Mathematical modelling and dynamical analysis of epidemic diseases

Abstract

Mathematical epidemiology is a multidisciplinary feld that merges mathematics with epidemiology to understand, predict, and control the spread of infectious diseases. This research work focuses on studying the dynamics of epidemic diseases through the construction and analysis of deterministic compartmental models, particularly the SIR (Susceptible Infectious Recovered) and SEIR (Susceptible Exposed Infectious Recovered) frameworks. These models are used to examine key mathematical properties such as positivity, boundedness, the basic reproduction number (R0), and the stability of the disease-free equilibrium. Numerical simulations complement the theoretical analyses to provide visual and quantitative insights into disease behavior. The work addresses fve distinct, yet interconnected problems, each exploring different real-world factors that inand#64258;uence disease transmission. The frst study, Mathematical Approach for Impact of Media Awareness on Measles Disease, investigates the role of media in controlling infectious outbreaks. Motivated by the behavioral changes observed during the COVID-19 pandemic due to media inand#64258;uence, an SEIR model with a media awareness compartment is developed to analyze measles transmission. Three scenarios delayed vaccination, regular vaccination, and newlinemedia-induced awareness are compared. Analytical and numerical results demonstrate newlinethat media awareness contributes signifcantly to reducing infection rates and confrm newlinethat disease eradication is feasible when R0 lt 1. Building upon environmental inand#64258;uences, the second study, Modelling TemperatureDependent Malaria Transmission with Varying Host Immunity, explores the temperaturesensitive nature of malaria transmission. The model incorporates temperature-dependent parameters that affect mosquito development throughout life stages while also considering varying levels of immunity in the human population.