| Abstract: | This paper describes how a parasite with distinct stages for replication within its host and for transmission among hosts should schedule the production of the two stages so that it achieves maximal transmission. A mathematical model of the within-host dynamics of a parasite and of its interactions with the immune response predicts that the optimal pattern of investment depends largely on the relationships between the growth rate of the parasite, the rate of increase of immunity against the parasite, and parasite-induced mortality of the host. We consider first a parasite with a constant, time-independent level of investment in transmission. If such a parasite grows rapidly and can therefore reach a density that kills the host before it is cleared by the immune response, it can achieve maximal transmission by producing transmission stages, and thus reducing its effective growth rate, to the extent that its peak density is just below the lethal density. This leads to the prediction that investment in transmission should be positively correlated with growth rate. In contrast, if the parasite grows more slowly and is cleared by the immune system before it can reach lethal density, the level of investment should be negatively correlated with growth rate. If a parasite can vary its investment into transmission during the course of infection, it should delay investment into transmission until it reaches lethal density or until shortly before it is cleared by the host′s immune system. If a parasite grows slowly in comparison with immunity, the optimal pattern of investment is a bang-bang pattern: the investment switches from total production of the replication stage to total production of the transmission stage shortly before the parasite is cleared by the immune response. If a parasite grows much more rapidly than immunity, the parasite initially replicates up to lethal density without producing any transmission stages, then produces transmission stages at the rate that reduces its effective growth rate to zero and thus allows it to be maintained at lethal density, and finally switches to complete investment into transmission stages shortly before it is cleared by the immune system |
