Effect of vaccination rate in multi-wave compartmental model

• Published in: European physical journal plus 2023-11, Vol.138 (11), p.995, Article 995
• Main Authors: Saiprasad, V. R., Vikram, V., Gopal, R., Senthilkumar, D. V., Chandrasekar, V. K.
• Format: Article
• Language: English
• Subjects: Applied and Technical Physics; Atomic; Complex Systems; Condensed Matter Physics; COVID-19 vaccines; Disease transmission; Epidemics; Equilibrium; Field strength; Hopf bifurcation; Infections; Infectious diseases; Mathematical and Computational Physics; Mathematical models; Molecular; Optical and Plasma Physics; Parameter identification; Pharmacists; Physics; Physics and Astronomy; Regular Article; Theoretical
• ISSN: 2190-5444; 2190-5444
• DOI: 10.1140/epjp/s13360-023-04634-6

We present a mathematical model to explore the dynamics of infectious diseases with multiple waves of infection. First, an analysis of the isolated community with multi-wave dynamics is considered. We find that the isolated community reaches disease-free equilibrium state from multi-wave state via endemic equilibrium. In addition to these states, the two-patch community facilitates the onset of birhythmicity, multi-stable states and heterogeneous endemic state for suitable parameter choices. We find that the dynamical transitions are mediated by Hopf bifurcation, transcritical bifurcation and saddle-node bifurcation on limit cycle. Specifically, we elucidate the interplay of the dispersal strength, the mean-field strength and the vaccination rate on the dynamics of the infected compartmental classes of the interconnected communities and identified the suitable ranges of these parameters to achieve disease-free equilibrium state. We also deduce the basic reproduction number ( R 0 ) using the framework of the next-generation matrix, which corroborates the stability of the endemic and disease-free equilibriums.