Fig 1.
Diagram of an individual-based network model that consists of a node transition graph and a contact network.
Circles in the node transition graph represent the four compartments susceptible (S), exposed (E), infectious (I), and recovered (R) of a node (i.e., of an individual cow), and arrows between the compartments show the direction of transition for each node (cow) with rates driven by parameters β (transmission rate), δ (infectious rate), and γ (recovery rate). Circles in the contact network, in turn, represent individual cows (i.e., nodes), and black lines linking circles represent opportunities for RVFV transmission.
Table 1.
Cows in different locations in the Kabale District; this data set was derived from the UBOS Statistical Report 2012, Kabale District [24].
Fig 2.
Locations of cattle contact networks in the Kabale District; circles represent center of each location.
Circles diameters are scaled to total number of cattle in each location. Bigger size of circle represents greater numbers of cattle within a location.
Fig 3.
Overall structure of the network; dense circular groupings of black dots represent different locations.
The inset shows a close-up of two such groupings, and one possible arrangement of links within and between them. Long black lines connect some locations, representing potential movement-related connections, and thus opportunities for mosquito-mediated transmission of RVFV between cows from different locations. The inset expands a small portion of the contact network showing the dense circular masses are made up of small black circles, each of which represents 20 cows and correspond to the nodes shown in the representative contact network. Likewise, the black lines among these nodes represent possible connections within and between locations in the inset.
Fig 4.
Comparisons among fractions of infected cattle for a homogeneous network for three different values of k and lower range of β; blue dots showed the fraction of infected for k = 0.1, while red rectangles and green triangles showed the fraction of infected for k = 0.01 and 0.001 respectively.
For the same value of transmission rate, we always had more infected cattle for greater values of k (0.1) than the smaller ones (0.01 and 0.001). Therefore, increasing movement probability meant more widespread epizootic. For example, the fraction of infected cattle at β = 0,005 was ~0.399, ~0.537, and ~1 for k = 0.001, 0.01, and 0.1, respectively.
Fig 5.
Comparisons among fractions of infected cows for homogeneous network for three different values of k and upper range of β; fractions of infected for all three values of k were almost overlapping, therefore, not sensitive to the movement probability.
They reached a value very close to one, i.e., the whole network became infected when transmission rate β reached 0.01 for the three networks. Therefore, fractions of infected cows were also independent of the transmission rate.
Fig 6.
Comparisons among fractions of infected cows for heterogeneous network for three different values of k and lower range of β; for k = 0.001 and 0.01, the maximum fraction of infected cows was less than 0.5 for the highest value of transmission rate in the lower range, which meant after the simulation period half of the cows became infected.
However, for k = 0.1, the infected cows reached up to 0.8. Therefore, we needed to reduce the value of k i.e., cattle movement, to reduce the fraction of infected cows.
Fig 7.
Comparisons among fractions of infected cows for heterogeneous network for three different values of k and for upper range of β; the fractions of infected reaches towards 1 rapidly and when the value of transmission rate is 0.03, the fraction of infected become one for all three networks.
Fig 8.
Comparisons among fractions of infected cows for heterogeneous and homogenous networks for lower range of β and a) k = 0.01 and b) k = 0.1.
Fig 9.
Comparisons among fractions of infected cows for heterogeneous and homogenous networks for the upper range of β and a) k = 0.01 and b) k = 0.1.
Fig 10.
Fraction of cows in each compartment with a 95 percent confidence interval for β = 0.001 (top left), 0.005 (top right), 0.01 (bottom left), and 0.03 (bottom right) and for a homogeneous network; increasing β showed an increasing trend in the overall fractions of infected (cumulative fractions of recovered).
Fig 11.
Fraction of cows in each compartment with a 95 percent confidence interval for β = 0.001 (top left), 0.005 (top right), 0.01 (bottom left), and 0.03 (bottom right) and for heterogeneous network; increasing β showed an increasing trend in the overall fractions of recovered (cumulative fractions of infected) which reaches to almost 1 for β = 0.03.
Table 2.
Table shows maximum infected fractions of cows, peak infection time, and rate at which that maximum is attained for a homogeneous network.
Table 3.
Table shows maximum infected fractions of cows, peak infection time, and rate at which that maximum is attained for a heterogeneous network and a single infected cow in the Kabale municipality.
Fig 12.
Peak infection time with transmission rate and for outbreaks starting in location/locations with (a) greater number of cows and (b) fewer number of cows.