Figure 1.
Schematic representation of the malaria model.
Horizontal solid lines denote transitions between epidemiological states, and dashed lines represent transmission of infection between human hosts and mosquito vectors. Dotted lines denote vectors feeding on livestock. The vector population consists of adult female anopheline mosquitoes.
Table 1.
Parameter values for modelling the effects of untreated livestock on malaria.
Table 2.
Parameter values for modelling the effects of insecticide-treated livestock on malaria.
Figure 2.
Temporal effect of introducing livestock in a setting with endemic malaria.
Effect of introducing livestock in a setting where only humans were present, when: Nv remains constant (black line), and when Nv increases until reaching a maximum, which depends on the carrying capacity, K (increasing from K = 5,000 (green) to 100,000 (red)). Nv(0) = 1000, Nh = 100 and Al = 0.5: the availability of livestock to vectors is the same as that of humans; = 0.25 (1 head of livestock per 4 persons). To achieve the same initial equilibrium Nv (and Ih) for various K values, the vector recruitment rate in the absence of density-dependence constraints was set to vary accordingly:
. Other parameters are as in Table 1.
Figure 3.
Effect of altering the relative livestock to human density, for different vector density scenarios, at the new endemic equilibrium.
Comparing a scenario where the availability of livestock to vectors is the same as that of humans (left, Al = 0.5) versus where it is 9 times higher than that of humans (right, Al = 0.9). Along the x-axis, representing = Nl/Nh, the livestock density Nl is varied relative to a fixed human density Nh = 100. Nv(0) = 1000. Effect of introducing livestock when: Nv remains constant (black line), and when Nv increases until reaching a maximum, which depends on the carrying capacity, K (coloured lines: K increasing from 5,000 (green line) to 100,000 (red line)). The effects of introducing livestock on the human blood index (HBI) and on the vector mortality rate (
) are independent from the vector density scenarios (A, B). The vertical line in the left panels highlights the new endemic equilibrium that is reached after the introduction of 1 head of livestock per 4 persons (
= 0.25), corresponding to the end of the timeline in Figure 2. Other parameters are as in Table 1.
Figure 4.
Predicted impact of Insecticide Treatment of Livestock on malaria prevalence, without diversion ().
This figure shows the combination of values of coverage and insecticidal probability required to achieve a given prevalence ratio (PR: prevalence with ITL / baseline prevalence). Blue line: PR = 0.46 (like the observed in the Pakistan trial); White line: PR = 0; Dashed line: k = 0.1, as estimated for the Pakistan trial. The colour bar shows the scale of PR values, from 0 to 1. Other parameters are as in Table 2.
Figure 5.
Predicted impact of Insecticide Treatment of Livestock on malaria prevalence – with repellency () or attractancy (
) for k = 0.1.
This figure shows how the diversionary properties of the insecticide affect the coverage required to achieve a given prevalence ratio (PR: prevalence with ITL / baseline prevalence). Blue line: PR = 0.46 (like the observed in the Pakistan trial); White line: PR = 0; Red line: PR = 1 (above which treating livestock increases malaria prevalence). Along the y axis, is varying from no diversion (
) to maximum repellency (
) or maximum attractancy (
). The colour bar shows the scale of PR values, from 0 to ≈11 in Pakistan and up to ≈5 in Ethiopia. Other parameters are as in Table 2.
Figure 6.
Critical proportion of ITL as a function of the insecticidal (k), and diversionnary effect ().
The lines show the combination of values of coverage and insecticidal probability required to achieve R0 = 1, above which R0 will be decreased below 1, for a given diversion probability (). Black line:
, no repellency or attractancy (is the same as the white line in Figure 4); Red lines:
, repellency increasing from 0.1 to 0.5 (top), at intervals of 0.1; Green lines:
, attractancy increasing from −0.1 to −0.5 (bottom), at intervals of 0.1. Other parameters are as in baseline simulations (Table 2).