BackgroundThe WHO considers leishmaniasis as one of the six most important tropical diseases worldwide. It is caused by parasites of the genus Leishmania that are passed on to humans and animals by the phlebotomine sandfly. Despite all of the research, there is still a lack of understanding on the metabolism of the parasite and the progression of the disease. In this study, a mathematical model of disease progression was developed based on experimental data of clinical symptoms, immunological responses, and parasite load for Leishmania amazonensis in BALB/c mice.ResultsFour biologically significant variables were chosen to develop a differential equation model based on the GMA power-law formalism. Parameters were determined to minimize error in the model dynamics and time series experimental data. Subsequently, the model robustness was tested and the model predictions were verified by comparing them with experimental observations made in different experimental conditions. The model obtained helps to quantify relationships between the selected variables, leads to a better understanding of disease progression, and aids in the identification of crucial points for introducing therapeutic methods.ConclusionsOur model can be used to identify the biological factors that must be changed to minimize parasite load in the host body, and contributes to the design of effective therapies.

This review gives an overview of the mathematical models of the immune response to leishmaniasis. Mathematical modelling is based on the choice of key variables and interactions between them, which are quantified as parameters. Choice of variables is based on biological knowledge, parameter values are derived by fitting to the experimental data. Ordinary differential equation models describe model dynamics - changes in the populations of cells and other body agents. Biological knowledge is needed to set up the model, knowing influences and interactions among body cells. Immune response models target on the prediction of disease progression and identification of the most sensitive parameters, which are assumed to be feasible targets for therapy. All the mathematical models of the biological systems represent a simplification of reality and thus may yield wrong results. However, they offer a fast and systematic search for optimal strategies that would possibly be neglected by experimentally based research. If mathematical models are applied to obtain ideas for new directions in experimental work, they offer a promising tool in pharmaceutical research.