On modelling environmentally transmitted pathogens

Abstract

Many pathogens are able to replicate or survive in abiotic environments. Disease transmission models that include environmental reservoirs and environment-to-host transmission have used a variety of functional forms and modelling frameworks without a clear connection to pathogen ecology or space and time scales. We present a conceptual framework to organize microparasites based on the role that abiotic environments play in their lifecycle. Mean-field and individual-based models for environmental transmission are analysed and compared. We show considerable divergence between both modelling approaches when conditions do not facilitate well mixing and for pathogens with fast dynamics in the environment. We conclude with recommendations for modelling environmentally transmitted pathogens based on the pathogen lifecycle and time and spatial scales of the host-pathogen system under consideration.

Keywords: environmental transmission; individual-based models; infectious diseases; mean-field models.

Figure 1.

The solutions to model (3.1) using parameter set A. The initial conditions are S₀ = 960, I₀ = 40, R₀ = 0, P₀ = 40. The susceptible, infected, recovered and pathogen are compared where Case 1 (dotted blue), Case 2 (dashed purple), Case 3 (dotted red) and Case 4 (dashed green) are plotted in each panel. (Online version in colour.)

Figure 2.

The solutions to model (3.1) using parameter set B. The initial conditions are S₀ = 960, I₀ = 40, R₀ = 0, P₀ = 40. The susceptible, infected, recovered and pathogen are compared where Case 1 (dotted blue), Case 2 (dashed purple), Case 3 (dotted red) and Case 4 (dashed green) are plotted in each panel. (Online version in colour.)

Figure 3.

Comparison between four different transmission terms implemented in an individual-based model. Simulation A uses parameter set 1 with a movement rate μ = 0.01 and homogeneous initial condition. Simulation B uses parameter set 2 with μ = 0.01 and heterogeneous initial condition. Left-hand panels compare S, I, R populations while right-hand panels compare pathogen units P. (Online version in colour.)

Figure 4.

Comparisons between ODE model and IBM for parameter set A, for a variety of movement rates, μ, and initial conditions. The dashed ODE line is shown in each panel for comparison.(Online version in colour.)

Figure 5.

Comparisons between ODE model and IBM for parameter set B, for a variety of movement rates, μ, and initial conditions. The dashed ODE line is shown in each panel for comparison. (Online version in colour.)