Homework assignment 3 * Due date: Monday April 13, 2009. 1. In class we solved McKendrick’s problem: u a ( a,t ) + u t ( a,t ) =-d ( a ) u ( a,t ) , with BC : u (0 ,t ) = B ( t ) , and IC : u ( a, 0) = u0 ( a ) . Here we consider the special case where the survival function is exponential: l ( a ) = e-μa , for some μ >0 . • Find the instantaneous death rate d ( a ). • Find the basic reproduction number R0 (i.e. the expected number of oﬀspring per female over her lifetime) if the maternity function is given by:
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Probability theory, Patrick De Leenheer, instantaneous death rate