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. 2019 Oct 19;4:265–285. doi: 10.1016/j.idm.2019.10.001

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© 2019 The Authors

This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

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Fig. 6 — The backward bifurcation and local stability of the steady-state solution $P_{3}$ . We vary $ϕ_{w}$ and set values the following key parameters as: $R_{0 \bar{w}} = 122.5$ , $ρ_{1} = 0.1$ , $ρ_{2} = 0.06$ and $σ = 0.02$ . (a) Shows the backward bifurcation of the general model association with equilibrium points $P_{2}$ and $P_{3}$ . (b) and (c) establish the local stability of the equlibrium point $E_{4}$ using Routh-Hurwitz conditions - (b), $e_{1} > 0$ , $e_{2} > 0$ , $e_{3} > 0$ , $e_{4} > 0$ and (c), $e_{1} e_{2} e_{3} > e_{3}^{2} + e_{1}^{2} e^{4}$ .