The asymptotic behavior of bacterial and viral diseases model on a growing domain

ABSTRACT

This paper is concerned with a reaction–diffusion system on a growing domain describing the spatial spreading of bacterial and viral diseases induced by fecal–oral transmission. We introduce a threshold parameter ${\mathrm{\Theta }}_0^{\rho }$ by means of the eigenvalue problem to explore the stability of the disease-free and endemic equilibria. By overcoming the difficulty induced by the time-dependent diffusion rates, we are further able to investigate the asymptotic behavior of solutions to the reaction–diffusion system. Compared to the model counterpart with fixed domain, biological impacts of a growing domain on the spreading of infectious diseases are obtained. We conclude that the growth of the domain is detrimental to the prevention and control of infectious diseases.

KEYWORDS:

• Reaction-diffusion system
• bacterial and viral diseases
• growing domain
• asymptotic behavior

2020 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 35K61
• 92D30

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The work is partially supported by PRC grant NSFC [12171418, 11871065] and NSF of Jiangsu Province [grant number SBK20181450].