Question

Consider the dynamics of a directly transmitted viral microparasite to be modelled by the system 1 d X dY where b, B and r are positive constants and X, Y and Z are the number of suscep- tibles, infectives and immune populations respectively. Here the population is kept constant by births and deaths (with a contribution from each class) balancing. Show that there is a threshold population size, Ne, such that if N < Nc = (b + r) the parasite cannot maintain itself in the population and both the infectives and the immune class eventually die out. The quantity BN/(b+r) is the basic reproductive rate of the infection.

Answer 1

dt di wuth liu (bt*) y = bth) 70 b十ん Y70

obulatim uace whım, u씨.ech ves no