I) In emergency situations the

2 Model formulation. The models of time-delay-related viral and time-delay rumors as well as the optimal control models were examined in the above paragraphs. People in the group are aware that the occurrences of emergencies and the anxiety that results from the occurrence of emergencies can have a delayed impact.1

However, the model for spreading panic in time-delayed emergency situations was not discussed. The model that is delayed corresponds more closely to the phenomena immediately following the occurrence. In reality emotions influence on the behavior of people and, in particular, anxiety.

We therefore develop a model of panic spreading that is delayed in time, based on the model of epidemic.1 In addition emotions possess three distinct characteristics which include holistic, process and individual variability, of which individual variation is the most prominent characteristic. (I) In emergency situations the individual differences in traits (gender age, gender personality, etc.) can affect the individual’s ability to spread panic.1 Individual differences in emotional expression are determined by the personality of the individual. The main focus is on the influence of the individual’s personality upon panic spread. Different people have different emotions perception capabilities. So, in the light of studies on personality [47the group was divided into an unpatient group and the calm group.1 Most of the time, those who are anxious have a tendency to be emotionally affected and irrational however, calm and rational people are more rational.

The first is adventurous and reckless, and easily influenced by feelings of other people. So, it is essential to be aware of the different personalities of individuals personalities in spreading anxiety in the face of emergencies.1 Contrarily, the second is shrewd and considerate and will remain calm when confronted with challenges. This is a great way to simulate the process of emotional expression in actual life.

A key characteristic of a well-informed group is that panic can get out of the group that is agitated. Thus, it is of major theoretical and practical value to investigate the effects of delay in time on the spreading of panic.1 The impatient group is able to spread infection within the group. The remainder of this research is structured in the following manner in Section 2. an algorithm for time-delayed spreading of panic is discussed. The rates of infection of both groups is a bilinear infection rate In Section 3., the local and general stability of the two equilibriums are studied through mathematical analysis. (II) The number of vulnerable individuals rises quickly because of the lack of knowledge about the frequency of emergencies.1 We formulate the optimal control model, and we solve crucial conditions for an optimally designed solution using the maxima principle of Pontryagin in Section 4. The logistic model can greatly take into account elements that influence the rate at which the number is restricted by the environmental (e.g.1 emergency) so the models for growth in the logistic sector are more suited for the specific circumstances. In Section 4, the theoretical outcomes of analysis using numerical simulation are described in Section 5. So, in the anxious group as well as the calmer group, the vulnerable individuals are governed by the classic single-species logistic growth model.1

A brief summary is presented in Section 6. where K is the capacity of carrying as well as r being the fundamental rise rate constant. 2 Model formulation. (III) In times of emergency due to the length of period of time that is required for susceptible people to get in contact with the surrounding anxious people to develop the symptoms of people, we define the specific time as the spread time, which is determined by t1 and t 2 .The speed of growth for the patient group that is infected depends not only on the number at the moment before between t1 and t1, as well as the chance that the affected impatient group was able to survive from the time that t1 – t1 occurred until the moment of t .1 People in the group are aware that the occurrences of emergencies and the anxiety that results from the occurrence of emergencies can have a delayed impact. Similar to changing the speed of progression for the affected level-headed population is dependent not only on the number at the moment before that t was t, as well as the chance that the affected level-headed population lived from the moment the t-t-2 point to the moment of t .1 The model that is delayed corresponds more closely to the phenomena immediately following the occurrence. (IV) The people who are cured of the patient group as well as the calm group have the possibility of permanent immunity.

We therefore develop a model of panic spreading that is delayed in time, based on the model of epidemic.1 The model is described as follows. (I) In emergency situations the individual differences in traits (gender age, gender personality, etc.) can affect the individual’s ability to spread panic. d S 1 d t = r 1 S 1 ( 1 – S 1 K 1 ) – b 1 I 1 S 1 – d S 1 , d I 1 d t = e – d t 1 b 1 S 1 ( t – t 1 ) I 1 ( t – t 1 ) – ( d + d 1 ) I 1 , d R 1 d t = d 1 I 1 – d R 1 , d S 2 d t = r 2 S 2 ( 1 – S 2 K 2 ) – b 2 I 1 S 2 – d S 2 , d I 2 d t = e – d t 2 b 2 S 2 ( t – t 2 ) I 1 ( t – t 2 ) – ( d + d 2 ) I 2 , d R 2 d t = d 2 I 2 – d R 2 . ( 3 ) The main focus is on the influence of the individual’s personality upon panic spread.1 In this model the patient group and the calm group could be split into three states that include susceptible, infected and recovering, represented by S 1, I 1 , as well as R 1, and S 2, I 2 , as well as R 2 at the time t according to.

So, in the light of studies on personality [47the group was divided into an unpatient group and the calm group.1 The d value represents the death rate of the person. The first is adventurous and reckless, and easily influenced by feelings of other people.

B 1 and B 2 represent the mortality rates of the susceptible impatient group as well as the level-headed group as well as the level-headed group.