A MATHEMATICAL MODEL OF IMMUNE RESPONSE IN CUTANEOUS LEISHMANIASIS

The TH1/TH2 paradigm has been largely used in the interpretation of several diseases, particularly in leishmaniasis. As far as we know there is no mathematical description of this model related to leishmaniasis. We have extended and modified a previous published set of equations1 in order to adapt it to leishmanial disease particularities. The main modifications were: (1) the analysis of logistic and exponential parasite growth curves, (2) the assumption of the TH2 arm of the immune response having a positive action on parasite growth. The set of three simultaneous differential equations describing the TH1 arm, TH2 arm and parasite growth were analyzed for conditions of existence and stability of the solutions. Stable solutions valid for the logistic and exponential parasite growth models, with its possible clinical correlations, were obtained in the following situations: (1) parasite and TH2 extinction [TH1 cure], (2) parasite extinction and TH1/TH2 co-existence [TH1/TH2 cure], (3) TH1 and parasite co-existence, TH2 extinction [stable TH1 infection], and (4) TH1, TH2 and parasite co-existence [stable TH1/TH2 infection]. TH2 and parasite co-existence associated to TH1 extinction [stable TH2 infection] was obtained only with the logistic growth model. The model also provides an alternative hypothesis for TH1 bias in resistant mice and emphazises the importance of natural immunity for the existence of chronic states.