Answer:
The rate of spread of disease is:
[tex]R = CD(P-D)[/tex]
Step-by-step explanation:
We are given the following information:
The rate R that a certain disease spreads is proportional to the number of infected individuals and is also proportional to the number of uninfected individuals.
Total Population = P
Number of infected population = D
Number oh uninfected population = P - D
It is given that:
[tex]R \propto D\\R \propto P-D\\\Rightarrow R \propto D(P-D)\\\Rightarrow R = CD(P-D).\\\text{where C is the constant of proportionality.}[/tex]
Thus, the rate of spread of disease is:
[tex]R = CD(P-D)[/tex]
The rate of spread of the disease interms of the number of infected and uninfected persons is R =CD(T - D)
Total population, P
Number of infected individuals, D
Proportionality Constant, C
Rate, R
Using the information ;
Number of uninfected individuals = (Total population - Number of infected individuals)
Therefore,
Number of uninfected individuals = T - D
Rate α number of infected individuals α number of uninfected individuals
R α D α (T - D)
R = C × D × (T - D)
R = CD(T - D)
THEREFORE, the rate of spread of the disease in terms of C can be expressed as R = CD(T - D)
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