State-by-state influenza outbreaks and oversee: A Markov chain study of California and North Carolina, USA

Abstract

Influenza, a significant public health concern, spreads rapidly and causes seasonal epi- demics and pandemics. Mathematical models are essential tools for devising effec- tive strategies to combat this pandemic. Various models have been utilized to study

influenza’s transmission dynamics and control measures. This paper presents the SEIRS

(Susceptible-Exposed-Infectious-Recovered-Susceptible) model to analyze the dis- ease’s transmission dynamics. The model analyzes real data from California and North

Carolina to assess trends, identify key factors, and project the nationwide spread of the

disease. Subsequently, we calculate the basic reproduction number (R0) using the next- generation matrix method. Sensitivity analysis using Latin Hypercube Sampling (LHS)

has been conducted to identify the model’s most influential parameters. We graphically demonstrate how different parameters affect the exposed and infected populations, as well as the variation in the basic reproduction number with changes in parameters. We illustrate the interconnected behavior of the effective reproduction number alongside the

different compartments and the basic reproduction number. We use phase plane anal- ysis to examine the relationship between two compartments under varying parameters.

Visual tools like boxplots, contour plots, and heat maps provide insights into how dif- ferent factors influence the basic reproduction number and disease transmission. We

investigate the stochastic behavior of the model by transforming it into a Continuous- Time Markov Chain (CTMC) model and visualizing the results graphically. We apply the

SEIRS model to real influenza data, showcasing its effectiveness in analyzing transmis- sion dynamics, predicting outbreaks, and evaluating public health strategies for better

epidemic management.