Global Stability Analysis and Parameter Estimation for a Diphtheria Model: A Case Study of an Epidemic in Rohingya Refugee Camp in Bangladesh
Zahurul Islam, Shohel Ahmed, R. Saidur, M.F. Karim, Maryse Amin
Abstract
In this article, we have developed a deterministic Susceptible-Latent-Infectious-Recovered (SLIR) model for diphtheria outbreaks. Here, we have studied a case of the diphtheria outbreak in the Rohingya refugee camp in Bangladesh to trace the disease dynamics and find out the peak value of the infection. Both analytical and numerical investigations have been performed on the model to find several remarkable behaviors like the positive and bounded solution, basic reproductive ratio, and equilibria such as disease extinction equilibrium and disease persistence equilibrium which are characterized depending on the basic reproductive ratio and global stability of the model using Lyapunov function for both equilibria. Parameter estimation has been performed to determine the values of the parameter from the daily case data using numerical technique and determined the value of the basic reproductive number for the outbreak as <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" id="M1"> <a:msub> <a:mrow> <a:mi mathvariant="script">R</a:mi> </a:mrow> <a:mrow> <a:mn>0</a:mn> </a:mrow> </a:msub> <a:mo>=</a:mo> <a:mn>5.86</a:mn> </a:math> .