Figure 1.
Schematic representation of the host-multipathogen metapopulation system.
At the macroscopic level the system is composed by a network of subpopulations connected via communication links that allow individuals to migrate from one subpopulation to the other. Inside each subpopulation the epidemic process take place. Susceptible individuals can be infected by the slow (fast) strain and change their status to
; infected individuals enter into the recovered class
at rate
and
, for the slow and fast strain, respectively. Different epidemic waves are produced by the two strains when unfolding independently in a population, as shown by the number of new cases (incidence) over time.
Table 1.
Model variables and their corresponding values.
Figure 2.
(A) Fraction of subpopulations infected by the fast and slow strains as a function of . The quantity plotted is the median and the
confidence interval over 2000 stochastic runs. Simulations were performed on a random homogeneous network. (B) Ratio
as a function of
for both homogenous and heterogenous networks. The inter-quartile range is not displayed for the sake of visualization. In both panels the networks have average degree
. Both strains have
. Other parameters are
and
.
Figure 3.
Coexistence probability within the same patch.
is defined as the probability that within the same subpopulation both strains produce at least
of the population infected. The quantity plotted is the average and the standard deviation over 2000 runs. The parameters used for the simulations are the same as in Figure 2.
Figure 4.
Within-patch coexistence and strain-specific attack rates.
A,B,C: heatmaps showing the frequency of occurrence of a given epidemic outcome within the patches, expressed in
as obtained by numerical simulations. D,E,F: histogram of the within-patch attack rate
(in
) for the slow and fast strains. From left to right, three different mobility regimes are displayed:
in which the fast strain dominates (A,D),
corresponding to the cross-over point (B,E), and
in which the slow strain dominates (C,F).
Figure 5.
Probability of coexistence within a patch as a function of the patch connectivity .
Homogenous (A) and heterogeneous (B) cases are shown. Different traveling regimes are compared: they correspond to the scenarios in which the fast strain dominates (the highest value of considered in the two plots), the two strains coexist (intermediate value of
) and the slow strain dominates (smallest value of
). The quantity plotted is the average over 2000 runs; error bars are not displayed for the sake of visualization.
Figure 6.
Competition between strains per connectivity class in the cross-over regime.
Fraction of subpopulations infected by each strain within the degree class ,
, in the homogeneous (A) and heterogenous (B) networks. The two plots depict the behavior in the cross-over mobility regime (
in panel (A) and
in panel (B)). The quantity plotted is the average over 2000 runs; error bars are not displayed for the sake of visualization.
Figure 7.
Dependence of the cross-over diffusion rate on the epidemiological parameters.
Cross-over diffusion rate along with estimation error as a function of the reproductive number
(A) and of
(B) in the homogeneous and heterogeneous cases. The networks have average degree
. Other parameters are
,
(A) and
(B).
Figure 8.
Comparison between the numerical and theoretical cross-over diffusion rate as a function of the reproductive number
for the case of homogeneous network. Numerical results are the average over
stochastic runs, whereas theoretical values are obtained solving Eq. (9). The networks have average degree
. Other parameters are
and
.