236
8 Solving Ordinary Differential Equations
Fig. 8.13 Including loss of immunity
Fig. 8.14 Increasing β and reducing ν compared to Fig. 8.13
8.3.8 Incorporating Vaccination
We can extend the model to also include vaccination. To this end, it can be useful
to track those who are vaccinated and those who are not. So, we introduce a fourth
category, V, for those who have taken a successful vaccination. Furthermore, we
assume that in a time interval Δt, a fraction pΔt of the S category is subject to a
successful vaccination. This means that in the time Δt, pΔtS people leave from the
S to the V category. Since the vaccinated ones cannot get the disease, there is no
impact on the I or R categories. We can visualize the categories, and the movement
between them, as
8 Solving Ordinary Differential Equations
Fig. 8.13 Including loss of immunity
Fig. 8.14 Increasing β and reducing ν compared to Fig. 8.13
8.3.8 Incorporating Vaccination
We can extend the model to also include vaccination. To this end, it can be useful
to track those who are vaccinated and those who are not. So, we introduce a fourth
category, V, for those who have taken a successful vaccination. Furthermore, we
assume that in a time interval Δt, a fraction pΔt of the S category is subject to a
successful vaccination. This means that in the time Δt, pΔtS people leave from the
S to the V category. Since the vaccinated ones cannot get the disease, there is no
impact on the I or R categories. We can visualize the categories, and the movement
between them, as