The rate of increase of susceptible SARS victims is proportional to the number of susceptible persons and number of infected persons. If there are S0 susceptible persons and 1-infected person at a time t0 then
i) set up the equation for the spread of the disease
ii) solve the resulting equation
iii) give a physical interpretation of the same by putting the epidemic curve
iv) write the limitations of this model.
i) Setting up the equation for the spread of the disease:
Let's denote the following variables:
- S(t) represents the number of susceptible individuals at time t.
- I(t) represents the number of infected individuals at time t.
- β is the transmission rate (rate of infection spread).
- t0 is the initial time when there are S0 susceptible individuals and 1 infected individual.
The rate of increase of susceptible individuals (dS/dt) is proportional to the product of the number of susceptible individuals and the number of infected individuals. This can be expressed as:
dS/dt = -β * S(t) * I(t)
This is a differential equation that models the spread of a disease, known as the SIR (Susceptible-Infectious-Recovered) model. It describes how the number of susceptible individuals changes over time based on their interactions with infected individuals.
ii) Solving the resulting equation:
The solution to this differential equation depends on
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