Fig. 4

Optimal strategies for releases and drug treatments can substantially reduce the cost of managing malaria. a The proportion of infected humans under six control scenarios (where w is the host treatment proportion and u is the insect release ratio with respect to the wild vector population): no control (x-axis label “0,0”), \(w=w_0\), \(u=0\) (x-axis label “\(w_0\),0”), \(w=0\), \(u=u_0\) (x-axis label “0,\(u_0\)”), \(w=w_0\), \(u=u_0\) (x-axis label “\(w_0\),\(u_0\)”), \(w=0\), \(u=u^*(t)\) (x-axis label “0,\(u^*\)”), \(w=w^*(t)\), \(u=u^*(t)\) (x-axis label “\(w^*\),\(u^*\)”), where \(w_0 = 0.05\), \(u_0 = 0.2\) (\(5\%\) drug coverage and releasing \(20\%\) of the wild male population per day) and \(w^*\), \(u^*\) are the optimal control strategies defined in (18) and (29), respectively. b The total cost of the scenario, including spending on traditional healthcare (h), spending on artemisinin treatment (w) and spending on insect releases (u). Early-acting SIT is assumed. Quadratic cost functions of h, w and u are assumed