Awareness programs control infectious disease - Multiple delay induced mathematical model

David Greenhalgh, Sourav Rana, Sudip Samanta, Tridip Sardar, Sabyasachi Bhattacharya, Joydev Chattopadhyay

Research output: Contribution to journalArticle

34 Citations (Scopus)

Abstract

We propose and analyze a mathematical model to study the impact of awareness programs on an infectious disease outbreak. These programs induce behavioral changes in the population, which divide the susceptible class into two subclasses, aware susceptible and unaware susceptible. The system can have a disease-free equilibrium and an endemic equilibrium. The expression of the basic reproduction number and the conditions for the stability of the equilibria are derived. We further improve and study the model by introducing two time-delay factors, one for the time lag in memory fading of aware people and one for the delay between cases of disease occurring and mounting awareness programs. The delayed system has positive bounded solutions. We study various cases for the time delays and show that in general the system develops limit cycle oscillation through a Hopf bifurcation for increasing time delays. We show that under certain conditions on the parameters, the system is permanent. To verify our analytical findings, the numerical simulations on the model, using realistic parameters for Pneumococcus are performed.
LanguageEnglish
Pages539-563
Number of pages25
JournalApplied Mathematics and Computation
Volume251
Early online date15 Dec 2014
DOIs
Publication statusPublished - 15 Jan 2015

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Disease control
Multiple Delays
Infectious Diseases
Time Delay
Time delay
Mathematical Model
Mathematical models
Fading Memory
Positive Systems
Basic Reproduction number
Endemic Equilibrium
Hopf bifurcation
Time Lag
Bounded Solutions
Mountings
Limit Cycle
Hopf Bifurcation
Divides
Oscillation
Verify

Keywords

  • epidemic model
  • numerical simulation
  • Hopf bifurcation
  • stability analysis
  • time delay
  • awareness programs

Cite this

Greenhalgh, David ; Rana, Sourav ; Samanta, Sudip ; Sardar, Tridip ; Bhattacharya, Sabyasachi ; Chattopadhyay, Joydev. / Awareness programs control infectious disease - Multiple delay induced mathematical model. In: Applied Mathematics and Computation. 2015 ; Vol. 251. pp. 539-563.
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Awareness programs control infectious disease - Multiple delay induced mathematical model. / Greenhalgh, David; Rana, Sourav; Samanta, Sudip; Sardar, Tridip; Bhattacharya, Sabyasachi; Chattopadhyay, Joydev.

In: Applied Mathematics and Computation, Vol. 251, 15.01.2015, p. 539-563.

Research output: Contribution to journalArticle

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