1.In the SIRV model with time-dependent vaccination from Sect. 8.3.9, we want to test the effect of an adaptive vaccination campaign where vaccination is offered

2.We consider the SIRV model from Sect. 8.3.8, but now the effect of vaccination is time-limited. After a characteristic period of time, π, the vaccination is no more effective and individuals are consequently moved from the V to the S category and can be infected again. Mathematically, this can be modeled as an average leakage −π−1V from the V category to the S category (i.e., a gain π−1V in the latter). Write up the complete model, implement it, and rerun the case from Sect. 8.3.8 with various choices of parameters to illustrate various effects.