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A mathematical model of the evolution and spread of pathogenic coronaviruses from natural host to human host

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  • Bozkurt, Fatma
  • Yousef, Ali
  • Baleanu, Dumitru
  • Alzabut, Jehad

Abstract

Coronaviruses are highly transmissible and are pathogenic viruses of the 21st century worldwide. In general, these viruses are originated in bats or rodents. At the same time, 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 currently 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 global stability by employing an appropriate Lyapunov function. To analyze the outbreak in early detection, we incorporate the Allee effect at time t and obtain stability conditions for the dynamical behavior. Furthermore, it is shown that the model demonstrates the Neimark-Sacker Bifurcation. Finally, we conduct numerical simulations to support the theoretical findings.

Suggested Citation

  • Bozkurt, Fatma & Yousef, Ali & Baleanu, Dumitru & Alzabut, Jehad, 2020. "A mathematical model of the evolution and spread of pathogenic coronaviruses from natural host to human host," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    • Handle: RePEc:eee:chsofr:v:138:y:2020:i:c:s0960077920303301
    DOI: 10.1016/j.chaos.2020.109931
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    References listed on IDEAS

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    2. Okposo, Newton I. & Adewole, Matthew O. & Okposo, Emamuzo N. & Ojarikre, Herietta I. & Abdullah, Farah A., 2021. "A mathematical study on a fractional COVID-19 transmission model within the framework of nonsingular and nonlocal kernel," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    3. Abdullah, & Ahmad, Saeed & Owyed, Saud & Abdel-Aty, Abdel-Haleem & Mahmoud, Emad E. & Shah, Kamal & Alrabaiah, Hussam, 2021. "Mathematical analysis of COVID-19 via new mathematical model," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    4. Matouk, A.E., 2020. "Complex dynamics in susceptible-infected models for COVID-19 with multi-drug resistance," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    5. Hussain, Takasar & Aslam, Adnan & Ozair, Muhammad & Tasneem, Fatima & Gómez-Aguilar, J.F., 2021. "Dynamical aspects of pine wilt disease and control measures," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).

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