Threshold dynamics of reaction-diffusion partial differential equations model of Ebola virus disease

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

We study the reaction-diffusion Ebola PDE model that consists of equations that govern the evolution of susceptible, infected, recovered and deceased human individuals, as well as Ebola virus pathogens in the environment, with diffusive terms in all except the equation of the deceased human individuals. Under the setting of a spatial domain that is bounded, we prove the global well-posedness of the system; in contrast to the previous work on similar models such as cholera, avian influenza, malaria and dengue fever, diffusion coefficients may be different. Moreover, we derive its basic reproduction number, and under the condition that the diffusion coefficients of the susceptible and infected hosts are same, we prove the global stability of the disease-free-equilibrium, and uniform persistence in cases when the basic reproduction number lies beneath and above one, respectively. Again, we do not require that the diffusion coefficients of the recovered hosts be the same as the diffusion coefficients of the susceptible and infected hosts, in contrast to previous work on other models of infectious diseases. Another technical difficulty in our model is that the solution semiflow is not compact due to the lack of diffusion in the equation of the deceased human individuals; we overcome this difficulty using functional analysis techniques concerning Kuratowski measure of non-compactness.

Original languageEnglish
Article number1850108
JournalInternational Journal of Biomathematics
Volume11
Issue number8
DOIs
StatePublished - Nov 1 2018

Keywords

  • Basic reproduction number
  • Ebola
  • persistence
  • stability

Fingerprint Dive into the research topics of 'Threshold dynamics of reaction-diffusion partial differential equations model of Ebola virus disease'. Together they form a unique fingerprint.

Cite this