Fig 1.
The flow diagram of the LSD model (3.1).
The model was inspired by the experimental studies in [10] and [11] which showed that the importance of quarantine and vaccination in mitigating the risk of LSD transmission, and the mathematical modelling studies in [29,17,31] which focused only on the vaccinated effect and did not consider the impact of the quarantine on the LSD infection.
Table 1.
Parameters description.
Fig 2.
Bifurcation diagram for the two steady states calculated of the model (3.1); and
, as the parameters are varied: (a) rate of infection of susceptible cattle (
),
; (b) rate of infection of vaccinated cattle (
),
; (c) vaccinated rate of of susceptible cattle (
),
.
Sub-plot (i) shows S vs. parameter, while Sub-plot (ii) show I vs. parameter. Here "BP1" presents the bifurcation point where the state bifurcates out of the
state as we increase
above
, and "BP2" presents the bifurcation point where the
state bifurcates out of the
state as we increase
above
and "BP3" presents the bifurcation point where the
state bifurcates out of the
state as we decrease
below
.
Fig 3.
Sensitivity index vs. different parameters.
Table 2.
Sensitivity index of to the model parameters.
Fig 4.
Simulation of the fractional system (3.1) with varying fractional orders, we choose and other parameters as in Table 1, we get
.
Fig 5.
Simulation of the fractional system (3.1) with varying fractional orders, we choose and other parameters as in Table 1, we get
.
Fig 6.
Simulation of the fractional system (3.1) with and without vaccination.
Fig 7.
Effect of on exposed and infected cattle for different fractional orders.
Table 3.
Impact of vaccination on exposed cattle population at EE point for different fractional orders.
Table 4.
Impact of vaccination on infected cattle at EE point for different fractional orders.
Fig 8.
Effect of on exposed and infected cattle for different fractional orders.
Fig 9.
Effect of q on infected cattle populations for different fractional orders.
Table 5.
Impact of quarantine on infected cattle at EE point for different fractional orders.
Fig 10.
Change in population dynamics of model (3.1), as we vary the following parameters: (a) and (b) quarantine rate q of exposed cattle; (c) and (d) vaccination rate of susceptible cattle; (e) and (f) infection rate
of susceptible cattle.
Fig 11.
Variations in the basic reproduction number with key parameters of the model (3.1).