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. Contrarily, the second is shrewd and considerate and will remain calm when confronted with challenges.1

D 1 and 2 represent the rates of recovery of the vulnerable impatient group as well as the level-headed group as well as the level-headed group. A key characteristic of a well-informed group is that panic can get out of the group that is agitated. The t 1 and the t2 are the time delays for the susceptible impatient group as well as the level-headed group.1 The impatient group is able to spread infection within the group. We will assume that the original conditions are. The rates of infection of both groups is a bilinear infection rate To calculate Model (3), the basic reproduction number may be calculated as [49, 50[49, 50] (II) The number of vulnerable individuals rises quickly because of the lack of knowledge about the frequency of emergencies. 3.1 The logistic model can greatly take into account elements that influence the rate at which the number is restricted by the environmental (e.g. emergency) so the models for growth in the logistic sector are more suited for the specific circumstances.

Stability analysis. 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 It is important to note that the two equations that are recovered are separate of Model (3) which means they are not affecting the dynamic analysis. where K is the capacity of carrying as well as r being the fundamental rise rate constant. Model (3) is able to be separated from Model (3) to produce an equivalent model as follows: (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 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 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 . ( 5 ) 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 We review the model’s design Model (5) as follows: (IV) The people who are cured of the patient group as well as the calm group have the possibility of permanent immunity. (i) In the case of any possible parameter that can be considered, the E zero ( 0,0.0.0. ) equilibrium point will always be present.1 The model is described as follows. (ii) It contains three equilibrium points. 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 ) These are, E 1 0 = ( K 1 ( R 1 – D ) ( r 1 , 0 ), K 2 ( R 2 – D ) ( r 2, 0 ) , E 2 0 = ( K 1 ( R 1 – D ) R 1, 0,0 ) , and E 3 zero = ( 0,0 , K2 ( R 2 – D ) R 2, 0 ) as long as the conditions of r 1 – > zero and r2 and more than 0 are satisfied.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. (iii) The singular positively equilibrium point, E * ( S 1 *, I 1 * S 2 * , I * ) (iii) when R 0 > 1, R 1 – D > zero, and r2 – – d – b 2 I 1 > 1 .1 The d value represents the death rate of the person. In this case, S 1 * = d d 1 B 1 E – D 1. * = r1 – the d 1 ( 1 R 0 – 1 ) ( 1 – 1 R 0 ) equals ( the d and the 2 ) I 2 * b 2 e – 2 I 1 , and the I2 * is ( the r 2 is a the d- b 2 1 * ) K 2 B 2 I * I 1 * e – d 2 R 2. ( 2) ) . 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. 3.1 Stability of the equilibrium in a panic-free state.1 D 1 and 2 represent the rates of recovery of the vulnerable impatient group as well as the level-headed group as well as the level-headed group. Theorem 3.1. the equilibrium without panic E 1 0 . is locally asymptotically steady in the event that R 0. The t 1 and the t2 are the time delays for the susceptible impatient group as well as the level-headed group. [ l – ( r 1 – d – 2 r 1 S 1 K 1 ) ] [ l – e – ( d + l ) t 1 b 1 S 1 + ( d + d 1 ) ] [ l – ( r 2 – d – 2 r 2 S 2 K 2 ) ] [ l + ( d + d 2 ) ] = 0 . ( 6 ) We will assume that the original conditions are.1

Evidently, according to (6) the equation, we can obtain the Eigenvalues. To calculate Model (3), the basic reproduction number may be calculated as [49, 50[49, 50] L 2 = R 1 – d 2 R 1 S 1 1 = r1 – 2 r 1 K 1 K 1 ( R 1 – D ) 1. ( the 1st – the second ) 3. L 3 = R 2 (d) – 2 r 2. Stability analysis. S 2.1 It is important to note that the two equations that are recovered are separate of Model (3) which means they are not affecting the dynamic analysis. K 2 = the r 2 – the d 2 R 2 K 2 K 2 ( R 2 – D ) R 2 = – ( R 2 – D ) Model (3) is able to be separated from Model (3) to produce an equivalent model as follows: Then, the second Eigenvalue of (6) is rewritten to be.1 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 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 . ( 5 ) If you have t 1 = zero and R 0 is zero then, suppose that l4 = i and v ( V is greater than zero ) and transform I v with (10).1

We review the model’s design Model (5) as follows: The separation of imaginary and real parts using the Euler formula is possible to obtain. (i) In the case of any possible parameter that can be considered, the E zero ( 0,0.0.0. ) equilibrium point will always be present. We square and then add to the equations for (11) and (11) to yield. (ii) It contains three equilibrium points.1 Because R 0.0 .The Eigenvalues for the equilibrium value E 2 zero are: l 1 = – ( the ratio r 1-d ) ( L 2 = R 2 + d > 0 the equation l 3 is d + d 2 > 0 and L 4 = K 1. ( the ratio r 1 – D ) ( e ( d – ( the d and the ) T 1 b 1r1 – ( the sum of d and d ) Thus, E 2 0 isn’t locally asymptotically steady.1