Fig 1.
Schematic representation of the metacommunity model.
Variables and parameters are defined in Table 1. On the right, a simplistic illustration of the river metacommunity model including 25 different habitat patches represented by grey disks of different sizes, the triangle area corresponds to the river delta and the light grey depicts the downstream area for which an effect is sought. On the left, local population interactions and organism dispersal among habitat patches. The blue lines correspond to the main river and tributaries, and constitutes connectivity in the metacommunity system. F: local freshwater fish subpopulation in patch i; A: local aquatic macroinvertebrate subpopulation in patch i; Bo: local free-living bacteria subpopulation in patch i. The black arrows represent the saprophytic process through decaying organic matter recycling for both fish and aquatic macroinvertebrates. The red arrows describe bacterial adhesion on surface of corresponding living biomass, i.e., fish and macroinvertebrate. The blue arrows show the dispersal of organic biomass and bacteria.
Table 1.
Meaning of the variables and parameters used in the mathematical model.
Fig 2.
Illustration of different areas favorable for the development of Mycobacterium ulcerans, responsible for causing Buruli ulcer, and representative of local patches or subcommunities in the mathematical model developed in this paper.
Upper left: lower river area close to the Mana river, French Guiana, South America (photo credit: J-FG, 2021); lower left: upper area of the Sinnamary river, French Guiana (photo credit: MEB, 2021); upper right: middle area of the Nyong river, central Cameroon, Africa (photo credit: J-FG, 2014); lower right: a small stream habitat in Benin, western Africa (photo credit: MEB, 2016). All these sites harbor a diverse community of species, including free-living mycobacteria, freshwater fish and macroinvertebrate species, fish-associated mycobacteria and macroinvertebrate-associated mycobacteria. The different patches from a same catchment area can be more or less connected to each other, depending on geographical distance, according to the schematic illustration in Fig 1.
Fig 3.
Time-dependence of biomass and free-living bacteria reproduction rates, and of free-living bacteria migration rate.
(A) The blue dashed line represents the overall biomass reproduction rate, while the purple line represents the free-living bacteria reproduction rate. (B) The green line represents the free-living bacteria migration rate. Note that the y scales are different for the two subfigures.
Fig 4.
Red curves represent the concentration of free-living bacteria provided by the primary source upstream to the lower catchment area. Blue curves represent the concentration of free-living bacteria provided by both primary and secondary sources to the lower catchment area. (A) saprophytic reproduction rate from dead fish σF = 2 and saprophytic reproduction rate from dead macroinvertebrate σA = 4. (B) σF = 2 and σA = 2.
Fig 5.
Relative sensitivity to biomass-related parameters.
Panel (A) represents the relative contribution of fish and macroinvertebrate biomass types; the blue curve shows the dynamics when both biomass types are present, the red curve is that with absence of fish and that in cyan the dynamics observed in absence of macroinvertebrates. Parameters for illustration are: σA = 2 and σF = 4. Panel (B) illustrates the effect of reduction by 10% of the bacilli attachment rates on macroinvertebrate ξ (purple curve), panel (C) the effect of the same reduction by 10% on macroinvertebrate-associated bacilli growth rates θ (brown curve), and panel (D) the effect of the same reduction by 10% on bacilli release rate (saprophytism) from macroinvertebrate death σA (green curve), on the abundance of the lower catchment area free-living bacteria. In each subfigure, the blue curve shows the dynamics given with initial values.
Table 2.
Comparison of biomass influence on the average annual concentration of free-living bacilli in lower catchment area for different saprophytic rates.
Percentage values give the reduction of bacilli abundance.