Awareness programs control infectious disease – Multiple delay induced mathematical model

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.

A generic model for a single strain mosquito-transmitted disease with memory on the host and the vector

“…This fact implies that human memory is related to some kind of awareness, which lessens the human contact rate with the vector over time. This result agrees with the previous findings from the literature (see, Acharya et al (2005); Rosenbaum et al (1995); Sardar et al (2014);Greenhalgh et al (2014)), where they argued that human awareness about epidemic spread will effectively reduce the dengue incidence in some area.…”

Behavioural change models for infectious disease transmission: a systematic review (2010–2015)

“…The largest category embodies 76 references managing information as a dynamic parameter [3,25,34,40,43,47–50,53,55,60,61,65–68,70,71,74,77,80,82,86,92,94–96,99,100,102,104–109,113,115–117,119–126,128–131,133,134,137,148,149,153,157,161,165,166,168,171–178,184–186,188,189]. In this category, instead of a threshold, the information is a continuous input in the decision-making process of individuals.…”

Optimal media reporting intensity on mitigating spread of an emerging infectious disease

“…In recent years, a growing number of studies have focused on understanding and quantifying the impact of such behaviour influencing factors on the spread of infectious diseases [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. A number of studies have employed mathematical models to assess the impact of media reports on emerging infectious disease prevention and control [4,5,[19][20][21][22][23][24][25][26][27][28][29][30]. Recently, Greenhalgh et al [19] presented a brief and nice commentary on the literature related to awareness and their effects on the dynamics of diseases.…”