The scaling of contact rates with population density for the infectious disease models

Abstract

Contact rates and patterns among individuals in a geographic area drive transmission of directly-transmitted pathogens, making it essential to understand and estimate contacts for simulation of disease dynamics. Under the uniform mixing assumption, one of two mechanisms is typically used to describe the relation between contact rate and population density: density-dependent or frequency-dependent. Based on existing evidence of population threshold and human mobility patterns, we formulated a spatial contact model to describe the appropriate form of transmission with initial growth at low density and saturation at higher density. We show that the two mechanisms are extreme cases that do not capture real population movement across all scales. Empirical data of human and wildlife diseases indicate that a nonlinear function may work better when looking at the full spectrum of densities. This estimation can be applied to large areas with population mixing in general activities. For crowds with unusually large densities (e.g., transportation terminals, stadiums, or mass gatherings), the lack of organized social contact structure deviates the physical contacts towards a special case of the spatial contact model - the dynamics of kinetic gas molecule collision. In this case, an ideal gas model with van der Waals correction fits well; existing movement observation data and the contact rate between individuals is estimated using kinetic theory. A complete picture of contact rate scaling with population density may help clarify the definition of transmission rates in heterogeneous, large-scale spatial systems.

Predictive spatial risk model of poliovirus to aid prioritization and hasten eradication in Nigeria

“…Although increased population density is thought to increase poliovirus transmission potential [51], we find no association in either portion of the model. Due to data limitations, population density was calculated at the district level, which may be a poor representation of the experienced population density on more functional scales of transmission, such as the population density immediately surrounding the household reporting a WPV case.…”

Systematic review of modelling assumptions and empirical evidence: Does parasite transmission increase nonlinearly with host density?

“…If transmission is best viewed as a nonlinear continuum from DD transmission at low host densities to FD transmission at high host densities (Antonovics et al, ; Hu et al, ; Lafferty et al, ), then most modellers either assume that they are working at just one end of the continuum or that they are working at a single point in the continuum (i.e. constant host density).…”

“…Furthermore, several parasite groups are conspicuously absent or understudied in our dataset, including sexually transmitted and vector‐transmitted parasites, macroparasites and parasites with reptile and bird hosts. And even when multiple transmission functions were compared, studies often only considered two (DD vs. FD) or three host densities, making it difficult to quantify nonlinearities, and perhaps leaving out the intermediate host densities at which nonlinearity is the most notable and important (Borremans, Reijniers, Hughes, et al, ; Hu et al, ).…”

“…This choice is often simplified into a dichotomy between the two linear, canonical transmission functions: density‐dependent transmission (hereafter DD transmission) and density‐independent or frequency‐dependent transmission (hereafter FD transmission; Figure ; also see Appendix ). However, the two linear functions should perhaps be viewed as end points on a continuum from DD transmission at relatively low host densities to FD transmission at relatively high host densities (Antonovics et al, ; Hu, Nigmatulina, & Eckhoff, ; Lafferty et al, ; Figure ). When spliced together, the resulting nonlinear transmission–density relationship might be more biologically realistic than assuming that contact rates increase infinitely with host density (DD transmission function) or assuming that contact rates never decline, even when population density is vanishingly small (FD transmission function; Antonovics et al, ).…”

Shifting Climates, Foods, and Diseases: The Human Microbiome through Evolution

“…However, these two major divisions represent only a fraction of our collective evolutionary history and its role in microbiome and human codiversification. [110,111] Furthermore, with increased agriculture and environmental manipulation, more landscapes became disease prone as they favored the reproduction of parasites (e.g., Plasmodium) and their vectors (e.g., Anopheles). First, between the divergence from our common ancestors and the Neolithic revolution, humans developed increasing reliance on tool use and cooking, increased sedentism, and massive population growth and structuring.…”