A mathematical model in natural sciences as engineering, chemistry, physics, biology, etc, is a set of definitions and axioms that are consistent and independent. Theorems are facts which can be proved using the proposed axioms.
In brief, the mathematical model includes theorems and not the converse.
Theory is a statement aimed at explaining a phenomenon. It may include the governing equations and methodology. A model is a representation of reality and something that is physical and practical.
The following publications/links (discussions) may further help in clarification/elaboration.
Abend, G. (2008) The meaning of 'theory', Sociological Theory, 26, 2, pp. 173-199.
Cooper, D. R. and Schindler, P. S. (2014) Business Research Methods. 12th edn. New York, NY: McGraw-Hill/Irwin. (See: Theory / Models, pp. 61-64, 660, 668).
Nilsen, P. (2015) Making sense of implementation theories, models and frameworks, Implementation Science, 10, 53, pp. 1-14.
What is difference between a theory and a model?: https://www.researchgate.net/post/What_is_difference_between_a_theory_and_a_model
Is there any difference between a framework and model?: https://www.researchgate.net/post/Is_there_any_difference_between_a_framework_and_model
What is the difference between the terms 'a theory' and 'a theoretical framework' in research?: https://www.researchgate.net/post/What_is_the_difference_between_the_terms_a_theory_and_a_theoretical_framework_in_research