On a reaction–diffusion system modelling infectious diseases without lifetime immunity
European Journal of Applied Mathematics
; 33(5):803-827, 2022.
Article
in English
| ProQuest Central | ID: covidwho-2315409
ABSTRACT
In this paper, we study a mathematical model for an infectious disease caused by a virus such as Cholera without lifetime immunity. Due to the different mobility for susceptible, infected human and recovered human hosts, the diffusion coefficients are assumed to be different. The resulting system is governed by a strongly coupled reaction–diffusion system with different diffusion coefficients. Global existence and uniqueness are established under certain assumptions on known data. Moreover, global asymptotic behaviour of the solution is obtained when some parameters satisfy certain conditions. These results extend the existing results in the literature. The main tool used in this paper comes from the delicate theory of elliptic and parabolic equations. Moreover, the energy method and Sobolev embedding are used in deriving a priori estimates. The analysis developed in this paper can be employed to study other epidemic models in biological, ecological and health sciences.
Mathematics; Infectious disease model for Cholera; reaction–diffusion system; global existence and uniqueness; asymptotic behaviour and global attractor; 35K57; 92C60; Infectious diseases; Partial differential equations; Immunity; Mathematical models; Pandemics; Epidemics; Bacteria; Medical research; Cholera; Influenza; Elliptic functions; Viruses; Asymptotic properties; Energy methods; Coronaviruses; Biological models (mathematics); COVID-19
Full text:
Available
Collection:
Databases of international organizations
Database:
ProQuest Central
Language:
English
Journal:
European Journal of Applied Mathematics
Year:
2022
Document Type:
Article
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