Modelling of P. vivax malaria with bimodal incubation time

Malaria parasites are transmitted between mosquitoes and humans. If an infectious mosquito bites a host, symptoms occur after a certain incubation period. The incubation period can vary depending on the species of parasite or the regions. In particular, incubation period of Plasmodium vivax - the malaria inducing parasite species most prevalent in temperate zones in Korea - shows bimodal distribution, with short term and long term incubation periods. In this talk, I compare transmission models for P. vivax malaria having different expression for the incubation period, where we model the long term incubation period using ordinary differential equations or delay differential equations. We show that, while the qualitative behaviors of the two models are similar, the ODE model overestimates the basic reproduction number and also the level of endemicity, compared to the DDE model. However, when we incorporate seasonality, the interplay of the time delay and the periodicity results that in some situations the DDE model predicts higher prevalence of malaria.