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Fig. 2 | Malaria Journal

Fig. 2

From: Theory of reactive interventions in the elimination and control of malaria

Fig. 2

Bifurcation diagrams showing fixed points of prevalence for RCD models. The solid blue lines correspond to locally asymptotically stable equilibria. The dashed red lines to unstable equilibria. The infectious period for all models is set to 200 days and the transmission parameter, \(\beta\), is varied to provide the appropriate value of \(R_{0}\). a Model (a): \(\uptau = 5\), weekly total number of neighbours tested (product of \(\upiota\) and \(\upnu\)) is 150. The disease-free equilibrium point is locally asymptotically stable for \(R_{0}\) less than a critical value and unstable above this value (where a transcritical bifurcation occurs). The endemic equilibrium point is locally asymptotically stable for \(R_{0}\) greater than the critical value. b Model (b): \(\varphi = 150\). The disease-free equilibrium point is locally asymptotically stable for any value of \(R_{0}\). There are two endemic equilibria for values of \(R_{0}\) greater than a certain threshold (where a saddle node bifurcation occurs). The larger endemic equilibrium point is locally asymptotically stable and the smaller endemic equilibrium point is unstable. c Model (c): \(\upiota = 3\), \(\upnu = 50\); the targeting ratio,\(\uptau\), is calculated for the endemic prevalence in the absence of RCD. The disease-free equilibrium point is locally asymptotically stable for any value of \(R_{0}\). There are two endemic equilibria for values of \(R_{0}\) greater than a certain threshold (where a saddle node bifurcation occurs). The larger endemic equilibrium point is locally asymptotically stable and the smaller endemic equilibrium point is unstable. d Model (c): \(\upiota = 50\), \(\upnu = 3\); \(\uptau\) is calculated for the endemic prevalence in the absence of RCD. the disease-free equilibrium point is locally asymptotically stable for any value of \(R_{0}\). There are two endemic equilibria for values of \(R_{0}\) greater than a certain threshold (where a saddle node bifurcation occurs). The larger endemic equilibrium point is locally asymptotically stable and the smaller endemic equilibrium point is unstable

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