Vol. 7 No. 1 (2024)

In this study, we propose a deterministic double dose vaccination model of COVID-19 transmission dynamics optimal control with cost-effectiveness analysis. It is imperative for decision-makers and the government to prioritize the application of preventive and control measures for COVID-19 based on efficiency and costbenefit analysis. This is pivotal in resource-constrained regions where the disease is endemic. Thus, this work is mainly devoted with the development and analysis of an optimal control for COVID-19 dynamics with five timevarying functions; first dose vaccination, second dose…

In this study, we illustrate the incorporation of two vaccine doses into a discrete SIR model to aid in the decision-making process for optimal vaccination strategies. We present a basic model of a human interaction network synthesized to depict social contacts within a population, taking into account the number of connections and the level of interaction among individuals. Under a limited number of available vaccine doses, we explore various vaccination scenarios considering factors such as the distribution of vaccines, the proportion of vaccinated individuals, and the timing of vaccination…

In this paper, we develop and analyze a mathematical model that describes the dynamic interactions and competitions among tumor cells, normal cells, immune cells, and transforming growth factor-beta within the tumor microenvironment. We conducted qualitative analyses to examine the persistence or extinction of each cell population and analyzed the regions of stability and instability across various equilibria. Additionally, we formulated and solved an optimal control problem using the Pontryagin’s maximum principle, aiming to minimize tumor size and the concentration of transforming growth…

We propose and analyze a simple modification to the Rosenzweig-MacArthur predator (zooplankton)-prey (phytoplankton) model to account for the interference of the predators with the impacts of nanoparticles. We have taken into account the influence of predators by quantifying the impact of nanoparticles in actual environments. It is shown that the influence of the nanoparticles may reduce the prey

Human mobility can be identified as one of the main factors that directly affect the spread of COVID-19. Accordingly, human mobility must be controlled in a proper way to deficit the spread of COVID-19 as the economy of a country depends on human mobility. Nevertheless, due to the lack of proper management of the lockdown restrictions, the economy of many countries has already suffered a severe decline. In this research, a compartmental model (SIR) has been presented using optimal control theory to deficit the spread of COVID-19. Thus, the districts of Sri Lanka were divided into three…

The compartmental model stands as a cornerstone in quantitatively describing the transmission dynamics of diseases. Through a series of assumptions, this model can be formulated and subsequently validated against real-world conditions. Leveraging the abundance of COVID-19 data presently available, this study endeavors to reverse engineer the model construction process. Specifically, we analyse the compartmental model governing two notable variants of COVID-19: Delta and Omicron, utilizing empirical data. Employing the SINDy method, we extract parameters that define the model by effectively…

Tuberculosis (TB) remains a pressing global health concern, demanding urgent attention to mitigate its spread and impact. In this study, we present a rigorous mathematical model of TB transmission that incorporates early case detection and addresses the critical issue of treatment failure. Through the development of a system of nonlinear ordinary differential equations, we conduct comprehensive analyses to assess the dynamics of TB transmission and the efficacy of intervention strategies. Our findings underscore the urgent need for effective TB control measures. Mathematical analyses reveal…

Type 2 diabetes mellitus is a non-communicable medical condition that is most commonly suffered in compare to type 1 diabetes, gestational diabetes, or diabetes that is caused by pathogen or disorders. The other important non-communicable medical condition is cardiovascular disease that occurs due to impaired blood circulation in the heart and blood vessels. The unhealthy lifestyle behaviors that mainly influenced by social interactions play an important role to increase the number of prevalence for those diseases. In this paper, we consider a mathematical model of the social interactions…