We now reflect on the advantages of
targetted vaccination. In particular we use the model structure
developed in Program 3.1 to consider the advantages of targetting
vaccination towards high-risk or low-risk individuals. (Program 3.1
provides the basic details of the model).
Again we allow for a delay, such that
vaccination is begun after time tV.
All rates are
|| is the matrix of transmission
rates and incorporates the encounter rate between susceptible and
infectious individuals together with the probability of transmission.
called the removal
or recovery rate, though often we are more interested in its reciprocal
(1/γ) which determines the average infectious period.
|is the birth rate for
the high risk group. The proportion of the population in the high-risk
group is μH/μ
||is the birth rate for
the low risk group. The proportion of the population in the high-risk
group is μL/μ
the per capita death rate and is equal to μH+μL.
the proportion of the high-risk group that are vaccinated at birth
the proportion of the low-risk group that are vaccinated at birth
||is the time at which the
vaccination program is begun.
proportion of the population that are both susceptible and in
risk group X.
proportion of the population that are both infectious and in risk group
All parameters must be positive, and nH ≤ 1, IH(0)≤
Python Program, Parameters, MATLAB Code.