Fig. 5
From: Dynamic modeling and optimal control of cystic echinococcosis
Advantage of optimal control. a–d Time series of the infections corresponding to the time-independent control (solid curves) and the optimal control (dashed curves). e–h The optimal control strategies for health education \(({p}^{*}(t))\), sheep vaccination \(({\omega }^{*}(t))\), domestic dog deworming \(({\gamma }^{*}(t))\) stray dog disposing \(({\theta }^{*}(t))\). Here C1 = C2 = C3 = C4 = 3 × 105, other parameter values are listed in Table 1, and the initial conditions are \({H}_{s}\left(0\right)=4 580 000, {H}_{e}\left(0\right)=26 058, {H}_{i}\left(0\right)=2525, {L}_{s}\left(0\right)=1 958 000, V\left(0\right)=2 038 000, {L}_{i}\left(0\right)=590 321, {D}_{1s}\left(0\right)=96 900, {D}_{1i}\left(0\right)=29 090, {D}_{2s}\left(0\right)=145 350, {D}_{2i}\left(0\right)=42 892, E\left(0\right)=271 400 000.\) In the time-independent control, \(p = 0.1, \omega = 0.3, \gamma = 0.65\) and \(\theta = 0.43.\)