Consumer-resource coexistence as a means of reducing infectious disease

Figures & data

Table 1. Variables/parameters for the model.

Variables/parameters	Meaning	Unit
S	Density of susceptible resources	$g/m^2$
I	Density of infected resources	$g/m^2$
Y	Density of consumers	$g/m^2$
P	Density of pathogen in the environment	$g/m^2$
r	Growth rate of resources	/year
K	Carrying capacity of S resources	$g/m^2$
α	S removal by Y	/year
ρ	Half-saturation constant for S [23,45]	$g/m^2$
c	Conversion of S biomass into Y biomass	Dimensionless
σ	Reduction of Y due to other factors	/year
β	Exposure of S to P	/year
δ	P at which the force of infection is halved [12,35]	$g/m^2$
μ	Death rate of I	/year
γ	Recovery rate of I	/year

Table 2. Parameters values used for model simulation with their source (σ and onwards were estimated in order to yield reasonable model behaviour).

Parameters	Value	Unit	Source
r	0.014	/day	[16]
K	500	$g/m^2$	[16,38]
α	0.025	/day	[16]
ρ	40	$g/m^2$	[16]
c	0.75	Dimensionless	[16,38]
σ	0.0175	/day	–
δ	25	$g/m^2$	–
β	0.005r	/day	–
γ	0.800	/year	–
μ	0.002	/year	–
ν	0.0275	/year	–
ξ	0.0333	/year	–

Figure 1. Plot showing the possible long term dynamics for a fixed value of ${\mathcal{R}}_0=0.5257<1$ and various values of $C_0$ (see text for details). In each case, the disease is eradicated but as $C_0$ is increased this eradication is quicker. (a) $C_0=0.9921<1$. (b) $C_0=1.2401>1$. (c) $C_0=1.7361>1$. (d) $C_0=3.4722>1$.

Figure 2. Plot showing the possible long term dynamics for a fixed value of ${\mathcal{R}}_0=2.1026>1$ and various values of $C_0$ (see text for details). For $R_0>1$, the disease increases as expected as shown in (a) and (b). However, for greater values of $C_0$ the disease decreases (c) and if large enough can be eradicated (d). (a) $C_0=0.9921<1$. (b) $C_0=1.2401>1$. (c) $C_0=1.7361>1$. (d) $C_0=3.4722>1$.

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