Racism Dissemination Model and Simulation Analysis Considering Crowd Classification with Intervention Strategies

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Introduction
In real-life activities, all humankind has its social environment and network [1,2].Tese networks are linked to formulating an extensive and complex multicultural social network [3,4].Troughout this linkage, individuals can disseminate manifold information, such as personal opinions or mindsets toward things or behaviors, and infuence each other [5].Meanwhile, in the network formation, racebased segregation insidiously perpetuates racism [6].Racism and racial bigotry bear multiple shapes and challenge everyone's daily life [7,8].Te derivative perpetuates racial crowd mistreatment in public policies, institutional rules, and cultural manifestations [9].Racism can be manifested at structural and individual levels [10,11].Te myriad articulations of racism can infuence numerous activities of the community's straightforward and indirect pathways.Structural racism has been and sustains the fundamental causality of persistent multiple services disparities in the community [12].Recent research works verifed that people who experience racism more than rates of sicknesses.In the health system, racism is an absolute cause of health disparities [11] the situation is noticed in the COVID-19 pandemic [13].
Te blow of racism is unexpected and ultimately harms everyone's social harmony.Develop empathy about how it impacts people and the wider community, thereby allowing to change mindsets and behaviors.Te racism awareness programs are structured to support controlling the issues of disparity and the absence of endorsement of others among individuals [14].It enhances to provide that social network settings are comprehensive and reward cohesion without racial imbalance or racism.Antiracist education enables pupils to understand the destructive results of racism and nurtures them to resist and stop wherever it emerges [15,16].In addition, confning racist networks and activity is also worthwhile to remove racism [17].Systems science approaches developed to advance essential social aspects suggest a scientifc method in backing community decisionmaking to reduce the efects of racism.
System dynamic models are used to compute and analyze physical, biological, and social phenomena in realworld problems.Numerous dynamic system models of many types have been formulated and studied to provide an understanding of the transmission of infectious diseases [18][19][20][21].Recently, various research studies real-life phenomena using fractional order models [22,23].Te process of rumor spread is similar to the process of epidemic spreading; many researchers study the propagation of rumors in social networks [24][25][26].In opinion dynamics, researchers have constructed some achievements in information spreading in social networks [27,28] and its control [29].Based on emotion contagion and opinion dynamic emotion difusion model was designed and analyzed [30].Furthermore, some researchers study racial segregation dynamics and interconnected social impacts [31][32][33][34].Chen and Wang studied the rumor-spreading model considering rumor credibility, correlation, and crowd classifcation based on personality [35].We comprehend from previous research that rumors, misinformation, and all categories of crud information and opinions are spreading on social networks.It pivots out that racist speech is also one of these categories of crud information and opinions.Te contagiousness of racism in multiracial societies acts as the trigger for hate crimes and physical violence.Mamo recently studied the dynamical process of racism propagation on cyberspace [36,37].Recently, Teklu and Terefe studied animosity and racism and violence codynamic dynamics using compartment models [38,39].
Nevertheless, we review that none of the previous research incorporates racism dissemination dynamics with the crowd classifcation.In each information dissemination process, individuals will convince, reluctant, or reject the information disseminated by hostile individuals [40].In idea-building modeling, one must assume the personality varieties of an individual within the total population.An individual's personality represents inherent human attributes that conscript behavior preference.Constantly some people immediately assemble racist ideology.However, some people are calm and desire to follow assurance instantly.Te varieties of individual essence are the factor that afects the racism disseminating process and should consider in the study of racism propagation.Furthermore, antiracism education boosts community resilience and removes the susceptible radical personality.Community awareness programs foster personal opinions against racism and nullify radical personalities.Antiracism education is a proactive measure to mitigate the propagation and remove the harmful threat of racism.Yet, some radical racists strive in their toxic attitude and intentionally disseminate racism in a multicultural society.Racist individuals threaten social solidarity and introduce socioeconomic fux and political crises.Regulations against racial discrimination and hate crimes allow for confning racist and racist assertions via social networks.We consider racist confnement within treatment as one of the racism-consolidating intervention strategies.Te racist confnement could reduce the racism dissemination rate by restricting racist individuals and their racist ideas.
In the next section, we introduce the model assumption that governs the model formulation process.After that, in Section 3, we present the theoretical analysis, obtaining the racism-free equilibrium and computing the efective reproduction number.We prove the local and global stability of equilibrium points.In Section 4, we evaluate model parameter sensitivity and its interpretation.In Section 5, we carried out a numerical simulation of dynamical systems, which confrmed theoretical analysis and assessed the impact of intervention strategies.Eventually, Section 6 is reserved for the conclusion.

Model Description
Te propagation of racism is a peril to social, political, and cultural stability and has threatened the harmony of various nations.Te spread of racism may difuse via a social connection process in which racist ideologies bear complex contagiousness.Consequently, to propose compartmental models for the study of racialism is valid.Accordingly, we formulate the governing mathematical model for the study of racism dissemination and assess the impact of intervention strategies by splitting the entire population into seven mutually exclusive compartments, namely, calm susceptible (S 1 ), radical susceptible (S 2 ), awarded susceptible (S 3 ), hesitant (H), racist (R), confned racist (C), and immunized (I).Te model considers susceptible individuals' crowd categories based on personality and fosters cohesion via antiracism campaigns and racist custody as intervention strategies.

Model Assumptions.
To develop the dynamics of racism in multicultural societies, we designate the following scene of explicit assumptions about the phenomenon that discloses clear distinctions with epidemic models: (A1) Te susceptible crowds are separated into three subgroups, namely, calm susceptible (S 1 ), radical susceptible (S 2 ), and aware susceptible (S 3 ).We assume that the portion of the recruited susceptible Established on the above-given assumptions and conditions of hypothesis and the schematic diagram in Figure 1, a system dynamics of racism dissemination considering the roles of racist confne and community awareness within the crowd classifcation model can be described by the following equation: ( with the initial conditions 2.2.Basic Properties of the Model.For system (1), describing the dynamics of racism with the behavioral status of individuals, all state variables and parameters of the model are non-negative.It is essential to confrm that all of the solutions with initial conditions (2) remain positive for all t ≥ 0 .Consider the pursuing social-feasible region for the model:
is the solution of model ( 1), we obtain the following equation: with the continuity of the solution of the system (1), Te summation of all of the equations in the model (1) gives the following equation: ( Since all parameter values of mode 1 are positive, from (5), it follows that Furthermore, the solution of equation ( 5) is as follows: At any time t > 0, the total population is less than the upper bound (lim t⟶∞ N(t) ≤ Λ/μ) if N(0) ≤ Λ/μ.Hence, for system (1), all trajectories stay inside the region Ω.Tus, the region Ω is positively-invariant and attracts all solutions trajectories of the model (1); in other words, the existence and uniqueness of solutions are provided.Terefore, model ( 1) is mathematically and socially well-posed [41].

Theoretical Analysis of the Model
In this section, we provide the threshold value, R e , which is the efective reproduction number of the model (1).Te number is defned as the average number of susceptible individuals recruited by each racist individual while remaining in the racist group.We bear it as racism strength because it is the size of the recruitment and retention capability of the racist group.Tis parameter is equivalent to the basic reproduction number in epidemiological models [42][43][44].Ten, we investigate the stability properties of the racism-free equilibrium of the system (1), which is equal to Lemma 1. Te efective reproduction number R e of the system ( 1) is given by the following equation: Proof.We consider the next-generation matrix method [44,45] to fnd R e .Now, we rewrite the system (1) as X � (H, R, C) T , then it follows from system (1) that dX/dt � F − V. Tus, we obtain the following equation: 4 Complexity Evaluate the zF/zX and zV/zX at E 0 , we get the following equation: Using the next-generation matrix approach the threshold value R e is the spectra radius of (FV − 1 ).Hence, with a direct computation, we obtain ( 9) In the absence of intervention strategies, the efective reproduction number (R e ) reduces to basic reproduction number (R 0 ), given by the following equation: Local Stability of Racism-Free Equilibrium.In the absence of racism (by setting racist compartment R � 0, H � 0), we get a unique racism-free equilibrium (8).
Theorem .Racism-free equilibrium point E 0 of the system ( 1) is locally asymptotically Proof.Te Jacobian matrix of the system (1) at racism-free equlibium point E 0 is Clearly, we get the eigenvalues λ 1 � λ 2 � − (μ + ξ), λ 3 � λ 4 � − μ, and the remaining eigenvalues are computed by using the following subcharacteristics polynomial: where Here, we get a 0 > 0, a 1 > 0, a 3 > 0, and a 1 a 2 − a 0 a 3 > 0 if the efective reproduction number R e < 1.Hence, using Ruth-Hurwitz Complexity stability criteria all the eigenvalues of J(E 0 ) have negative real part if R e < 1. Terefore, the racism-free equilibrium point E 0 is locally asymptotically stable.Te social implication of Teorem 2 denotes that the racist group does not continue to conceive a reasonable capacity for tempting susceptible individuals or retaining its contemporary fellows if R e < 1.

Global Stability of Racism-Free Equilibrium
Theorem 3. Te racism-free equilibrium E 0 of system ( 1) is globally asymptotically stable in Proof.Suppose (S 1 , S 2 , S 3 , H, R, C, I) be a non-negative solution of system (1).To complete the proof, it is sufcient to show that this non-negative solution tends to the racism-free equilibrium E 0 at t approaches to positive infnity.
Proof.Te Jacobian matrix of the system (1) at where S * 1 , S * 2 , and S * 3 are obtained from (20), and R * is obtained from (23).Te characteristics polynomial of J(E * ) is Obviously, we obtain negative eigenvalues λ 1 � − μ and λ 2 � − K 1 .Te eigenvalues of J(E * ) satisfy the polynomial where Complexity 7 where Here, all the coefcients of the polynomial ( 26) are positive if R e > 1.By using the Routh-Hurwitz criteria, we obtained a Routh-Hurwitz array that had no sign change.Terefore, the racism-addicted equilibrium E * of the system (1) is locally asymptotically stable.□

Global Stability of Racism-Addicted Equilibrium
Theorem 5. the racism-addicted equilibrium E * of the system ( 1) is globally asymptotically stable if R e > 1.
Proof.Consider the positive-defnite function, where M � (S 1 , S 2 , S 3 , H, R, C, I).By employing the derivative of the function with respect to t we get the following equation: Te derivative of the function L(M) is greater than zero, and it is equal to zero at the endemic equilibrium point , and I � I * .Te strictly Lyapunov function indicates that the endemic equilibrium (E * ) is globally asymptotically stable in the invariant region Ω.Socially, this result implies that racism will continue to exist in the community for a long period of time.Hence, the proof is complete.
Te social meaning of Teorem 5, in this case, conforms to racist groups that grew towards more efcient strength in at least one of the aspects of recruitment and retention, which gripped inadequate intervention strategies and vulnerable community cohesion.

Model Parameter Sensitivity
In Section 3, the theoretical analysis results investigate whether racism dissemination is suppressed or prevails in society pivoting on the reproduction number R e .Consequently, it is reasonable to analyze the efect of control parameters on the racism dissemination process specifed on the reproduction number R e .To estimate how much the parameter sensitizes the system, we illustrate the graph of the parameter versus R e .We begin by depicting the infuence of contact rate β ∈ (0, 1) and awarded hesitancy rate θ ∈ (0, 1) on R e by assigning baseline parameter values Λ � 0.01, μ � 0.01, η � 0.05, ψ � 0.75, σ � 0.034, ω � 0.01, θ � 0.25, β � 0.5, κ � 0.6, ρ � 0.01, c � 0.056, and ξ � 0.05.
Figures 2 and 3, we investigate the efect of contact rate β and awarded susceptible hesitancy probability θ on R e .Te result illustrates efective reproduction is greater than unity if the value of β > 0.3547 and θ > 0.1024, respectively.Tis provides an insight into the racism dissemination that the contact and hesitancy rate below 0.3547 and 0.1024 has not a signifcant efect.Racist strength advance into a malicious phase if the efective contact rate, β > 0.3547, and the likelihood of awarded hesitation is θ > 0.1024.Consequently, declining the contentiousness of racist groups and boosting the rejection strength of susceptible individuals is imperative to construct a social environment beyond racism.
As we noted previously, antiracism education and racist confnement are the proposed intervention strategies.Here, we present the sensitized infuence of the rate, ξ ∈ (0, 1) and ξ ∈ (0, 1) on R e .
In Figures 4 and 5, the functional interchange of the parameters ξ and η with the threshold value R e depict, respectively.Both fgures show that the R e value decreases if the value of ξ and η increases.As we observed in 4, antiracism education is admiringly sensitive at the onset and declines its sensitiveness gradually.Tis sensitivity analysis suggests that approximately beyond 19.68% of antiracism education coverage with more than 75% racist idea rejection competency (which means less than 25% hesitation probability) will be moderately reduced Complexity racism spreading.Furthermore, additional intervention is required to build a racism-free social environment.Racist confnement is highly sensitive and signifcantly reduces community threats.Te result provides beyond 7.877% racist restriction required to control the dissemination.

Numerical Simulation Result and Discussion
In this section, we conduct an extensive numerical simulation of model ( 1) to obtain in-depth insight into the system dynamics.For simulation purposes, we set the non-negative initial values of model variables (S 1 (0), S 2 (0), S 3 (0), H(0), R(0), C(0), I(0)) � (0.889, 0.1, 0.0, 0.01, 0.001, 0.0, 0.0) and baseline parameter values are listed in Section 4. Furthermore, we verify the theoretical analysis using numerical simulations and assess the impact of proposed intervention strategies in manifold scenarios.

Stability Based on Numerical
Simulations.In this subsection, we perform the time series evaluation of system 1 to verify the asymptotic stability of the equilibrium points.
Given that R e < 1, society is in a susceptible state before the arrival of the racist group.According to the result in Section 3, under these conditions, the only equilibrium point of system 1 is E 0 .Furthermore, we obtained a unique positive racist-addicted equilibrium point E * if R e > 1.Now, we explain equilibrium stability numerically by varying the initial conditions.
In Figure 6, we evaluate the dynamical changeover of the system by setting the parameters β � 0.15 with baseline parameter values.Tis time series evaluation shows that all solution trajectories which start from the diferent initial conditions are stable toward the equilibrium point E 0 � (0.35, 0.15, 0.5, 0, 0, 0, 0).Te result implies that as a time t ⟶ ∞, the densities of individuals in class H, R, C, and I decline to zero.Further, we computed the racist strength threshold value operating the formula (13) and obtained the value R 0 � 0.5307.Terefore, the numerical result verifes that the racism-free equilibrium point is locally and globally asymptotically stable and agrees with Teorem 2 and 3. Te result gives an insight into a small portion of the racist group that emerges, it will disintegrate, and the population will quickly return to a maximum level of susceptible class.Tis situation implies that racist groups do not create a suitable capacity for attracting susceptible or retaining their contemporary fellows.
Figure 7 displays the uncertainty of racism dissemination with the parameter setting β � 0.5, η � 0.05, ρ � 0.01, ξ � 0.01, θ � 0.5.Based on the formula (9), we obtain R e � 4.8939, which is greater than one.Tis estimation implies that each racist can pollute approximately fve susceptible.Tis time series evaluation shows that the system dynamic solution trajectories are skeptical to their respective extreme values and then locally and globally asymptotically steady towards the racism-addicted equilibrium E * � (0.0599, 0.02, 0.0530, 0.1281, 0.1306, 0.0198, 0.5887).Equivalent to Teorem 4 and 5, this numerical simulation displays that racism dissemination persists in the society, if R e > 1.Consequently, this claims the status of racist groups that unfolded emphatic convection strength in at least one of the aspects of recruitment and retention, which tempt sickly cohesive community.

Te Impact of Proposed Intervention Strategies.
To assess the impact of intervention strategies on the racism dissemination process, we will conduct various numerical simulations to allow a deep insight into the dynamics and its impact.Te assessment starts by evaluating the efect of 10 Complexity contact rate on susceptible and racist compartments by setting the values β � 0.01, 0.05, 0.1, and 0.5.Figure 8 shows that as the β value increase, racism dissemination rises to a peak level, and the susceptible individual is accordingly contagious with racism.For example, at β � 0.5 , the result indicates approximately 95% of the susceptible individuals switch to the next stage.Besides, the impact of β on racist class R(t) simulate in Figure 9, and the result implies that it has positively fostered the racist density.Mass dissemination of racism recorded losses of social cohesion, formulated racial segregation, and boosted structural racism.Bailey, Zinzi et al. [9] "Structural racism refers to the totality of ways in which societies foster racial discrimination through mutually reinforcing systems of housing, education, employment, earnings, benefts, credit, media, health care, and criminal justice."Tus, to avoid the catastrophic consequences of racism, responsible organizations and ofcials must introduce bold antiracism education and racism sentiment source restriction.Furthermore, every day, each individual can stand up against racial bigotry and disrespectful attitudes using suitable intervention strategies is compulsory.
Social connections recreated a fundamental role in racism difusion because the spread of racist ideologies and their eventual structuralism depended not only on personal "infection" via exposure to creation but also on active convection and publicity of that idea through personal Complexity networks [46].Te fght against racism is everyone's struggle, and all are triumphs when we eliminate racial bigotry from our societies.Everyone has played a role in building s world beyond racism.Here, we assess the impact of awareness creation against racism and the likelihood of the intervention to improve the racism rejection mastery of susceptible individuals.
In Figure 10, we simulate the impact of antiracism education using the baseline parameter and varying ξ � 0.0, 0.05, 0.1, 0.5 and θ � 1 (which means in the absence of awarded recovery).Tis numerical result shows the impact of awareness on radical susceptible individuals, and 50% awareness coverage obtains around a 4% reduction of racist density (those individuals upgrade from straightforward convection to hesitation status).As we noted in Figures 4 and 11 also endorsed antiracism education without rejection competency has not retained a remarkable impact on antiracism crusades.Tus, we assess the efects of hesitancy or rejection mindset likelihood of awarded susceptible in Figure 11 with 20% antiracism education coverage.Indepth recognized antiracism education improves susceptible competency with high rejection probability.Our numerical result implies that efective antiracism campaigns build the attitude that moves us beyond the narratives of separatism, prejudice, division, anxiety, and hatred of others.Enrich racism rejection probability intensively and lecture to society via all feasible options (such as in school, at work, in public transportation, on social and broadcast media, at home, and on the sports feld), eventually eliminating the racist threats.Hence, reasonable antiracism coverage with efcient rejection likelihood is an efcacious intervention measure.
Racist individuals are the root cause of racism propagation, and they disseminate their racial attitudes through various communication channels (such as social media, broadcasting media, and impersonal connections).An international Convention of the United Nations declared to criminalize hate speech and criminalize membership in racist organizations [47].Hence, confning or restricting racialist perspectives spreading within proper therapy is one of the intervention strategies.
For simulation purposes, we set η � 0.0, 0.01, 0.05, 0.5 and obtained the time series evaluations of susceptible and racist compartments of system 15.In the absence of racist restriction policy and action, racism disseminates in the  12 Complexity community and aggravates mistrust, founding skepticism on all aspects and pulling apart the social fabric.In addition, numerical simulation Figure 12 in Figure 13 depicts exceeding 95% of susceptible individuals who are contagious with racism.However, beyond 26%, racialist restriction using racist confnement intervention virtually reduces the dissemination of racism.Besides, the upgrade of the racist confnement intervention strategy accordingly reduces the racist density (see Figure 13).Te time series evaluations imply that being reluctant to fght racism harms everyone's life directly and indirectly.Meanwhile, beyond marginal values fghting against racism through communication channels and law order has eradicated racism.
In the above-given various scenarios, we assess the sole impact of the control parameter of the model.Here, we will now be evaluating the integrated infuence of intervention strategies.Te simulations are carried out using baseline parameter values, with various values of the awareness rate ξ and racist confnement rate η.
In Figure 14, the impacts of integrated interventions are illustrated with various combinations.Te scenarios are expressed in the following cases: (i) Case I: if both η � ξ � 0.0, the racism dissemination rises to a peak level, and eventually, the racism persists in the community.In this case, no intervention strategies were employed.(ii) Case II: if ξ � 0.05 and η � 0.0, the racist density declines from 27.89% to 17.89% and reaches its equilibrium slowly.Te intervention, moderates the racist density, but racist strength still performed well and spread racism in the community.(iii) Case III: if ξ � 0.0 and η � 0.05, the racist density decrease from 27.89% to 6.59% and is proximate to the second case and uncertainly steady to its equilibrium.Nevertheless, when we compare antiracism education at the same rate of intervention, racist confnement is more infuential in reducing the racist density and afliated catastrophes.(iv) Case IV: if both η � ξ � 0.05, the result shows that the racist density converges to zero and racismbased catastrophes are under control.Tis result implies that the integrated measures are more effective and reasonable to build the world beyond racism.

Conclusion
We considered the real-life phenomenon and prior studies, frst adopting SIR type epidemic model to S 1 S 2 S 3 HRCI model considering the personality status.Secondly, we incorporate antiracism education and racist confnement as control intervention measures against to racism dissemination process.Tirdly, theoretical and numerical analyses of the proposed model are rigorously studied.Tis analysis includes racist strength threshold value existence and asymptotic stability of racism-free and racism-addicted equilibrium points.
We established on noted key assumptions a new nonlinear system dynamics compartmental model was formulated.We proved the well-posedness of the developed model via system positivity and boundedness.Using the nextgeneration matrix approach, we computed racists strength threshold value R e (efective reproduction number).Troughout the rigorous theoretical analysis, we obtained unique racism-free and racism-addicted equilibrium points E 0 and E * , respectively.Te racism-free equilibrium point is locally and globally asymptotically stable if R e < 1.In this situation, the racists have weak strength to attract susceptible or retain their members.Besides, the racism-addicted equilibrium E * exists and is asymptotically stable whenever one racist individual convinced more than one susceptible individual (where R e > 1).Our sensitivity analysis suggested that the racist contract rate and hesitancy probability have a key role to advance the dissemination process at the devastation level.Conversely, antiracism education coverage with a high reasonable level of racism rejection and racist confnement rate reduces and eventually builds weak strength of racism.
Numerous research outcomes are such that in the absence of interventions, racism propagation revs racial segregation, creates a socioeconomic imbalance, and facilitates ethnic cleansing of minority groups.Cogent antiracism education with everyone's participation reduces the racism dissemination.Confnement of racist activities via law order and individuals' fght against racism has a mimic role in the reduction of racism burden and dissemination scope.Various numerical simulation studies were carried out to assess the impact of intervention strategies.In the absence of any intervention measures, approximately 95% of the total population will be afected by racists.Our simulation depicted antiracism education with efective rejection ability to avoid racism from the societies.In addition, racist confnement also conquered racist density and build a racism-free social environment.Further, racism dissemination is stemmed by a minimum of 50 50% antiracism education coverage and 95 95% rejection likelihood of awarded individuals.Also, approximately more than 28.5% of racist confnement is rational to mitigate the racism propagation.As compared to a sole intervention impacts racist confnement is more efective than antiracism education.Meanwhile, 5% of combined intervention strategies is adequate to reduce and eliminate the sovereignty of racism in the community.We conclude that every individual joining the antiracism campaign which avails rejection level awareness via a feasible approach has a signifcant role in the building process of a suitable social environment free from racism.
In general, founded on our rigorous theoretical and numerical, we recommended more intensity on the rejection ability of the awareness process rather than coverage.Furthermore, confned racists with treatment and integrated intervention are more relevant to build harmonized and resilient societies.In this research work, we can not be considered individual heterogeneity, the mean-feld theory of social networks, algorithm-based racist message fltration, and the infuence of the structured routine of racism.In future work, we will incorporate the list of limitations of our Complexity

Figure 1 :
Figure 1: A schematic representation of the interactions between the populations.