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Saudi Arabia has become one of the leading top five countries based on the number of Snapchat users as of October 2018. In this project, we build a novel mathematical model to explore the future of Snapchat in general and in Saudi Arabia particularly. The model incorporates the trend of “famous Snapchatters” that is highly observed in Saudi Arabia. The model is governed by a system of nonlinear differential equations. We analyze the system qualitatively and numerically. As a result, three equilibrium points are obtained. By considering their stability, we outline different possible scenarios for the future of Snapchat. Moreover, parameter analysis is performed to investigate key parameters in the model. Furthermore, an online survey is conducted to estimate the values for the parameters in the model to explore which scenario is likely to happen in Saudi Arabia.

Snapchat is a multimedia and direct messaging application that enables users to send quick pictures, videos and messages to other users. These “Snaps” are only available to be viewed for a short time span before it is deleted permanently. This feature perhaps makes it, for some users, different and more attractable than other social network applications. Snaps posted by a user can be viewed either by “Friends” or “Followers”. Friends add each other to their contact list in order to view each other snaps. However, followers may view the snaps of users they follow without being added to their contact list. It is not easy to find friends on Snapchat without knowing their username. However, Snapchat made it easy to add friends using their phone numbers under a service called “Find Friends”. One final feature of Snapchat worth mentioning is “My Story” where snaps posted there last for twenty-four hours to be seen by friends and followers before it disappears.

Usage of Snapchat has been grown rapidly ever since its initiation in 2011 by its founders who were three undergraduates at Stanford University [

The rise of Snapchat led researchers to investigate its impact on users: in particular, how individuals use and value Snapchat, what do they share, and with whom [

Saudi Arabia has become one of the leading top five countries based on the number of Snapchat users as of October 2018 [

To our knowledge, no one has searched the future of Snapchat in Saudi Arabia based on present data, especially, as a mathematical model. In this paper, we build a mathematical model to predict the future of Snapchat. This work is motivated by a similar study that was concerned about the future of Facebook [

The dynamics of Snapchat may be formulated as a mathematical model by first assuming that the population is divided into four distinct groups: Susceptible (S), Infected (I), Removed (R) and Famous (F). Susceptible refers to those who are not currently members of Snapchat, but there is a possibility that they may join at any time. Whereas, infected refers to those who are currently members of Snapchat and can recruit susceptibles to join as well. However, Removed refers to those who no longer use Snapchat. Finally, Famous refers to those who are famous and using Snapchat.

Snapchat can only thrive if it has active members, in this section, we will investigate the flow of individuals by analyzing the mathematical model to predict a possible future of Snapchat.

We assume that the typical flow of individuals from one group to another is as follows. Firstly, individuals who become older than 10 years are considered to be susceptibles and enter the model with constant enter rate. As for individuals who are older than 70 years are assumed to exit the model with constant exit rate, as well as those who leave the population as a result of death. For simplicity both enter and exit rates are assumed to be equal. Also, the exit rate will affect all groups equally. Secondly, we assume that susceptibles move to the infected group due to active users of Snapchat from family and friends, and also due to the need to follow some famous Snapchatters. In addition, active Snapchatters may gain more followers and become famous and move to the famous group. On the other hand, users of Snapchat may lose interest over time in Snapchat due to the influence of their family or friends who are no longer using Snapchat, and hence move to the removed group. However, the removed individuals may over time be subject to rejoin Snapchat again, and thus regain susceptibility; this may happen when some friends move away, so the only way to keep daily contact is through Snapchat. From the above assumptions, we may define the model’s parameters and variables as follows :

S ( t ) = Number of susceptibles at time t,

I ( t ) = Number of infected at time t,

R ( t ) = Number of removed at time t,

F ( t ) = Number of famous at time t,

b = Per-capita infection rate [time^{−1}∙individuals^{−1}],

a = Per-capita removed rate [time^{−1}∙individuals^{−1}],

c = Per-capita famous rate [time^{−1}∙individuals^{−1}],

d = Rate at which infected individuals become famous [time^{−1}],

v = Rate at which removed individuals regain susceptibility [time^{−1}],

μ = Per-captia enter and exit rate [time^{−1}].

Note that all parametes are assumed to be positive, whereas the state variables are assumed to be nonnegative.

The dynamics of the model are illustrated in

S ′ = μ + v R − b S I − c S F − μ S (1)

I ′ = b S I + c S F − d I − μ I − a I R (2)

R ′ = a I R − v R − μ R (3)

F ′ = d I − μ F (4)

Let N ( t ) be the population size in this model, that is, N ( t ) = S ( t ) + I ( t ) + R ( t ) + F ( t ) . Also, let N 0 be the initial population size. By adding all the Equations in (1)-(4), we obtain the following initial-value problem:

N ′ = μ ( 1 − N ) , N ( 0 ) = N 0 .

This can be solved for N to obtain N ( t ) = − e − μ t μ ( N 0 − 1 ) + 1 . Thus, over a long period of time, the population approaches size 1. Hence, we choose to study the system in the following region:

Γ = { ( S , I , R , F ) : S + I + R + F ≤ 1 , S > 0 , I ≥ 0 , R ≥ 0 , F ≥ 0 } .

To find the equilibrium points of the system, we equate the right-hand side of Equations (1)-(4) to zero, that is,

μ + v R − b S I − c S F − μ S = 0 (5)

b S I + c S F − d I − μ I − a I R = 0 (6)

a I R − v R − μ R = 0 (7)

d I − μ F = 0 (8)

From Equation (7) we have, R ( a I − v − μ ) = 0 , thus, either R = 0 or a I − v − μ = 0 . If R = 0 , then from (8), we get F = d μ I . By substituting for R and F in (6) we obtain I ( b S + c S d μ − d − μ ) = 0 , thus, either I = 0 or

b S + c S d μ − d − μ = 0 . If I = 0 then F = 0 . Substituting in (5), we have μ − μ S = 0 , thus, S = 1 . Hence, the first equilibrium point is E 0 = ( 1 , 0 , 0 , 0 ) .

Next, if I ≠ 0 , then b S + c S d μ − d − μ = 0 , which yield S = μ ( d + μ ) b μ + d c . Moreover, from (5) we have I = μ 2 ( 1 − S ) S ( b μ + c d ) . By substituting for I in (8) we obtain F in terms of I. Hence, the second equilibrium point is E 1 = ( S 1 , I 1 , 0 , F 1 ) , where

S 1 = μ ( μ + d ) μ b + c d , I 1 = μ 2 ( 1 − S 1 ) ( b μ + c d ) S 1 , F 1 = d I 1 μ .

Finally, if R ≠ 0 , then from (7) we get I = v + μ a , which implies, from (8), that F = d ( v + μ ) a μ . By substituting for I and F in (6), we have I ( b S + c S d μ − d − μ − a R ) = 0 , and since I ≠ 0 , then b S + c S d μ − d − μ − a R = 0 , which implies that R = 1 a ( S ( b + c d μ ) − d − μ ) . Now, when substituting for I, F and R in (5) we get S. Hence, the third equilibrium point is E * = ( S * , I * , R * , F * ) , where

S * = a μ − v ( μ + d ) c d + a μ + b μ , I * = v + μ a , F * = d ( v + μ ) a μ ,

R * = 1 a μ ( c d + a μ + b μ ) ( b μ + c d ) ( a μ − v ( d + μ ) − ( a μ + b μ + c d ) ( μ + d ) μ ) .

To summarize the above, we found three equilibrium points and they exist with the following conditions:

1) E 0 = ( S 0 , I 0 , R 0 , F 0 ) = ( 1 , 0 , 0 , 0 ) , where E 0 exists always since all the values of S 0 , I 0 , R 0 and F 0 are nonnegative. We denote this equilibrium point by free-users since the infected class is zero.

2) E 1 = ( S 1 , I 1 , 0 , F 1 ) , where S 1 = μ ( μ + d ) μ b + c d , I 1 = μ 2 ( 1 − S 1 ) ( b μ + c d ) S 1 , F 1 = d I 1 μ ,

which also exists without any condition since S 1 < 1 . We refer to this equilibrium point as persistent-users since the removed class is zero.

3) E * = ( S * , I * , R * , F * ) , where S * = a μ − v ( μ + d ) c d + a μ + b μ , I * = v + μ a ,

R * = 1 a μ ( c d + a μ + b μ ) [ ( b μ + c d ) ( a μ − v ( d + μ ) ) − ( a μ + b μ + c d ) ( μ + d ) μ ] ,

F * = d ( v + μ ) a μ .

This point exists if K 2 = a μ v ( μ + d ) > 1 and K 3 = ( b μ + c d ) ( a μ − v ( d + μ ) ) μ ( μ + d ) ( a μ + b μ + c d ) > 1 . We name this equilibrium point as an endemic point since all classes exist together.

Here, we use the linearization method [

J ( S , I , R , F ) = [ − b I − c F − μ − b S v − c S b I + c F b S − d − μ − a R − a I c S 0 a R a I − v − μ 0 0 d 0 − μ ] .

1) Free-users equilibrium point E_{0}:

Theorem 1

The free-users equilibrium point ( E 0 ) is locally asymptotically stable if K 0 = b 2 μ + d < 1 and K 1 = μ b + c d μ ( μ + d ) < 1 .

Proof.

Substituting E 0 into J ( S , I , R , F ) to obtain the following:

J ( E 0 ) = J ( 1 , 0 , 0 , 0 ) = [ − μ − b v − c 0 b − d − μ 0 c 0 0 − v − μ 0 0 d 0 − μ ] .

The eigenvalues of this matrix are: λ 1 = − μ , λ 2 = − v − μ and λ 3,4 satisfy the characteristic equation:

a 2 λ 2 + a 1 λ + a 0 = 0 , (9)

where a 2 = 1 , a 1 = 2 μ + d − b and a 0 = μ 2 + μ ( d − b ) − c d . Now, for E 0 to be locally asymptotically stable, the eigenvalues must be negative. It is clear that λ 1 and λ 2 are negative. However, for λ 3 and λ 4 , to be negative, we must show that a 1 , a 2 and a 0 are all positive. Clearly, a 2 is positive, as for a 1 and a 0 they are positive if K 0 = b 2 μ + d < 1 and K 1 = μ b + c d μ ( μ + d ) < 1 respectively.

2) Persistent-users equilibrium point E_{1}:

Theorem 2

The persistent-user equilibrium point ( E 1 ) is locally asymptotically stable if K 1 = μ b + c d μ ( μ + d ) > 1 and

K 3 = ( b μ + c d ) ( a μ − v ( d + μ ) ) μ ( μ + d ) ( a μ + b μ + c d ) < 1 .

Proof.

Evaluate the Jacobian at the equilibrium point E 1 , we obtain

J ( S 1 , I 1 , 0 , F 1 ) = [ − b I 1 − c F 1 − μ − b S 1 v − c S 1 b I 1 + c F 1 b S 1 − d − μ − a I c S 1 0 0 a I 1 − v − μ 0 0 d 0 − μ ] .

By solving the characteristic equation | J − λ I | = 0 , we obtain one eigenvalue explicitly, λ 1 = a I 1 − v − μ , and the others satisfy the equation:

a 3 λ 3 + a 2 λ 2 + a 1 λ + a 0 = 0 ,

where

a 3 = 1 ,

a 2 = b μ ( b μ + 2 c d + μ d + μ 2 ) + c d ( c d + d 2 + 3 μ d + 2 μ 2 ) ( d + μ ) ( c d + b μ ) ,

a 1 = b d μ ( b μ + 2 c d + 4 c μ − d μ − 2 μ 2 ) + b μ 3 ( 2 b − μ ) + c 2 d 2 ( d + 2 μ ) ( d + μ ) ( c d + b μ ) ,

a 0 = μ c d + b μ 2 − d μ 2 − μ 3 .

By substituting for I 1 in λ 1 we get λ 1 = a μ ( c d + b μ − d μ − μ 2 ) ( d + μ ) ( c d + b μ ) − v − μ , which is clearly negative if K 3 = ( b μ + c d ) ( a μ − v ( d + μ ) ) μ ( μ + d ) ( a μ + b μ + c d ) < 1 . To prove that λ 2 , λ 3 and λ 4 are negative, we use Routh-Hurwitz Criterion [

a 2 a 1 − a 0 = ( b 2 μ 2 + 2 b c d μ + c 2 d 2 + c d 3 + 2 c d 2 μ + c d μ 2 ) × ( 2 b 2 μ 3 + 4 b c d μ 2 + c 2 d 3 + 2 c 2 d 2 μ + c d 2 μ 2 + c d μ 3 + b c d 2 μ + b 2 d μ 2 + b c d 2 μ − ( b d 2 μ 2 + b d μ 3 ) _ ) / ( d + μ ) 2 ( c d + b μ ) 2 .

Simplifying the under line terms, we obtain

b 2 d μ 2 + b c d 2 μ − ( b d 2 μ 2 + b d μ 3 ) = ( b d 2 μ 2 + b d μ 3 ) ( b 2 d μ 2 + b c d 2 μ b d 2 μ 2 + b d μ 3 − 1 ) = ( b d 2 μ 2 + b d μ 3 ) ( b μ + c d d μ + μ 2 − 1 ) = ( b d 2 μ 2 + b d μ 3 ) ( K 1 − 1 ) .

If K 1 > 1 then a 2 a 1 > a 0 . Hence, λ 2 , λ 3 and λ 4 are negative by Routh-Hurwitz Criterion [

3) Endemic equilibrium point E^{*}:

Theorem 3

The endemic equilibrium point E * is locally asymptotically stable provided A i > 0 , where i = 0 , 1 , 2 and A 1 A 2 > A 0 . Here A 0 , A 1 and A 2 are provided in the proof.

Proof.

Evaluate the Jacobian at the equilibrium point E * , we obtain

J ( S * , I * , R * , F * ) = [ − b I * − c F * − μ − b S * v − c S * b I * + c F * b S * − d − μ − a R * − a I * c S * 0 a R * 0 0 0 d 0 − μ ] .

Here we have used that a I * − v − μ = 0 since R * ≠ 0 . By solving the characteristic equation | J − λ I | = 0 , we obtain one eigenvalue explicitly, λ 1 = − μ , and the others satisfy the equation:

λ 3 + A 2 λ 2 + A 1 λ + A 0 = 0 ,

where

A 2 = b I * + c F * + a R * + 2 μ + d − b S * ,

A 1 = a 2 I * R * + ( b I * + c F * + μ ) ( d + μ + a R * ) − S * ( c d + b μ ) ,

A 0 = a 2 μ I * R * + a R * ( b I * + c F * ) ( a I * − v ) .

It is easy to observe that A 0 > 0 since a I * − v = μ . Hence, by Routh-Hurwitz criterion, the local asymptotic stability of E * is guaranteed under the conditions stated in the theorem.

Remark 1

Note that if E 0 is stable, then E 1 is not stable and vice versa, since they have opposite conditions for stability. Also, one of the stability conditions of E 1 is the exact opposite to one of the existence conditions of E * , which means that if E * exists then E 1 is unstable or if E 1 is stable then E * does not exist.

In this section, we will demonstrate the numerical simulations of the model by solving the system numerically using Matlab. In addition, we will show the agreement of the qualitative results with the numerical simulations.

Firstly, we choose parameters to satisfy the conditions of the free-users equilibrium point E 0 , namely, K 0 < 1 and K 1 < 1 . We let μ = 0.015 , b = 0.01 , c = 0.01 , d = 0.01 , a = 0.01 and v = 0.01 . In

Secondly, we choose μ = 0.015 , b = 0.05 , c = 0.01 , d = 0.01 , a = 0.05 and v = 0.01 to satisfy the conditions of the persistent-users equilibrium point E 1 , that is, K 1 > 1 and K 3 < 1 .

Finally, we change the parameters to the following values: μ = 0.015 , b = 0.05 , c = 0.05 , d = 0.01 , a = 0.07 and v = 0.01 which satisfy K 2 > 1 and K 3 > 1 , the conditions of the endemic equilibrium point E * .

The numerical simulations presented in this section, demonstrate good agreement with the qualitative results given in Section 4.

To have a better understanding of the impact of the parameters on the dynamics of the model, we vary the parameters in the simulations. In this section, we

analyze the system’s parameters by choosing one parameter to vary while keeping the other parameters fixed. Our goal is mainly to see the effect of the varying parameter on the infected compartment in relation to another compartment by using numerical simulations. Throughout the simulations, the initial conditions are set as follows:

S ( 0 ) = 0.4 , I ( 0 ) = 0.28 , R ( 0 ) = 0.2 , F ( 0 ) = 0.12.

First, we vary the parameter b, the per-capita infection rate, and fix all other parameters to be: μ = 0.01 , c = 0.01 , d = 0.01 , a = 0.01 , v = 0.01 .

Finally, we analyze the rate at which infected individuals become famous and the rate at which removed individuals regain susceptibility, that is, the parameters d and v respectively. We plot the relation between infected and famous compartments, which is illustrated in

small or large it reflects growth in Snapchat users since the increase in famous class means that Snapchatters are rising and becoming famous. On the other hand, As the parameter v increases, both infected and famous classes increase until they reach a peak, then infected class starts to decay, whereas, famous class continues to increase with time (see

In the previous sections, we illustrated three possible scenarios for the Snapchat mathematical model over a long period of time. The first scenario is that Snapchat becomes completely neglected by individuals in the population. On the other hand, the second scenario shows the potential persistence of Snapchat with a consistent amount of individuals being only users or susceptibles. Also, in the third scenario Snapchat continues to thrive in the population, but with some amount of individuals who no longer use the app.

In this section, we use the same mathematical model to predict a possible future of Snapchat in Saudi Arabia. This is accomplished by estimating the parameters in the model from statistical data gathered from an online survey conducted throughout the country of Saudi Arabia. We will explain further in the following subsections.

A cross-sectional online survey was carried out in Saudi Arabia (SA) on the 24^{th} of March till the 1^{st} of July 2018. Our objective was to explore to what extent does active and nonactive users of Snapchat influence individuals towards using or removing the app. Also, to investigate the impact of famous Snapchatters on the use of Snapchat.

The survey was conducted through electronic social networks. Participants were asked to complete an online questionnaire. The number of participants who completed the questionnaire was n = 1700. The questionnaire was divided into two sections. The first section contained demographic questions about the participant’s age, gender, living area and career. The second section included the participant’s behavior towards using or non-using Snapchat. We have analyzed the data obtained from the study by using Excel (descriptive analysis). The results are demonstrated in this subsection.

The age distribution of the participants were 149 (9%) adolescents, 971 (57%) young adults, 512 (30%) middle-aged adults, and 68 (4%) older adults. Thus, the majority of the participants were young adults. Also, most of them were female, 1524 (90%). Moreover, they were classified according to their career as follows: 584 individuals (34%) were students, 554 individuals (33%) were employees, 102 individuals (6%) were unemployed, 336 individuals (20%) were housewives, and 124 individuals (7%) were retired. In terms of participant’s living area, the majority (83%) lived in west of SA, followed by (9%) participants lived in the center of SA, (3%) lived in the south of SA, (3%) lived in the east of SA, and (2%) lived in the north of SA (see

The survey shows that (80%) of the participants use Snapchat.

Frequency | Percent | Cumulative percent | ||
---|---|---|---|---|

Age | 10 - 12 years | 5 | 0.3 | 0.3 |

13 - 15 years | 23 | 1.4 | 1.7 | |

16 - 18 years | 121 | 7.1 | 8.8 | |

19 - 29 years | 632 | 37.2 | 46 | |

30 - 39 years | 339 | 19.9 | 65.9 | |

40 - 49 years | 309 | 18.2 | 84.1 | |

50 - 59 years | 203 | 11.9 | 96 | |

>60 years | 68 | 4 | 100 | |

Gender | Male | 175 | 10.3 | 10.3 |

Female | 1525 | 89.7 | 100 | |

Living Area | North of Saudi Arabia | 25 | 1.5 | 1.5 |

South of Saudi Arabia | 58 | 3.4 | 4.9 | |

East of Saudi Arabia | 56 | 3.3 | 8.2 | |

West of Saudi Arabia | 1407 | 82.8 | 91 | |

Center of Saudi Arabia | 154 | 9.1 | 100 | |

Career | Student | 584 | 34.4 | 34.4 |

Employee in privet sector | 365 | 21.5 | 55.9 | |

Employee in government sector | 147 | 8.6 | 64.5 | |

Owned business | 42 | 2.5 | 67 | |

House wife | 336 | 19.8 | 86.8 | |

Looking for a job | 102 | 6 | 92.8 | |

Retired | 124 | 7.3 | 100 |

to gain helpful information, in particular, 593 (44%) use Snapchat as an educational tool. However, 515 (38%) stated that Snapchat consumes a lot of their time.

As for participants who are not currently using Snapchat, 8% of them reported that they do not know the app, 58% said that they knew the app but have not used it, and 34% stated that they used the app but chose to remove it. Moreover, from among those who removed the app, 5% declared the reason was that their family and friends no longer use the app. On the other hand, 18% said that they would reinstall Snapchat again to follow some famous Snapchatter. Finally, when participants were asked if they will rethink of using Snapchat, 11% said yes, 32% said no and 57% stated that they do not know (see

Frequency | Percent | Cumulative percent | ||
---|---|---|---|---|

Doyou use Snapchat now? | Yes | 1362 | 80.1 | 80.1 |

No | 338 | 19.9 | 100 | |

Did you know about Snapchat from a family member, friend, colleague or other people? | Yes | 1283 | 94.2 | 94.2 |

No | 79 | 5.8 | 100 | |

Was following a famousSnapchatter the reason behind using Snapchat? | Yes | 162 | 11.9 | 11.9 |

No | 1200 | 88.1 | 100 | |

How many famous Snapchattersyou often follow on Snapchat? | Between 1 and 10 | 757 | 56 | 56 |

0 | 605 | 44 | 100 | |

How many famous Snapchatters from whom you follow, do you think that Snapchat was the reason behind their fame? | Between 1 and 7 | 757 | 56 | 56 |

0 | 605 | 44 | 100 | |

Whom do you see their snaps more? | Family and friends | 850 | 62.4 | 62.4 |

Famous Snapchatters | 85 | 6.2 | 68.6 | |

Both | 427 | 31.4 | 100 | |

Do you use Snapchat as an educational tool? | Yes | 593 | 43.5 | 43.5 |

No | 769 | 56.5 | 100 | |

Does Snapchat consume a lot of your time? | Yes | 515 | 37.8 | 37.8 |

No | 847 | 62.2 | 100 | |

Do you consider Snapchat a useful tool to gain helpful information needed for your life? | Yes | 858 | 63 | 63 |

No | 504 | 37 | 100 | |

Do you think famous Snapchatters whom you follow provide useful information for you? | Yes | 775 | 56.9 | 56.9 |

No | 587 | 43.1 | 100 | |

Do you follow famous Snapchatters to keep updated with what is new in different areas? | Yes | 672 | 49.3 | 49.3 |

No | 690 | 50.7 | 100 | |

Is your preference for a consumer product over another because of the recommendation of a famous Snapchatter? | Yes | 345 | 25.3 | 25.3 |

No | 1017 | 74.7 | 100 | |

Do you find yourself preferring a brand over another because a famous Snapchatter is more acquaintance with this brand? | Yes | 262 | 19.2 | 19.2 |

No | 1100 | 80.8 | 100 |

Frequency | Percent | Cumulative percent | ||
---|---|---|---|---|

The reason for not using Snapchat is. | You do not know Snapchat | 26 | 7.7 | 7.7 |

You know Snapchat, but you have not used it | 197 | 58.3 | 66 | |

You have used it, but now youdo not | 115 | 34 | 100 | |

Have you ever deleted Snapchat then reinstalled it again in order to follow some famous Snapchatters? | Yes | 20 | 17.4 | 17.4 |

No | 95 | 82.6 | 100 | |

Haveyou stopped using Snapchat because no one in your family or friends uses it anymore? | Yes | 6 | 5.2 | 5.2 |

No | 109 | 94.8 | 100 | |

If you were a previous Snapchat user, but currently not, will you rethink of using it again? | Yes | 13 | 11.3 | 11.3 |

No | 37 | 32.2 | 43.5 | |

Do not know | 65 | 56.5 | 100 |

In this subsection, we will use the mathematical model formulated in Section 2 to predict a possible future of Snapchat in Saudi Arabia. The parameters in the model will be estimated from the data given in the previous survey. Here, we will distinguish between the entry and the exit rates. As mentioned before, Individuals who are ten years and older enter the model with a constant rate, B, however, individuals who are older than 70 years and who leave the population due to natural death exit the model with a constant rate, μ . The estimation of the entry and exit rates are B = 0.066 and μ = 0.018 per month respectively. These values are calculated according to the data presented in the Annual Yearbook 2017 published online by the General Authority of Statistics in Saudi Arabia [

Next, the proposed model in Section 2, with the parameters estimated here, is solved numerically to predict the long-term behavior of the solutions. Note that the entry rate is different from the exit rate. Therefore, Equation (1) changes to the form:

Parameter question | Estimated parameter^{ } | Value per year | Value per month | |
---|---|---|---|---|

Did you know about Snapchat from a family member, friend, colleague or other people? | b ^ | 0.942 | 0.078 | |

Was following a famousSnapchatter the reason behind using Snapchat? | c ^ | 0.12 | 0.01 | |

How many famous Snapchattersyou often follow on Snapchat? | c ^ | 0.7 | 0.058 | |

How many famous Snapchatters from whom you follow, do you think that Snapchat was the reason behind their fame? | ||||

Haveyou stopped using Snapchat because no one in your family or friends uses it anymore? | a ^ | 0.052 | 0.004 | |

If you were a previous Snapchat user, but currently not, will you rethink of using it again? | v ^ | 0.565 | 0.047 |

S ′ = B + v R − b S I − c S F − μ S

From this exploratory simulations, we may conclude that Snapchat continues to thrive in Saudi Arabia. Also, Snapchat is considered as a useful tool for individuals to become famous within the population, which again contributes in the prosper of Snapchat. This trend of Snapchat is being exhibited nowadays within the population of Saudi Arabia.

In this work, we proposed a mathematical model to predict the future of Snapchat. The motivation of this work came from a similar study that was conducted for Facebook [

The mathematical model was analyzed qualitatively and numerically. First, we examined the model by assuming that the enter and exit rates are equal. We

obtained three equilibrium points for the model and proved their stability according to conditions satisfied by the parameters. Some examples of how this model behaves are given in Figures 2-4. It is possible that Snapchat may decline and disappear (

When analyzing the parameters in the model, we found that Snapchat blooms if the rates of active users and famous Snapchatters, who recruit individuals, reach above a specific amount (

One of the aims of this work was to predict the future of Snapchat in Saudi Arabia. Therefore, an online survey was conducted to help in the estimations of the parameters in the model. The survey showed that Snapchat is growing in Saudi Arabia since 80% of the participants in the study were using Snapchat. Moreover, the survey reflected the significant role of active users in recruiting new individuals, since 94% of the participant said that they knew about Snapchat from family and friends. Based on the estimated values of the parameters from the survey (

In conclusion, this exploratory study helped in gaining a better insight as for how Snapchat can continue to thrive and when will it disappears. Also, how Snapchat in Saudi Arabia gave rise to famous Snapchatters, who in return contributes to the prosper of Snapchat.

The authors declare no conflicts of interest regarding the publication of this paper.

Al-Tuwairqi, S.M., Aloosh, B.K. and Bagies, R.A. (2019) The Future of Snapchat: A Mathematical Model. Journal of Applied Mathematics and Physics, 7, 841-860. https://doi.org/10.4236/jamp.2019.74057