermal animals and in humans.     

Some properties of a simple stochastic epidemic model of SIR type

We investigate the properties of a simple discrete time stochastic epidemic model. The model is Markovian of the SIR type in which the total population is constant and individuals meet a random number of other individuals at each time step. Individuals remain infectious for R time units, after which they become removed or immune. Individual transition probabilities from susceptible to diseased states are given in terms of the binomial distribution. An expression is given for the probability that any individuals beyond those initially infected become diseased. In the model with a finite recovery time R, simulations reveal large variability in both the total number of infected individuals and in the total duration of the epidemic, even when the variability in number of contacts per day is small. In the case of no recovery, R=infinity, a formal diffusion approximation is obtained for the number infected. The mean for the diffusion process can be approximated by a logistic which is more accurate for larger contact rates or faster developing epidemics. For finite R we then proceed mainly by simulation and investigate in the mean the effects of varying the parameters p (the probability of transmission), R, and the number of contacts per day per individual. A scale invariant property is noted for the size of an outbreak in relation to the total population size. Most notable are the existence of maxima in the duration of an epidemic as a function of R and the extremely large differences in the sizes of outbreaks which can occur for small changes in R. These findings have practical applications in controlling the size and duration of epidemics and hence reducing their human and economic costs.