Immune response to infection by Leishmania: A mathematical model

Leishmaniasis is a disease caused by the Leishmania parasites. The injection of the parasites into the host occurs when a sand fly, which is the vector, bites the skin of the host. The parasites, which are obligate, take advantage of the immune system response and invade both the classically activated macrophages (M1) and the alternatively activated macrophages (M2). In this paper, we develop a mathematical model to explain the evolution of the disease. Simulations of the model show that, M2 macrophages steadily increase and M1 macrophages steadily decrease, while M1+M2M1+M2 reach a steady state which is approximately the same as at healthy state of the host. Furthermore, the ratio of Leishmania parasites to macrophages depends homogeneously on their ratio at the time of the initial infection, in agreement with in vitro experimental data. The model is used to simulate treatment by existing or potential new drugs, and to compare the efficacy of different schedules of drug delivery.