UNDERSTANDING THE DIFFERENT OBJECTIVES OF INFORMATION AND THEIR MUTUAL IMPACT: MULTI-INFORMATION MODEL

In this article, we propose a new multi-information discrete-time model describing the dissemination of several pieces of information from one person to another, it can be shared word-to-mouth or in certain types of online environments such as Facebook, WhatsApp, and Twitter. First, we present the model and the different possible interactions between its compartments. Based on the fact that there is always a goal behind publishing information, in the modeling process, we distinguish between information that shares the same objective and information that shares a contrary objective, to study the effect of those pieces of information on the others. To do this, we divide the entire target population into three groups for each piece of information and consider the possible transition between these groups. Numerical simulations are carried out to illustrate these effects, and to study the sensitivity of the model on its parameters to identify the most influential parameter.


INTRODUCTION
Newer communication technologies have increased the possibilities for how people can send and receive information. Social media are one such technology that has seen increased usage as an information source [1]. These several different communication channels are playing a greater role in our daily lives and provide a unique opportunity to gain valuable insight on information flow and social networking within a society [2]. As the penetration of smart phones in societies increases there is a large growth in the use of mobile phones. This trend is followed by the fast growth in use of online social networking services. As a result, people become more and more addicted to the fact of posting and sharing informations with each other in the most popular social media technologies. Giving as example, social networking sites, micro-blogging sites, wikis, online forums, and online blogs [3]. It has been revealed that about 2 billion people use the Internet every day and its services [4].
People use online social tools to gather information, share stories, and discuss concerns [1].
Nowadays, it has become easy to access user messages to a wide audience [5]. As a consequence, information overload has become an ubiquitous problem in modern society , for the reason that social media users and micro-bloggers receive an endless flow of information often at a rate far higher than their cognitive abilities to process the information [6] .
As a new communication paradigm, social media has promoted information dissemination in social networks . However, little research has focused on the relationship between emotions and information diffusion in a social media setting. This study examines, whether sentiment occurring in social media content is associated with a user's information sharing behavior. On twitter for instance, this research has found that emotionally charged twitter messages tend to be retweeted more often ,and more quickly compared to neutral ones . This is one of the main reasons why companies pay more attention to the analysis of sentiment related to their brands and products in social media [7]. Taking into consideration the great impact of emotions ,and sentiments in the virtual world, it can affect the credibility of the information shared in the context of computer-mediated communication [3].
As more people rely on social media for political, social, and business events, it is more susceptible to become a place for evildoers to use it to spread misinformation and rumors [8].
Therefore, users have the challenge to discern which piece of information is credible or not.
They also need to find ways to assess the credibility of information. This problem becomes more important when the source of the information is not known to the consumer [9]. For this reason , evaluating the information honesty on social media platform has become an important issue for today information consumers, due to the lack of professional gatekeepers to monitor content [10].
For instance, the level of authenticity in the communicated messages now decides the blogger's credibility, rather than the communicator himself. Additionally, the legitimacy of the blogger is enhanced by the personal passion and devotion to the communicated content bring out the legitimacy of the blogger [11]. Another factor that people may consider as a way of measuring someone's credibility is the number of followers. The fact of being followed by few people could led to lower judgments of expertise and trustworthiness [12] . Unfortunately, none of these criteria assure the truthfulness of the information spread on the internet.
Unsecured information a term that connects to the defining characteristic of rumor as information that is suspect because of its uncertain origins within a social system [13],the World Wide Web is a fruitful environment for the massive diffusion of unverified rumors,also allows for the rapid dissemination of conspiracy theories that often elicit rapidly [14]. Rumors has been recognized as one of the most important contributing factors to violence, prejudice, and discrimination. Yet despite its significance in exacerbating societal discord and mistrust, little systematic scholarly attention has been paid to the political origins and consequences of rumor [15].
Thus, sharing a false information has a serious impact on many fields of society, giving as example economics; in March 1991, false rumors circulated that Tropical Fantasy Soda was manufactured by the Ku-Klux-Klan and caused black men to become sterile; sales plumed 70%, delivery trucks were attacked, and vendors dropped the product [16]. Politics are also targeted by rumors for personal purposes , such as decreasing the probability of voting for a specific candidate [17] or encouraging negative campaigns; when these rumors are e-mailed to friends and family they become more likely to be believed and shared with others and these patterns of circulation and belief exhibit strong political biases [18]. Concerning the health field , misinformation and rumors regarding COVID-19 are masking healthy behaviors ( hand washing, social distancing etc.) and promoting erroneous practices that increase the spread of the virus and ultimately result in poor physical and mental health outcomes among individuals. An example of hazards attributable to improper health communication can be drawn from Nigeria, where the health officials found several cases of overdose of Chloroquine (a drug used to treat malarial parasite) after the news regarding the effectiveness of the drug for treating COVID-19 spawned in the social media [19,20].
Rumor spreading resembles epidemics spread. Nevertheless ,there are three ideas that do link Virus and rumors very well. First, the idea of contagion is present in both processes, even though the definitions are different.Second is the idea that little changes have big effects on the population .In the case of influenza, it is possible for only a few coughs and sneezes to cause infection in many people.The same holds for rumors due to the fact that only a few people need to know the rumor in order to have rapid dissemination. The final similarity is that major events happen in a short amount of time. The potential for an outbreak to occur is present for both epidemics and rumors [21,22]. Therefore, the creation of rumor models had been necessary in order to understand the information dissemination laws, a standard model of rumor spreading was introduced by Daley and Kendall, which is called DK model. In this one, it is assumed that there are a number of people in the network are categorized into three groups [23] .Ignorants ( people who are ignorant of the rumor ), spreaders ( they actively spread the missinformation ), and the stiflers ( those who have heard the rumor , but no longer are interested in spreading it ) [24]. This model created by Daley and Kendall in which there exists three classes assume two distinct attitudes among suceptibles and spreaders: passive and active. The passive people are those who do not have many contacts, and active people are defined to be those who have many contacts [25]. Afterwards, Maki and Thomson developed another classical MK model, which focused on the analysis of the rumor spreading based on mathematical theory via direct contact between spreaders and others. After that , more and more scholars paid attention to the spread of rumors [26]. Then, a new rumor spreading model, Susceptible-Infected-Hibernator-Removed (SIHR) model, is developed. The model extends the classical Susceptible-Infected-Removed (SIR) rumor spreading model by adding a direct link from ignorants to stiflers and a new kind of people-Hibernators [27], this model incorporated the mechanisms of memory and forgetting [24].
To introduce the information transmission mechanism clearly, nodes in the network can have three states: ignorant, spreading and recovered. A node is ignorant if it is interested in the information but has not yet received it. Nodes that have possessed a copy of information and are willing to disseminate the information to others can be seen as spreading nodes. If a node is not interested in the information and not willing to disseminate it either, this node can be looked upon as a recovered node.Combined with three states of mobile nodes mentioned above, the detailed information dissemination process is introduced. Usually, mobile users may be willing to help their friends rather than anyone upon contact, which is a practical concern in the real world but ignored in most of existing works. In MSNs, we consider that there is only one node having the information initially, which is the spreading node. All of other nodes are interested in the information at first, and willing to receive the information. However, most of the nodes cannot maintain the same interest all along. Some ignorant nodes may lose the interest later, and refuse to receive it. In other words, an ignorant node can directly become a recovered node, which is called pre-immunity. In addition, a spreading node may stop dissemination when it encounters a recovered friend-node, which is called immunity. Moreover, spreading nodes may stop dissemination without any contacts due to their disinclination to deliver the information [28].
The fast exchanging of misinformation has been hard to be controlled especially with the huge number of the internet consumers, and perceived source credibility becomes an increasingly important variable to examine within social media, especially in terms of crisis and risk information. This is because of the increasing amount of information available through newer channels, the gatekeeping function seems to shift away from producers of content and onto consumers of that content [1]. Additionally, the problem of identifying rumors is of practical importance especially in online social networks, since information can diffuse more rapidly and widely than the offline counterpart, this unsecured information may affect a various fields of a society. The credibility is required to keep the information trustworthiness and save the whole community from the negative impact of rumors.
Infectious disease modeling is a tool used to study disease spread mechanisms, predict the future course of an epidemic, and evaluate epidemic control strategies [23,29,30,31,32,33,34].
Epidemiological protocols have become an important raw material for disseminating information in networks [35]. Glaring examples of so-called diffusion protocols [36]. It is possible to apply mathematical models to collect information about disseminating ideas and information, thus allowing the testing of social hypotheses [37,38,21].
The similarities between the spread of the epidemic and the spread of information allowed the researcher to use epidemiological models to model information dissemination. In this article, we propose a new multi-information model, in-which we divide the population into three groups for each information, which will make it possible to study the development of ignorant people (people who do not know the information), spreaders (people who are interested in this information and who find pleasure in sharing it), removed (people who see that this information lacks relevance and compatibility with their profiles, then they refuse to share it). We study the impact of the model's parameters on the evolution of information by providing different numerical examples.

PRESENTATION OF THE MODEL
Information is easily spread, by all means, word of mouth, emails, phone calls, social networks, etc. With the help of all the advanced technologies that facilitate human communication, information spreads quickly. One of the most important factors in spreading information is the option of "Share" that accompanies any status update, link, video, or image posted. Content viewers (for example, friends of the creator and subscribers) are allowed to share the post. For example, on almost social networks, if the content was originally posted publicly, anyone can view and share it [21].
We devise here a compartmental model to study the dissemination of p information in an online environment of N users (Facebook, WhatsApp or Tweeter groups or pages) by posting, sharing and discussing. In these online environments, when a user posts information (text, image, video etc.), only his neighbors can see it and decide whether this information is worth sharing again or not. If the information is very interesting and some neighbors decide to share it, the author's neighbors can see it and also re-share it. After that, the influence of the information goes beyond the local scope of the author and can be widely publicized on the network. On the other hand, if none of the original author's neighbors are attracted to this information, it will soon disappear and very few users will see it. At the same time, if neighbors see the message and do not immediately share it, they may gradually lose interest and ignore to share this information.
However, if the user notices that some information is being duplicated and shared by many of his neighbors, he will discuss it with his friends via chat tools or face to face, so that he can determine the relevance of this information and then decide to share it or not. When people debate a topic, they rely on a set of consistent information to validate their point of view, and thus persuade others who might have an opposing opinion. The aim of the discussion may not be to convince others of a dissenting opinion, but rather to persuade them not to publish more information that shows their point of view.
To incorporate all these considerations in our model, we assume that there are p information circulating on the internet, that is J = i 1 , i 2 , ..., i p where J is the set of all these information. Usually we find several information that appear different, but the goal of publishing them is the same. For example, the information on the daily death toll from traffic accidents and the information on the number of daily traffic violations recorded, these information have the same goal, which is to improve driving by respecting the laws. While we can find other information that has the opposite purpose, for example information on traffic jams at a certain time or information on the application of quarantine from a certain time, these information may have the opposite purpose, which is to create a state of panic among the people and thus increase the violation of traffic laws.
Therefore, we suppose that information z ∈ J share the goal G 1 , and the information x ∈ J share the goal G 2 .
If G 1 = G 2 , thus z and x are said media-compatible information.
If G 1 opposes G 2 , thus z and x are said media-incompatible information.
If G 1 = G 2 and G 1 is not opposed to G 2 , thus z and x are said media-independent information.
For an information z ∈ J we define the following sets: yet about the information j. The word "Sharer" (S j ) is used to denote that a person is attracted by the information j and/or he finds it funny or interesting, then he decides to share it. The term "Removed" (R j ) means a person who has seen and know about the information j and has decided not to share it. For example, because of irrelevance or for other personal reasons. We kept the term Removed from the classical SIR epidemiological model to denote individuals removed from the sharing system. All transmissions are modeled using the mass action principle, which accounts for the probability of transmission in contact between the different compartments.
Each information has the potential of sharing, but one can find some information not useful or does not fit the user interests, and then there is no need to share it. For example, if the information is about a concern of the public opinion (Raising costs of education, election cheats, public safety... ), the probability of shares will be very important. Therefore, the potential relevance of the information will be taken into account and it will be defined based on the proportions of sharers. Let's define the potential relevance of the information j by the average β j . After a contact between the ignorant I j of the information j with a sharer S k of the mediacompatible information k (where k ∈ C ( j)), the Ignorant I j becomes a Sharer S j just after he/she shares the information at the rate β k I j i S k i N j , for k ∈ C ( j). A sharer S j of the information j ∈ C (z) after a contact with a sharer S k of the mediaincompatible information k ∈C (z) he/she would loss interest of sharing the information j and then become a removed of the information j at a rate α j S j i S k i N j . Note that 1 α j represents the power of persuading people by the information j and the ease with which it is accepted: the smaller α j , the greater the strength of the information j.
Any sharer S j can lose interest of sharing and decide at any time not to share the information j anymore for personal or other reasons, thus he becomes a Removed R j at a rate γ j S j . All these interactions happen at the instant i, and N j i is the total targeted population by the information j at instant i, that this N j We propose a discrete-time compartmental model describing the interactions between the different information governed by the following equations: A flow chart example for the model is shown in Fig. 1, and parameters description can be found in Table 1.

NUMERICAL SIMULATIONS
We now present numerical simulations associated with the above-mentioned model. We write code in MATLAB T M and simulated our results using data from Table 1.
In these simulations, without loss of generality, we suppose that there are 4 different infor-     We can see from this figure that the parameter γ 1 has virtually no effect on the development of the ignorant groups for all information i 1 , i 2 , i 3 , and i 4 . We can say that the parameter γ 1 has a no impact on the ignoring populations of all opinions. inC (i 1 ), while it has no effect on the removed group of the media-compatible information in In figures 9, 10, and 11 we chose four different values of the parameter α 1 , 0.0004, 0.001, 0.0018, and 0.0029. The Fig.9 shows the impact of the parameter α 1 on the ignorant populations. We can see from this figure that the parameter α 1 has a remarkable effect on the ignoring population of the corresponding information i 1 , and a moderate impact on the ignorant populations of other information. Note that α 1 has a positive impact on the corresponding information and its media-compatible information C (i 1 ), and a negative impact on information of the opposite opinionC (i 1 ). The Fig.10 shows the impact of the parameter α 1 on the sharer populations. Where we can see that the parameter α 1 has a remarkable effect on the sharer population of the corresponding information i 1 , and a moderate impact on sharers of other information. Note that α 1 and the number of media-compatible information sharers S 1 and S 2 tend to very in a negative way, that is the higher the values of α 1 , the fewer participants S 1 and S 2 . We can say that the parameter α 1 has a negative impact on sharers of the corresponding information i 1 and its media compatible information.
While Fig.11 shows the impact of the parameter α 1 on the removed populations. Where we can see that the parameter α 1 has a remarkable positive effect on the removed population of the corresponding information i 1 , and a negative impact on its media-incompatible information C (i 1 ), while it has no effect on the removed group of the media-compatible information. The higher the values of α 1 , the higher number of removed R 1 .

CONCLUSION
In this article, we proposed a new multi-information discrete-time model to describe the dissemination of several information from one person to another, it can be shared word-tomouth or in certain types of online environments such as Facebook, WhatsApp and Twitter.
We presented the new model and the different possible interactions between its compartments.
We have assumed that the information set is composed of three subsets, information sharing an objective O 1 , information sharing the opposite objective O 2 , and neutral information.
We provided several examples to study the sensitivity analysis of the model to its parameters.
We found that the transmission parameter of an information i 1 has a negative effect on the sharer removed population of the corresponding information i 1 , and a negative impact on its mediaincompatible informationC (i 1 ), while it has no effect on the removed group of the mediacompatible information.

CONFLICT OF INTERESTS
The author(s) declare that there is no conflict of interests.