A mechanistic underpinning for sigmoid dose-dependent infection

Sigmoidal, dose-dependent infection: theoretical & empirical justification 

It has been proposed that biodiversity loss leads to reduced interaction between environmental and human microbiotas. Theoretical models of environmentally transmitted diseases often assume that transmission is a constant process, which scales linearly with pathogen dose. Here we question the applicability of such an assumption and propose a sigmoidal form for the pathogens infectivity response. In our formulation, this response arises under two assumptions: 1) multiple invasion events are required for a successful pathogen infection and 2) the host invasion state is reversible. The first assumption reduces pathogen infection rates at low pathogen doses, while the second assumption, due to host immune function, leads to a saturating infection rate at high doses. The derived pathogen dose:infection rate -relationship was tested against an experimental data on host mortality rates across different pathogen doses. Compared to two simpler alternatives, the sigmoidal function gave a better fit to patterns in host mortality rate (process), as well as host mortality (endpoint). Combining these alternative approaches made us more confident to conclude that the proposed model for disease transmission is theoretically sound, provides a good description of the data at hand, and is likely to be useful in developing more reliable models for infectious diseases.

A schematic illustration of a potential mechanism that gives arise to a sigmoidal infection response. In this model, each invading pathogen (with rate αP) moves the host towards the state Sn, from which the host may acquire an infection (with rate γ). Before an infection is acquired, the host immune system clears the invading pathogens (with rate β). A sigmoidal rate of infection formation requires that n > 2. See more details in: A mechanistic underpinning of sigmoid dose-dependent infection.