Modeling the impacts of awareness and limited medical resources on the epidemic size of a multi-group SIR epidemic model

Vijay Pal Bajiya, Jai Prakash Tripathi, Vipul Kakkar, Yun Kang

Research output: Contribution to journalArticlepeer-review

Abstract

The pharmaceutical interventions of emerging infectious diseases are constrained by the available medical resources such as drugs, vaccines, hospital beds, isolation places and the efficiency of the treatment. The awareness of the population also plays an important role in reducing contacts and consequently, reducing the disease transmission rate. In this paper, we propose a multi-group Susceptible, Infected and Recovered (SIR) epidemic model incorporating the awareness of population and the saturated treatment function that describes the effects of the availability of medical resources for treatment. We assume that the treatment of the infected individuals of a group is affected by the medical resources for the treatment of each group. We calculate the basic reproduction number R0 in the term of the awareness parameter using the next generation approach. We determine the local and global stabilities of equilibrium (disease free equilibrium and endemic equilibrium) in terms of R0 and the availability of medical resources for treatment. We obtain that backward bifurcation occurs at R0 = 1 along with the existence of multiple endemic equilibria when R0 < 1. Further, we consider the special case with a single group epidemic system and ensure the existence of multiple endemic equilibria. We showed a necessary condition on the parameter related to the availability of medical resources when backward bifurcation occurs. This situation indicates that reducing the basic reproduction number below unity is not sufficient to remove the disease when the medical resources for treatment are scarce. We used numerical simulations to support and counterpart our theoretical results and discussed the impacts of the awareness of susceptible population and availability of medical resources for treatment in each group, on the epidemic size of each group. Our findings suggest that in the case of limited medical resources, the high treatment rate and awareness of the population are very helpful to control the disease (to reduce the prevalence of infection) and the eradication of disease also depends on initial population sizes. More importantly, it is also obtained that sufficient medical resources for every group are required to eradicate the disease from an entire population.

Original languageEnglish (US)
Article number2250045
JournalInternational Journal of Biomathematics
Volume15
Issue number7
DOIs
StatePublished - Oct 1 2022
Externally publishedYes

Keywords

  • Multi-group epidemic model
  • backward bifurcation
  • basic reproduction number
  • global stability
  • graph-theoretic results
  • limited medical supply

ASJC Scopus subject areas

  • Modeling and Simulation
  • Applied Mathematics

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