Abstract

Abstract:

In this paper, we study an existence theory as well as stability results to the new fractional Nabla difference biological model of glucose–insulin regulatory system (GIRS) on diabetes mellitus involving the Atangana Baleanu–Caputo (ABC) derivative. We consider the proposed model under ABC derivative, and it has the nonsingular Mittag-Leffler function as its kernel. We utilize the fixed point technique for the existence and uniqueness analysis. The stability of the concerned solution in Hyers–Ulam sense is also investigated. Further to derive the approximate solution in the form of series to the considered model, we use iterative technique method. Numerical simulations are given to support the theoretical results. The results show that order of the fractional derivative has a significant effect on the dynamic process. Many informations on the dynamics of GIRS in diabetes mellitus were obtained using this model. It is recognized as a deterministic fractional Nabla difference model for diabetes mellitus that provides a better control approach at fractional values for the development of an artificial pancreas.

Abstract:

Transmission dynamics modeling is used to study how diseases spread within a population over time and space. The primary purpose of this modeling technique is to simulate the spread of infections and to inform public health decision-making by providing insights into the impact of interventions. In recent years, modeling approaches has undergone significant evolution and become innovative. In this talk, I will examine how the methodologies and approaches in modeling transmission dynamics and quantifying uncertainty have developed over time. I will also delve into the transformative impact of the COVID-19 pandemic on the thought processes, evidence generation, and the concept of value associated with understanding implications from public health interventions. Historically, transmission dynamics modeling has relied on conventional epidemiological tools. However, the emergence of the COVID-19 pandemic prompted a paradigm shift in this field. The need for rapid decision-making and the dynamic nature of the virus forced researchers to adapt and innovate. This shift has influenced not only the models and methods but also the very framework of evidence generation and decision-making in public health. I will explore the various modeling approaches from my research lab on neglected tropical diseases, non-communicable infections, and social problems, shedding light on the integration of novel data sources, real-time data analysis, and creating value for multiple stakeholders while helping with understanding of the implications of public health interventions, thereby guiding policy decisions and highlighting competencies for emerging next generation scientists.

Abstract:

Type 1 diabetes, also referred to as juvenile diabetes or insulin-dependent diabetes, is a condition driven by autoimmune processes that lead to the inadequate or complete absence of insulin production by the pancreas. Insulin plays a critical role in regulating blood sugar levels, and elevated blood sugar levels can result in damage to the body and a range of symptoms, such as excessive thirst, fatigue, and urinary infections. The cells responsible for producing insulin are known as β-cells, and in Type 1 diabetes, these cells are destroyed due to an abnormal immune response. Specifically, certain cytotoxic T-cells with specific clones infiltrate the pancreatic islets of Langerhans and eliminate them. 

In this talk, we present a cellular model that aims to explain the development of Type 1 diabetes in HIV-infected patients after undergoing immune restoration during highly active antiretroviral therapy (HAART). The study encompasses the derivation of the qualitative characteristics of the model and its comprehensive analysis using path-following techniques, leveraging the COCO continuation platform. Through this approach, we meticulously verify the primary theoretical predictions. Additionally, the numerical aspect of this research establishes precise parameter thresholds to ensure an effective treatment for the disease in HIV-infected individuals, thereby preventing the onset of Type 1 diabetes. It's worth noting that the development of Type 1 diabetes in individuals infected with the human immunodeficiency virus (HIV) is a rare occurrence.

Abstract:

Mosquito-borne diseases are primarily spread by female mosquitoes while taking a blood meal from living organisms such as humans, animals, and birds. A parasite, virus, or bacteria infected female mosquito can transmit those foreign agents to humans. For instance, the Dengue virus, Zika virus, yellow fever virus, and Chikungunya are transmitted from infected humans to uninfected human via a primary vector Aedes Aegypti mosquitoes. Currently, there are several methods to control Aedes Aegypti mosquitoes such as insecticide spraying, sterile insect technique, incompatible insect technique, combined sterile insect technique, and genetic modifications. World Mosquito Program (WMP) from Australia currently release Wolbachia infected mosquitoes over countries such as countries in Latin America, India, Sri Lanka, Vietnam, Indonesia, cities in Oceania. In that research, they found that Wolbachia is a self-sustaining bacterium and in the presence of Wolbachia infected mosquitoes there is zero possibility of having Dengue. The Wolbachia releasing strategy is more powerful than that of the above-mentioned control strategies in the sense that, it is self-sustaining, Affordable, only needs a small number of releases, the area covered is larger than the released area, and the most important thing is it is not harmful to human health.

So, in this talk, we see how an impulsive control strategy is implemented to maintain the self-sustainability of Wolbachia among Aedes Aegypti mosquitoes. The present paper provides a fractional order Wolbachia invasive model. Through fixed point theory, this work derives the existence and uniqueness results for the proposed model. Also, we performed global Mittag-Leffler stability analysis via Linear Matrix Inequality theory and Lyapunov theory. As a result of this controller synthesis, the sustainability of Wolbachia is preserved and non-Wolbachia mosquitoes are eradicated. Finally, a numerical simulation is established for the published data to analyse the nature of the proposed Wolbachia invasive model

Abstract:

Dengue fever epidemiological dynamics shows large fluctuations in disease incidence, and several mathematical models describing the transmission of dengue viruses have been proposed to explain the irregular behavior of dengue epidemics. Multi-strain dengue models are often modeled with SIR-type models where the SIR classes are labeled for the hosts that have seen the individual strains. The extended models show complex dynamics and qualitatively a very good result when comparing empirical data and model simulations. However, modeling insights for epidemiological scenarios characterized by chaotic dynamics, such as for dengue fever epidemiology, have been largely unexplored. The problem is mathematically difficult and to make the urgently needed progress in our understanding of such dynamics, concepts from various fields of mathematics as well the availability of good data for model evaluation are needed.
In this talk, I will present a set of models motivated by dengue fever epidemiology and compare different dynamical behaviors originated when increasing complexity into the model framework.

Abstract:

Leptospirosis, a zoonotic bacterial infection caused by various strains of Leptospira bacteria, poses a significant public health threat globally. This interdisciplinary academic talk explores the intricate world of leptospirosis through mathematical modelling techniques. By integrating epidemiological data, statistical analysis, and computational simulations, we will discuss the complex dynamics of leptospirosis transmission within different populations and environments. This presentation seeks to clarify the fundamental processes involved in disease transmission, taking into account elements such as host demographics, environmental factors, and pathogen characteristics.

The talk will highlight various mathematical models used to describe the epidemiology of leptospirosis, including compartmental models, network models, and spatial-temporal models. Through these models, we investigate the impact of interventions such as vaccination campaigns, environmental sanitation, and vector control strategies on disease prevalence and transmission rates. Additionally, the discussion will cover the challenges in parameter estimation, model validation, and the incorporation of uncertainties in mathematical predictions.

Abstract:

Epidemiological models serve as the cornerstone of public health analysis, providing essential tools for understanding the spread of diseases and evaluating intervention strategies. This talk explores the fundamental principles and components of epidemiological models, delving into their mathematical foundations, key variables, and model types. We will discuss the significance of model assumptions, data integration, and model validation, emphasizing their critical role in informing public health decision-making. By gaining insight into these building blocks, attendees will be better equipped to harness the power of mathematical modeling in epidemiology, ultimately contributing to more effective disease control and prevention strategies.