Modeling the Impact of Vaccination, Screening, Treatment on the Dynamics of Pneumonia

Authors

  • K. S. Rahman Department of Physics, Shri Siddheshwar College, Majalgaon, Beed (M.S.), India
  • S. R. Mitkari Department of Physics, Shri Siddheshwar College, Majalgaon, Beed (M.S.), India
  • S. Shaikh Department of Mathematics, Maulana Azad College, Aurangabad - 431001 (M.S.), India

DOI:

https://doi.org/10.3329/jsr.v12i4.45815

Abstract

In this paper we have presented a deterministic model for pneumonia transmission and we have used the model to avail the potential impact of therapy. The model is based on the vaccinated-susceptible-carrier-infected-recovered-susceptible compartmental structure and their possible interventions with the possibility of infected individual recovery from natural immunity. Here, we have modeled Pneumonia considering vaccination, screening and treatment with a system of nonlinear ordinary differential equation. The model reproduction number R0 is derived and the stability of the equilibria are derived. The stability of equilibrium points is analyzed. The results shows that there exists a locally stable disease free equilibrium points, E0 when R0<1 and a unique endemic equilibrium E1, when R0>1. Infection free point was found to be locally stable and if reproduction number is greater than unity, then there is unique endemic equilibrium point and if it is less than unity, the endemic equilibrium point is globally asymptotically stable and pneumonia will be eliminated.

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Published

2020-09-01

How to Cite

Rahman, K. S., Mitkari, S. R., & Shaikh, S. (2020). Modeling the Impact of Vaccination, Screening, Treatment on the Dynamics of Pneumonia. Journal of Scientific Research, 12(4), 525–536. https://doi.org/10.3329/jsr.v12i4.45815

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Section

Section A: Physical and Mathematical Sciences