The influence of awareness campaigns on the spread of an infectious disease: a qualitative analysis of a fractional epidemic model

Abstract

Mass-media coverage is one of the most widely used government strategies on influencing public opinion in times of crisis. Awareness campaigns are highly influential tools to expand healthy behavior practices among individuals during epidemics and pandemics. Mathematical modeling has become an important tool in analyzing the effects of media awareness on the spread of infectious diseases. In this paper, a fractional-order epidemic model incorporating media coverage is presented and analyzed. The problem is formulated using susceptible, infectious and recovered compartmental model. A long-term memory effect modeled by a Caputo fractional derivative is included in each compartment to describe the evolution related to the individuals’ experiences. The well-posedness of the model is investigated in terms of global existence, positivity, and boundedness of solutions. Moreover, the disease-free equilibrium and the endemic equilibrium points are given alongside their local stabilities. By constructing suitable Lyapunov functions, the global stability of the disease-free and endemic equilibria is proven according to the basic reproduction number . Finally, numerical simulations are performed to support our analytical findings. It was found out that the long-term memory has no effect on the stability of the equilibrium points. However, for increased values of the fractional derivative order parameter, each solution reaches its equilibrium state more rapidly. Furthermore, it was observed that an increase of the media awareness parameter, decreases the magnitude of infected individuals, and consequently, the height of the epidemic peak.

Challenges and difficulties in implementing and adopting isolation and quarantine measures among internally displaced people during the COVID-19 pandemic in Mali (161/250)

“…Spreading awareness was particularly identified as an efficient means, especially when conducted by influential people in the community such as religious and community leaders. These results are complemented by other researchers who found that public awareness is an efficient mean to limit the spread of infectious diseases ( Abdelhafiz et al, 2020 , Akdim et al, 2021 ). They suggest that the role of public awareness and that of influential people should not be overlooked in the context of a pandemic such as COVID-19 ( Wan et al, 2020 ).…”

Study of Fractional Order SEIR Epidemic Model and Effect of Vaccination on the Spread of COVID-19

“…Several fractional operators have been devised to explore the dynamics of epidemic systems, including Caputo-Fabrizio, Riemann-Liouville, Caputo, Hadamard, Atangana-Baleanu, Katugampola, and others. We employed the Caputo operator to examine the dynamics of COVID-19, since it has a nonlocal and nonsingular exponential kernel [35][36][37][38][39][40]. The dynamical and nonstandard computational study of a heroin epidemic model is discussed by Raza et al [41].…”

Qualitative analysis of a fractional-order two-strain epidemic model with vaccination and general non-monotonic incidence rate

“…In this regard, several fractional-order models have studied epidemic dynamics through a system of fractional ordinary differential equations [ 6 – 10 , 14 – 20 ]. Many works involving fractional calculus are mainly focused on SIR-type models (see for instance [ 6 , 14 , 15 , 19 ]). Saeedian et al [ 6 ] studied the effect of memory on the evolution of epidemics by means of fractional SIR epidemic model using the Caputo fractional operator.…”

“…Recently, Djilali et al [ 20 ] presented and analyzed a fractional epidemic model with nonlinear incidence rate. Lately, Akdim et al [ 19 ] have mainly studied the role of awareness campaigns strategies on the spread of an infectious disease using a Caputo fractional epidemic model with nonlinear-incidence function.…”