Lingeshwaran Shangerganesh

arXiv2024

Modeling the dynamics of the Hepatitis B virus via a variable-order discrete system

We investigate the dynamics of the hepatitis B virus by integrating variable-order calculus and discrete analysis. Specifically, we utilize the Caputo variable-order difference operator in this study. To establish the existence and uniqueness results of the model, we employ a fixed-point technique. Furthermore, we prove that the model exhibits bounded and positive solutions. Additionally, we explore the local stability of the proposed model by determining the basic reproduction number. Finally, we present several numerical simulations to illustrate the richness of our results.

q-bio.PE↗

arXiv2021

Optimal control of a heroin epidemic mathematical model

A heroin epidemic mathematical model with prevention information and treatment, as control interventions, is analyzed, assuming that an individual's behavioral response depends on the spreading of information about the effects of heroin. Such information creates awareness, which helps individuals to participate in preventive education and self-protective schemes with additional efforts. We prove that the basic reproduction number is the threshold of local stability of a drug-free and endemic equilibrium. Then, we formulate an optimal control problem to minimize the total number of drug users and the cost associated with prevention education measures and treatment. We prove existence of an optimal control and derive its characterization through Pontryagin's maximum principle. The resulting optimality system is solved numerically. We observe that among all possible strategies, the most effective and cost-less is to implement both control policies.

math.OC↗