3. (10 points) imagine that we can quarantine infected members of the population, so that they are unable to transmit the disease to others. let q represent the fraction of the infected population which is quarantined, and let 1-q represent the fraction of the infected population that is not quarantined and can transmit the disease to the susceptible individuals. a. rewrite the difference questions for sit+1] and it+1] (from question 1), to incorporate the effects of quarantine. (hint quarantine should affect the term representing the proportion of susceptible individuals who are infected each time step) b. quarantine can be viewed as a way of modifying the transmission coefficient (a) by reducing the number of individuals which can be infected. this modified transmission coefficient can be referred to as a. write an equation for a that incorporates both a and q.