Fig. 1 | Scientific Reports

Fig. 1

From: Impact of mild hyperthermia on tumor-immune dynamics explored through mathematical modeling

Fig. 1

Phase portraits showing the effect of small parameter variations on tumor-immune dynamics. (a,b) Increasing \(\alpha\) from 0.9816 to 1.0143 induces a saddle-node bifurcation, leading to the emergence of the separatrix (SP) and tumor escape (TE) states. (c,d) Decreasing \(\rho\) from 1.1310 to 0.6789 rearranges the existing fixed points (TC, SP, TE), shifting the separatrix and reducing the basin of attraction of the tumor control (TC) state. When one parameter changes, all other parameters remain: \(\alpha =1.636\), \(\rho =1.131\), \(\sigma = 0.1181, \eta = 20.19, \mu = 0.00311, \delta = 0.3743, \gamma =1\), and \(\beta = 2.0 \times 10^{-3}\).

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