Global dynamics of a general vector-borne disease model with two transmission routes

Sk Shahid Nadim; Indrajit Ghosh; Joydev Chattopadhyay

This leads to an unusual phenomenon of forward bifurcation with hysteresis effect, which is shown 431 numerically for our model (2.1). We find that our model exhibits a hysteresis effect where multiple 432 endemic equilibrium coexist for R 0 > 1 (see Fig. 2 ). The blue line represents two outer equilibrium, 433 which is stable while the green line represent the interior equilibrium, which is unstable. Further investigation reveals that the endemic equilibrium may also be stable in a region where 435 R 0 < 1 (see Fig. 3 ). This indicates that the disease may persist for R 0 < 1, even if the type of 436 transcritical bifurcation at R 0 = 1 is forward. Similarly, in case of hysteresis, these control measures will compel the solutions to the basin of attraction 447 of the lower endemic equilibrium. Here, we control the indirect transmission rate (β i ) for a certain period 448 of time, to force the solutions of the system to lower endemic value. We use the following to model this