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Universal Journal of Mathematics and Mathematical Sciences

Universal Journal of Mathematics and Mathematical Sciences
Volume 20, Issue 2 (In Progress), Pages 93 - 142 (December 2024)
http://dx.doi.org/10.17654/2277141724007

OPTIMAL CONTROL HARMONY: NAVIGATING DETERMINISTIC AND STOCHASTIC REALMS WITH A TWO-STRAIN MODEL USING PONTRYAGIN’S MAXIMUM PRINCIPLE

Andrew Kayanja, Benard Abola, Cliff R. Kikawa, Benedict Oyo and Amos Ssematimba

Abstract:

In this paper, we study optimal control solutions using a two-strain SARS-CoV-2 deterministic epidemic model characterized by standard incidence, alongside a two-strain stochastic model incorporating a random transmission rate. We present proofs demonstrating the existence, uniqueness, and boundedness of a positive solution for any positive initial value for both models. An algorithm for simulating the ensemble average optimal control solution is introduced and its realism is compared to both stochastic and deterministic solutions. Additionally, we include graphical representations to illustrate the dynamics and outcomes of our models. Our findings suggest that ensemble average optimal control simulations may offer enhanced visualization and realism compared to both stochastic and deterministic solutions.

Keywords and phrases:

deterministic modelling, stochastic modelling, multiple strains, Pontryagin’s maximum principle, ensemble averages.

Received: April 25, 2024; Accepted: July 20, 2024; Published: August 22, 2024

How to cite this article: Andrew Kayanja, Benard Abola, Cliff R. Kikawa, Benedict Oyo and Amos Ssematimba, Optimal control harmony: navigating deterministic and stochastic realms with a two-strain model using Pontryagin’s maximum principle, Universal Journal of Mathematics and Mathematical Sciences 20(2) (2024), 93-142. http://dx.doi.org/10.17654/2277141724007

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

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