A fractional SEIQR model on diphtheria disease

Mohammad Ghani, Ika Qutsiati Utami, Fadillah Willis Triyayuda, Mutiara Afifah

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)


The purpose of this paper is to study a fractional mathematical model on diphtheria disease, considering the parameters of natural immunity, treatment, and vaccination. This model includes five compartments, namely, the susceptible, exposed, infected, quarantined, and recovered sub population. All compartments involve the memory effect and long-rate interactions that is modeled by a Caputo fractional derivative. This paper starts with the study of some analytical results. We first present the preliminary concepts of fractional calculus. The well-posedness of our fractional model is proved based on the boundedness, non-negativity, existence, and uniqueness. The existence of local, and global stability are also studied based on the Magniton’s theorem and the appropriate Lyapunov function. We further apply the predictor–corrector scheme to establish the numerical simulations. The validation of our fractional model is based on the real data by using the least square technique. We also present the comparison results of root mean square error for varying fractional order α= 1 , α= 0.95 , α= 0.9 , α= 0.85 , and α= 0.8.

Original languageEnglish
Pages (from-to)2199-2219
Number of pages21
JournalModeling Earth Systems and Environment
Issue number2
Publication statusPublished - Jun 2023


  • Disease transmission
  • Fractional-order differential equation
  • Least square technique
  • Lyapunov function
  • Magniton’s theorem
  • Predictor–corrector scheme
  • Stability analysis
  • Vaccination


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