Systems of populations with multiple structures: modeling and analysis - Le Thi Thanh, An; Jäger, Willi; Neuss-Radu, Maria (Journal of dynamics and differential equations, 2015)
In this paper a class of functional-differential equations is considered, arising in modeling the dynamics of structured populations. This class includes model equations for diseases spreading by interactions of hosts, vectors and parasites considered in An (Drug Resistance in Infectious Diseases: Modeling, Analysis and Simulation, Doctoral thesis, University of Heidelberg, 2012) and An et al. (A structured population model for malaria including drug resistance. In preparation), where drug sensitive and drug resistant parasites and their effects on the infected host and vector populations are modeled via structural variables. In this paper, the evolution of n structured and m unstructured interacting populations is described by a coupled system of n functional-partial differential equations and m functional-ordinary differential equations. In general, besides initial conditions additional "boundary" conditions are required in order to determine missing data for the structure dependent variables. As the main result of this paper, we are going to present the analysis for the existence of unique, positive solutions.