This is why the use of a delay

Guo et al. (19) developed a brand new epidemic model that incorporates local mapping relationships within two layers of a time-varying network in order to investigate the impact of information diffusion on spreading of the epidemic. Based on this we determine the severity of measures taken by the government as control variables and develop the most efficient control model to minimize the spread.1 In natural as well as social events, patterns of a variety of models are correlated not just to the current situation , but also to the past developments, such as the time of incubation for viruses as well as the time delay of transmission signals.

The existence and the necessary conditions of the best solution are established.1 Therefore, the use of a time-delay to investigate the consequences of such events is extensively utilized within computer networks as well as biochemical systems across various areas. In the end, the accuracy of this conclusion can be proved through simulations using numerical models. Zheng et al. [27proposed a two-strain delay model, and determined both the equilibrium and threshold of this model.1

1 Introduction. Wu [28] proposed an nonlinear incidence and distributed latent delay model based on SIR and studied the moving waves near the point where equilibrium occurs in the model. With the rapid growth and the growth that the economy is experiencing, protection of disasters has become a popular subject in the daily lives of.1

With COVID-19 as the basis, Khan et al. [29] created an equation that incorporates random perturbations and time delays , and found the conditions for the elimination from the disease. Intense places and high-rise buildings are on the rise in popularity, and they are attracting a significant number of people, which can cause social stability and security when it comes to disasters like earthquakes, fires as well as a variety of other emergency situations.1 Similar to that, Rihan [30] proposed the SIAQR delay model that focuses on the spreading of the virus within populations. The effects of such emergencies are negative emotions such as anger, panic, and agitation that could take over the entire group [1-4], leading to a herding pattern which can lead to a clogging of the group [55.1

Xia et al. [31] investigated the impact of delayed recovery and non-uniform spread of disease on transmission within well-organized populations. This is why it is crucial to demonstrate emotions during emergency situations. Chen et al. [32] developed an improved model of rumor spreading that takes into account the time delay of the interactive systems.1 Epidemic models are frequently utilized in the development of transmission models because of their distinct features, like spreading of rumor [6-8] as well as virus spread [9 10, and emotion spread [11 12, 11[11, 12]. In recommending the related strategies this study can help limit the spread of rumor.1 For example, Hu et al. [13] created an rumor model that considered the number of wise people in a crowd.

Zhang et al. [33] discovered a time-delay model that modeled the transformation of public opinion and examined the impact of delay in time on the equilibrium point. They also investigated its impact on the spread of rumor.1 Hu [34] modelled the spread of reaction-diffusion theories using time delay as well in their variations, based on complex networks. Jiang et al. [14] suggested a new rumor model that analyzes the mechanisms that interact between spreading rumor and debunking processes. He also studied the spread within the boundary of the model as well as that of the Turing bifurcation.1 Liu et al. [15] designed a bird-to human spread model incorporating logistics growth, as well as an Allee effect, and explored the dynamic behaviour in the models.

Emergencies can lead to the spreading of unreliable information and panic and panic, and the government must adopt appropriate measures, like publicizing official information and preventing with the use of force.1 Chen [16] created the dynamic model through analysing the impact of sentiment of investors on the market for stocks and constructed a simulation of the relevant theoretical findings. The implementation of these actions can be described as the best control issue. Zhao et al. [17] used using the SIR method and the bond percolation theories to study the multi-route transmission of the epidemic using multiplex networks.1 The goal is to utilize the least amount of cost when tackling emergency situations. In addition, we identified the threshold of epidemic and size of outbreaks by calculating. Bolzoni et al. [35] looked at the problem of time-optimal control within an epidemiological model, and analyzed the most effective strategy can decrease the transmission of viruses.1

To analyze the impact of patch distribution on virus propagation, Zhao [18] proposed a hybrid patch distribution strategy by combining the advantages of both the traditional-centralized patch distribution strategy and the traditional-decentralized patch distribution strategy. Grandits [36] studied the stochastic control model for epidemics and utilized to solve the HJB equation to investigate the most effective control strategies.1 Guo et al. [19] have developed a novel epidemic model that uses local mapping relationships that are part of the form of a two-layer time-varying network that allows them to examine the effects of diffusion of information on the propagation of epidemics. Dai [37] looked at the semigroup theory and minimize sequences to establish the existence of certain estimates of the singular robust solution and the optimal combination of optimal control problems and.1

However, in both natural or social processes, changes of various models are linked not only to the present circumstances but also to previous growth dynamics, like the time it takes to incubate viruses as well as the delays in transmission signals. Hang et al. [38] suggested an optimal control strategy for avian influenza model that includes delay, and then analyzed the results using Pontryagin’s maximal principle.1 This is why the use of a delay in time to examine the effects that these phenomena cause is frequently employed for computer-based networks as well as biology [24-25] within numerous areas. Bashier [39] proposed an optimal control model using delay differential equations that are based on the SIR epidemic model, and then examined the sensitivity of two strategies to delays in time.1 Zheng et al. [27suggested a two-strain delayed model that calculated its threshold as well as the point at which the model reaches equilibrium.

Wu [40] studied nonlinear optimal control issues that involve multiple delays by with gradient-based optimization algorithms. Wu [28] has developed a distributed and nonlinear latent delay model based on SIR and examined the traveling waves that occur at the equilibrium of the model.1 To tackle the dynamics model of spread of viruses, Sun et al. [41] developed an explanation of disseminated FMD with an incubation time fixed and non-localized infections to investigate the most effective ways to control it.