Research has shown that the arrangement of potentially contagious contacts among the individuals of a society is a determining factor of disease spread: Both the repetition and the clustering of contacts diminish the size of an outbreak compared to a random mixing model [1
]. Further, the epidemic threshold is low if the degree distribution shows a high dispersion [4
]. In contrast to the vast body of literature that exists on the importance of network structure, only little emphasis has been put on the quality
of such potentially contagious contacts, i.e. how long they last and how intensive they are. In fact, mathematical models and computer simulations of disease propagation often assume a constant per-contact transmission probability [cf. [4
], e.g.: [7
]]. This approach ignores that, for instance, a short random encounter of two persons on a public bus is less likely to transmit a certain communicable disease than a rendezvous that lasted several hours.
Treating all contacts equally may lead to an overestimation of the individual transmission probability in cases of short, non-intense contacts and an underestimation in cases of intense, prolonged contacts. Allowing for heterogeneous transmission probabilities may then affect the model behaviour in various ways (e.g., altering the shape of the epidemic curves or changing the predictions of the effectiveness of intervention measures). In particular, the valuation of certain "risk groups," such as so-called super-spreaders defined as highly connected individuals [6
], may change.
Several authors have already introduced heterogeneous transmission probabilities in their models. To do so, field data was typically analysed statistically to extract differences due to age, the susceptible individuals' immune responses, the levels of infectiousness of the infectors, and different contact situations [11
]. For instance, in their model for Ebola epidemics, Legrand et al. differentiated the infection potential of hospital, funeral, and community settings [15
], while Ferguson et al. distinguished household and non-household contacts in their model for an influenza pandemic [14
]. The disadvantage of such a posteriori
statistical models is that they become invalid when their underlying determinants (e.g., how individuals interact with other individuals) change.
Only few epidemic simulations model infection processes mechanistically (i.e., based on an a priori
model instead of purely statistical analysis) to determine the transmission probability of differing contact situations: Alexandersen et al. [16
] and Sørensen et al. [17
], for example, show that basing large scale simulation models on quantities, such as intensity and duration of an exposure to infectious material, is possible and expedient. Existing mechanistic transmission models applied in simulations of disease propagation focus almost exclusively on aerosol transmission, but do not cover transmission by droplets and physical contact ("close contact"). Hence, simple mechanistic models of close contact contagion that can be used in simulations of disease spread are needed.
This paper is intended to highlight why mechanistic models of disease transmission are needed, to provide an example of how they can be built, and to show how they differ from the often-used transmission model that assumes a constant per-contact transmission probability. The proposed mechanistic approach for including the heterogeneity of transmission probabilities into disease spread simulations concentrates exclusively on diseases that are transmitted via close contact between an infector and a susceptible individual. We build on the fundamental knowledge that the risk of disease transmission is not only a function of the infectivity of the infectious agent and the quality of the immune response but also of the host's exposure to a specific infectious agent [18
]. Particularly, we present evidence suggesting that the common assumption that highly connected individuals act as super-spreaders [6
] might be misleading.