title: Solving inverse problems for biological models using the collage method for differential equations.
abstract: In the first part of this paper we show how inverse problems for differential equations can be solved using the so-called collage method. Inverse problems can be solved by minimizing the collage distance in an appropriate metric space. We then provide several numerical examples in mathematical biology. We consider applications of this approach to the following areas: population dynamics, mRNA and protein concentration, bacteria and amoeba cells interaction, tumor growth.
authors.affiliation: Department of Mathematics, University of Milan, Milan, Italy.
authors.forename: V
authors.initials: V
authors.lastname: Capasso
authors.forename: H E
authors.initials: HE
authors.lastname: Kunze
authors.forename: D
authors.initials: D
authors.lastname: La Torre
authors.forename: E R
authors.initials: ER
authors.lastname: Vrscay
mesh_terms: D000818:Animals; D004023:Dictyostelium / Q000254:growth & development / Q000382:microbiology; D005786:Gene Expression Regulation; D006801:Humans; D055641:Mathematical Concepts; D008954:Models, Biological; D009369:Neoplasms / Q000473:pathology; D011157:Population Dynamics / Q000706:statistics & numerical data; D011550:Pseudomonas aeruginosa / Q000254:growth & development / Q000472:pathogenicity; D013269:Stochastic Processes