Dynamical behaviour of SIR model with coinfection: The case of finite carrying capacity. (20th May 2019)

• Record Type: Journal Article
• Authors: Ghersheen, Samia; Kozlov, Vladimir; Tkachev, Vladimir G.; Wennergren, Uno
• Other Names: Vigo-Aguiar Jesus guestEditor.; Kumam Poom guestEditor.
• Is Part Of: Mathematical methods in the applied sciences. Volume 42:Number 17(2019)
• Page Start: 5805
• Page End: 5826
• Publication Date: 2019-05-20
• Subjects: carrying capacity -- coinfection -- global stability -- linear complementarity problem -- SIR model; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.5671
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : Multiple viruses are widely studied because of their negative effect on the health of host as well as on whole population. The dynamics of coinfection are important in this case. We formulated an susceptible infected recovered (SIR) model that describes the coinfection of the two viral strains in a single host population with an addition of limited growth of susceptible in terms of carrying capacity. The model describes five classes of a population: susceptible, infected by first virus, infected by second virus, infected by both viruses, and completely immune class. We proved that for any set of parameter values, there exists a globally stable equilibrium point. This guarantees that the disease always persists in the population with a deeper connection between the intensity of infection and carrying capacity of population. Increase in resources in terms of carrying capacity promotes the risk of infection, which may lead to destabilization of the population.