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 ℛ0 = 5.86.
Highlights
Diphtheria is a rapidly spreading disease which is generated by Corynebacterium diphtheriae
Due to the vulnerability of diphtheria epidemics in a confined area, we propose a controlled Susceptible-LatentInfectious-Recovered (SLIR) model, which is an extension of the simple Susceptible-Infectious-Recovered (SIR) model by adjoining a compartment (L) that tracks the latent people in the cohort
We have proposed a diphtheria epidemic model and found two steady-state equilibrium points: one is disease extinction equilibrium point E0 (37), and another is infectious persistence equilibrium point E∗ (38)
Summary
Diphtheria is a rapidly spreading disease which is generated by Corynebacterium diphtheriae. To break the transmission chains of the diphtheria outbreak in the Rohingya refugee camp in Bangladesh, emergency vaccination has been applied to children since December 12, 2017, and at the end of 2017, above 90% overall coverage [12]. In a discrete time epidemic model including vaccination and vital dynamics, Parsamanesh et al [17] investigated the stability and bifurcations. Matsuyama et al [30] have analyzed the sensitivity and ambiguity based on the basic reproductive ratio R0 of the diphtheria epidemic in the Rohingya refugee camp in Bangladesh. To illustrate the disease dynamics, parameter values are estimated from the daily case data of the outbreak in the Rohingya refugee camp in Bangladesh and found to be the equilibria of the system
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