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 highrisk or lowrisk individuals. (Program 3.1
provides the basic details of the model).
Again we allow for a delay, such that
vaccination is begun after time t_{V}.
Parameters
β 
is the matrix of transmission
rates and incorporates the encounter rate between susceptible and
infectious individuals together with the probability of transmission. 
γ 
is
called the removal
or recovery rate, though often we are more interested in its reciprocal
(1/γ) which determines the average infectious period. 
μ_{H}

is the birth rate for
the high risk group. The proportion of the population in the highrisk
group is μ_{H}/μ 
μ_{L} 
is the birth rate for
the low risk group. The proportion of the population in the highrisk
group is μ_{L}/μ 
μ 
is
the per capita death rate and is equal to μ_{H}+μ_{L}.

p_{H}

is
the proportion of the highrisk group that are vaccinated at birth

p_{L}

is
the proportion of the lowrisk group that are vaccinated at birth

t_{V} 
is the time at which the
vaccination program is begun. 
S_{X}(0) 
is
the initial
proportion of the population that are both susceptible and in
risk group X. 
I_{X}(0) 
is
the initial
proportion of the population that are both infectious and in risk group
X.

All rates are
specified
in years.
Requirements.
All parameters must be positive, and n_{H} ≤ 1, I_{H}(0)≤
n_{H}, I_{L}(0)≤
(1n_{H}), S_{H}(0)≤
n_{H}, S_{L}(0)≤
(1n_{H}),
Files
Python Program, Parameters, MATLAB Code.
