A Mathematical Model of the Evolution and Spread of Pathogenic Coronaviruses from Natural Host to Human Host

Bozkurt Yousef F., Yousef A., Baleanu D., Alzabut J.

Chaos Solitons & Fractals, cilt.1, sa.1, ss.1-30, 2020 (SCI-Expanded)

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 1 Sayı: 1
  • Basım Tarihi: 2020
  • Doi Numarası: 10.1016/j.chaos.2020.109931
  • Dergi Adı: Chaos Solitons & Fractals
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Compendex, INSPEC, zbMATH
  • Sayfa Sayıları: ss.1-30
  • Erciyes Üniversitesi Adresli: Evet

Özet

Coronaviruses are highly transmissible and are pathogenic viruses of the 21st century worldwide. In general, these viruses are originated in bats or rodents, while the transmission of the infection to the human host is caused by domestic animals that represent in the habitat the intermediate host. In this study, we review the current collected information about coronaviruses and establish a model of differential equations with piecewise constant arguments to discuss the spread of the infection from the natural host to the intermediate, and from them to the human host, while we focus on the potential spillover of bat-borne coronaviruses. The local stability of the positive equilibrium point of the model is considered via the Linearized Stability Theorem. Besides, we discuss the global stability by employing an appropriate Lyapunov function. To analyze the outbreak in early detection, we incorporate the Allee effect at time  and obtain stability conditions for the dynamical behavior. Furthermore, it is shown that the model demonstrates Neimark-Sacker Bifurcation. Finally, we conduct numerical simulations to support the theoretical findings. 

Coronaviruses are highly transmissible and are pathogenic viruses of the 21st century worldwide. In general, these viruses are originated in bats or rodents, while the transmission of the infection to the human host is caused by domestic animals that represent in the habitat the intermediate host. In this study, we review the current collected information about coronaviruses and establish a model of differential equations with piecewise constant arguments to discuss the spread of the infection from the natural host to the intermediate, and from them to the human host, while we focus on the potential spillover of bat-borne coronaviruses. The local stability of the positive equilibrium point of the model is considered via the Linearized Stability Theorem. Besides, we discuss the global stability by employing an appropriate Lyapunov function. To analyze the outbreak in early detection, we incorporate the Allee effect at time  and obtain stability conditions for the dynamical behavior. Furthermore, it is shown that the model demonstrates Neimark-Sacker Bifurcation. Finally, we conduct numerical simulations to support the theoretical findings.