The Impact of Awareness Programs with Recruitment and Delay on the Spread of an Epidemic

Abstract

A compartment epidemic model with delay is given to discuss the impact of awareness programs on the spread and control of infectious diseases in a given region. It is assumed that there is a constant recruitment rate in the cumulative density of awareness programs, and further it is assumed that awareness programs can influence the susceptible to a limited extent. The system exhibits two equilibria: the disease-free equilibrium is stable if the basic reproduction number is less than unity for any delay and the unique endemic equilibrium exhibits Hopf-bifurcation under certain conditions. Numerical simulations prove the results of analysis and the significance of awareness programs in preventing and controlling the diseases, by investigating the relationship between the proportion of the infective and the dissemination rate and the implementation rate, respectively.

Effects of awareness program and delay in the epidemic outbreak

“…Recently, a good number of research article has appeared in the literature of epidemiology, which considered the awareness program as a separate state variable, where the execution of the awareness program is proportional to the number of infected cases . However, the dynamics and the unit of the cumulative density of the awareness program are not always clear.…”

“… also studied the impact of information transmission on the dynamics of sexually transmitted infections assuming that the whole population is aware of risk but only a certain proportion chooses to respond by limiting their contact with infected individuals. Recently, researchers investigated the disease dynamics by incorporating the effect of awareness programs explicitly . They studied epidemic models considering the cumulative density of the awareness program as a separate state variable.…”

Dynamics of vaccination in a time-delayed epidemic model with awareness

“…If δ = 0, this describes a perfect vaccine, while δ > 0 describes a vaccine resulting in temporary (waning) immunity. Similar to some earlier works [2,52,53], it is assumed that upon losing immunity, a certain proportion, p, of individuals will join the aware susceptible class while the remaining proportion, q = 1 − p, will return to the unaware susceptible class. With these assumptions, a modified model has the form Parameter Definition b birth rate (same as the death rate) β disease transmission rate σ s rate of reduction in susceptibility to infection due to being aware r recovery rate α o growth rate of disease awareness from the reported number of infections α growth rate of disease awareness arising from aware individuals ω o growth rate of disease awareness from global awareness campaigns λ o rate of loss of awareness generated by awareness dissemination λ rate of loss of awareness in susceptible individuals…”

Estimador Robusto Recursivo para Sistemas Singulares Incertos com Atraso Invariante no Estado via Método de Elevação

“…Por outro lado, os sistemas com atraso no estado constituem uma classe de sistemas cuja dinâmica futura depende dos estados atual e passado. Esta classe está presente em diversas aplicações, como sistemas em rede (Liu et al, 2014), problemas de atraso na transferência de informações e risco de perda de dados (Zhang et al, 2013), propagação de epidemias (Zuo et al, 2015) e em sistemas de veículos aéreos não tripulados (Li et al, 2016). O atraso pode afetar consideravelmente as características da planta, alterando sua dinâmica e aumentando a dificuldade na análise de estabilidade e no projeto de estimadores.…”