Effect of negligence and length of time delay in spontaneous behavioural changes for the response to epidemics

It is understood that public health education and informal communications can impact on perceptions of disease threat, which could result in influencing behaviour of individuals to take any possible self‐protective measures. On the other hand, the information about the actual status of the disease dynamics, on which the public health education is based, can be known only after its data are collected and processed. This may take a significant amount of time, and therefore, there is a time gap between what the public knows about the prevalence of the disease and the actual distribution of the disease in the population. Furthermore, there is a memory decay and negligence from the side of the population in applying protective mechanisms as the disease becomes endemic. In this paper, a mathematical model for human disease epidemics that takes a change in human behaviour and effect of negligence into account is formulated and analysed. The model investigates the effect of negligence (from the side of the population) and time lag (in disclosing the actual prevalence of the disease) in the dynamics and control of the disease. The numerical results show that the length of the delay has a significant impact on the control strategy rather than on the dynamics without control. In addition, announcing the prevalence value once every time it is updated and keeping that value constant has the same effect on the dynamics as compared with updating the same continuously. Moreover, it is also shown that the negligence parameter significantly affects the overall prevalence of the disease.