Partial Rank Research Articles

Improving ranking-based question answering with weak supervision for low-resource Qur’anic texts

AbstractThis work tackles the challenge of ranking-based machine reading comprehension (MRC), where a question answering (QA) system generates a ranked list of relevant answers for each question instead of simply extracting a single answer. We highlight the limitations of traditional learning methods in this setting, particularly under limited training data. To address these issues, we propose a novel ranking-inspired learning method that focuses on ranking multiple answer spans instead of single answer extraction. This method leverages lexical overlap as weak supervision to guide the ranking process. We evaluate our approach on the Qur’an Reading Comprehension Dataset (QRCD), a low-resource Arabic dataset over the Holy Qur’an. We employ transfer learning with external resources to fine-tune various transformer-based models, mitigating the low-resource challenge. Experimental results demonstrate that our proposed method significantly outperforms standard mechanisms across different models. Furthermore, we show its better alignment with the ranking-based MRC task and the effectiveness of external resources for this low-resource dataset. Our best performing model achieves a state-of-the-art partial Reciprocal Rank (pRR) score of 63.82%, surpassing the previous best-known score of 58.60%. To foster further research, we release code [GitHub repository:github.com/mohammed-elkomy/weakly-supervised-mrc], trained models, and detailed experiments to the community.

Modeling Zika Virus Disease Dynamics with Control Strategies

In this research, we formulated a fractional-order model for the transmission dynamics of Zika virus, incorporating three control strategies: health education campaigns, the use of insecticides, and preventive measures. We conducted a theoretical analysis of the model, obtaining the disease-free equilibrium and the basic reproduction number, and analyzing the existence and uniqueness of the model. Additionally, we performed model parameter estimation using real data on Zika virus cases reported in Colombia. We found that the fractional-order model provided a better fit to the real data compared to the classical integer-order model. A sensitivity analysis of the basic reproduction number was conducted using computed partial rank correlation coefficients to assess the impact of each parameter on Zika virus transmission. Furthermore, we performed numerical simulations to determine the effect of memory on the spread of Zika virus. The simulation results showed that the order of derivatives significantly impacts the dynamics of the disease. We also assessed the effect of the control strategies through simulations, concluding that the proposed interventions have the potential to significantly reduce the spread of Zika virus in the population.

Chaos and feasibility analysis of a healthy lifestyle’s sustainability using fractional-order polycystic ovarian syndrome’s effect on infertility

In this study, we developed a fractional-order model for polycystic ovarian syndrome issue transmission in women through four compartments with the Mittag-Leffler kernel. For biological feasibility, we discussed the positivity and boundedness of solutions with fixed point mappings in Banach spaces. Sensitivity analysis is performed using different variables as response functions each time, employing Latin Hyper-cube Sampling (LHS) and Partial Rank Correlation Coefficient (PRCC) with 200 iterations. Further, the reproductive number is determined for the model’s biological feasibility with an analysis of parameter impact through Matlab software. The solutions are examined for global stability using the Lyapunov function with a first derivative. Chaos Control will use the regulate for linear responses approach to bring the system to stabilize according to its points of equilibrium. Numerical solutions are derived by using a Newton polynomial in the generalized form of the Mittag-Leffler kernel, which illustrates the effect of the fractional operator and parameters involved in the system. Results are also analyzed with different assumptions of parameter values and initial conditions to observe the different impacts of treatment to overcome the risk of infertility in women. Such type of investigation will be useful to investigate the spread of disease as well as helpful in developing control strategies to overcome the risk of problems and best management care pre-detection of the issue and for treatment.

Effective Pest Control Through Natural Predators: A Dynamical Plant–Pest–Predator Model

The impact of pests on crop yield is a significant worry for farmers, and finding an effective strategy to control insect population growth has become a pressing matter. This study explores the dynamic analysis of a model that incorporates natural predators to control crop pests. In the research, an analysis is conducted on the model’s positivity and boundedness, followed by an examination of the existence and stability of the equilibrium points. The study focused on analyzing bifurcations at a biologically feasible equilibrium point. The parameters considered for bifurcation are the predation rate by pests and the consumption rate of natural predators. In addition, an optimal control technique has been employed to enhance the growth of the plant population through the utilization of Pontryagin’s maximum principle. Moreover, the impact of the nine parameters on the model is examined through sensitivity analysis using the partial rank correlation coefficient method. Numerical simulations are conducted to validate the analytical findings, revealing the occurrence of bifurcation and the positive impact of control on plant population growth.

Spatiotemporal Dynamics of an Intraguild Predation Model with Intraspecies Competition

Different species in the environment compete with one another for shared resources and suitable habitats. As a result, it becomes crucial to identify the essential components involved in preserving biodiversity. This paper describes the emergence of a wide range of temporal and spatiotemporal dynamics of an intraguild predation (IGP) model with intraspecies competition and Holling type-II response function between the IG-prey and IG-predator. To explore the dynamics of the temporal model, we study the local stability of all the biologically feasible steady states, global stability of the interior steady state, and Hopf bifurcation. Performing partial rank correlation coefficient (PRCC) sensitivity analysis, we picked more sensitive parameters and plotted the stability regions in two-parameter spaces. The dynamics exhibited by the system can demonstrate some important hallmarks noticed in the environments, such as the existence and nonexistence of oscillatory behavior in the IGP model. The analytical formulations for the stability and bifurcation of the coexistence of the steady-state are not easy to obtain, but we have verified numerically that the limit cycle bifurcates from the coexistence of the steady-state and there eventually emerges a chaotic behavior through period-doubling bifurcations. By plotting the largest Lyapunov exponent (LLE), we have verified that the temporal system experiences chaotic behavior. It is demonstrated that in the case of a diffusive system, diffusion may cause the coexistence of the steady state, which is otherwise stable, to become unstable. Criteria for the occurrence of Turing instability connected to the IGP model are derived. Our numerical illustrations demonstrate that diffusion-driven instability develops different stationary patterns based on the different initial conditions and diffusion parameters. The spatiotemporal patterns are observed in the Turing, Hopf–Turing, and Hopf regions.

Dynamics of autonomous and nonautonomous Leslie–Gower model for the impacts of fear and its carry‐over effects including predator harvesting

Recently, certain biological field experiments and research findings have revealed that predators not only reduce prey populations through direct predation (lethal effect) but also indirectly affect the growth rate of prey by inducing fear; these nonlethal effects can be carried over seasons or generations. In this paper, we proposed an autonomous and a nonautonomous Leslie–Gower model incorporating some biological factors such as fear and its carry‐over effects, prey refuge, and nonlinear predator harvesting. In the autonomous model, first, we examined the well‐posedness, positivity solutions, and their boundedness. Also, it is shown that new equilibrium points emerge and disappear with the change in intrinsic growth rate of predator. Further, we compute and analyzed the local and global stability at the interior equilibrium points. Furthermore, Hopf bifurcation and direction and stability of limit cycle at interior equilibrium points are established. Moreover, the sensitivity analysis of the biological parameters is carried out numerically with two statistical methods via Latin hypercube sampling and partial rank correlation coefficients. It was found that at the small values of fear factor, carry‐over effect, and refuge behavior of prey parameters, the autonomous system exhibits oscillatory behavior, whereas for small values of prey birth rate and harvesting effort, the system remains stable. However, when intrinsic growth rate of predator increases from a low value to a higher value, the system shows transition from stability to instability and back to stability. We also explore the effects of seasonal variations in biological parameters in the nonautonomous model. Additionally, we investigate the theoretical existence of positive periodic solutions using the continuation theorem. The influences of seasonal variations in some parameters such as prey's birth rate, fear, and its carry‐over effects; refuge behavior of prey; intrinsic growth rate of predator; and harvesting effort are then numerically investigated. The results reveal the emergence of positive periodic solutions and bursting patterns in the seasonally forced model.

Properties, estimation, and applications of the extended log-logistic distribution

This paper presents the exponentiated alpha-power log-logistic (EAPLL) distribution, which extends the log-logistic distribution. The EAPLL distribution emphasizes its suitability for survival data modeling by providing analytical simplicity and accommodating both monotone and non-monotone failure rates. We derive some of its mathematical properties and test eight estimation methods using an extensive simulation study. To determine the best estimation approach, we rank mean estimates, mean square errors, and average absolute biases on a partial and overall ranking. Furthermore, we use the EAPLL distribution to examine three real-life survival data sets, demonstrating its superior performance over competing log-logistic distributions. This study adds vital insights to survival analysis methodology and provides a solid framework for modeling various survival data scenarios.

Development of a Brief Assessment Tool to Evaluate Early Low Nutrition Risk in Community Elderly. Creation of the tool and examination of its reliability and criterion-related validity.

To date simple assessment tool to evaluate early low nutrition risk in general older population has not been available. This study aimed to create such tool and examined its reliability and criterion-related validity. 1,192 community elderly with a mean age of 74.7(5.8) years responded to a questionnaire consisting of 48 (Hatoyama) or 34 items (Kusatsu), which have been reported to be associated with nutritional state in older people. Item analysis was conducted on the 34 common items, and items were selected based on the following criteria: adequate pass rates and discriminative power, no gender and regional differences, and a certain level of commonality based on factor analysis. Next, the factor structure of the candidate items was examined through exploratory factor analysis, and confirmatory factor analysis was conducted as the final scale structure. Furthermore, Spearman's partial rank correlation coefficients (sex- and age-adjusted) between the created index and important health indicators were examined to determine the criterion-related validity. Finally, we obtained a semantic coherence of 4 factors (named health beliefs, dietary status, physical activity, and food-related quality of life) totaling 13 items; confirmatory factor analysis of the 4-factor solution yielded good model fit values, χ2 (59) =275.4 (p<0.001), CFI=0.930, and RMSEA=0.056. The factor loadings for each factor ranged from 0.43 to 0.82, indicating adequate loadings. The reliability of the index was shown to be high by Good-Poor analysis and Cronbach's α. The index showed statistically significant correlations with all health indicators. We have developed a simple assessment tool to evaluate early low nutrition risk in general older population.

Untangling the memory and inhibitory effects on SIS-epidemic model with Beddington–DeAngelis infection rate

The dynamical behaviors of an epidemic model based on the susceptible–infected–susceptible (SIS) model are investigated. The Beddington–DeAngelis functional response is used for the infection rate to present the dependence of the transmission of the infection on the ratio of both susceptible and infected populations. A Caputo fractional derivative is applied to show the existence of memory in nature affects population dynamics. The disease-free and endemic equilibrium points are obtained as the equilibrium points that describe the condition when the population is free from the disease or the disease exists in the population throughout time. The existence, uniqueness, non-negativity, and boundedness are proven which state the biological validity of the mathematical model. The local and global stability of each equilibrium point is studied including the basic reproduction number and its influence on the dynamical behaviors. Some numerical simulations are portrayed to explore more about the dynamics of the model which are relevant to the analytical findings. The partial rank correlation coefficient is presented to investigate the dominant parameter with respect to the basic reproduction number and the density of susceptible and infected populations. The parameter continuations are demonstrated to show the impact of infection rate and the inhibitory effect which lead to the occurrence of forward bifurcations. The memory effect is also demonstrated numerically to show the changes in convergence rate due to the changes in memory strength.

Modelling the role of tourism in the spread of HIV: A case study from Malaysia

This study aimed to assess the role of tourism in the spread of human immunodeficiency virus (HIV) using Malaysian epidemiological data on HIV and acquired immunodeficiency syndrome (AIDS) incidence from 1986 to 2004. A population-level mathematical model was developed with the following compartments: the population susceptible to HIV infection, the clinically confirmed HIV-positive population, the population diagnosed with AIDS, and the tourist population. Additionally, newborns infected with HIV were considered. Sensitivity analyses and variations in fixed parameter values were used to explore the effect of changes to various parameter values on HIV incidence in the model. It was determined that variations in the rate of HIV-positive inbound tourist entries and the rate of foreign tourist exits (i.e., the duration of time tourists spent in Malaysia) significantly impacted the predicted incidence of HIV and AIDS in Malaysia. The model's fit to observed HIV and AIDS incidence was evaluated, resulting in adjusted R2 values of 53.3% and 53.2% for HIV and AIDS, respectively. Furthermore, the reproduction number (R0) was also calculated to quantify the stability of the HIV endemicity in Malaysia. The findings suggest that a steady-state level of HIV in Malaysia is achievable based on the low value of R0 = 0.0136, and the disease-free equilibrium was stable from the negative eigenvalues obtained, which is encouraging from a public health perspective. The Partial Rank Correlation Coefficient (PRCC) values between the proportion of newborns born HIV-positive, the rate of Malaysian tourist entries returning home after contracting HIV, and the rate of foreign tourist exits have a significant impact on the R0. The methods provide a framework for epidemiological modelling of HIV spread through transient population groups. The model results suggest that the role of tourism should not be overlooked within the set of available measures to mitigate the spread of HIV.

The wisdom of the crowd with partial rankings: A Bayesian approach implementing the Thurstone model in JAGS.

We develop a Bayesian method for aggregating partial ranking data using the Thurstone model. Our implementation is a JAGS graphical model that allows each individual to rank any subset of items, and provides an inference about the latent true ranking of the items and the relative expertise of each individual. We demonstrate the method by analyzing data from new experiments that collected partial ranking data. In one experiment, participants were assigned subsets of items to rank; in the other experiment, participants could choose how many and which items they ranked. We show that our method works effectively for both sorts of partial ranking in applications to US city populations and the chronology of US presidents. We discuss the potential of the method for studying the wisdom of the crowd and other research problems that require aggregating incomplete or partial rankings.

Boosting Healthiness Exposure in Category-Constrained Meal Recommendation Using Nutritional Standards

Food computing, a newly emerging topic, is closely linked to human life through computational methodologies. Meal recommendation, a food-related study about human health, aims to provide users a meal with courses constrained from specific categories (e.g., appetizers, main dishes) that can be enjoyed as a service. Historical interaction data, important user information, is often used by existing models to learn user preferences. However, if a user’s preferences favor less healthy meals, the model will follow that preference and make similar recommendations, potentially negatively impacting the user’s long-term health. This emphasizes the necessity for health-oriented and responsible meal recommendation systems. In this article, we propose a healthiness-aware and category-wise meal recommendation model called CateRec, which boosts healthiness exposure by using nutritional standards as knowledge to guide the model training. Two fundamental questions are raised and answered: (1) How can the healthiness of meals be evaluated? Two well-known nutritional standards from the World Health Organization and the United Kingdom Food Standards Agency are used to calculate the healthiness score of the meal. (2) How can the model training be guided in a health-oriented manner? We construct category-wise personalization partial rankings and category-wise healthiness partial rankings, and theoretically analyze that they meet the necessary properties and assumptions required to be trained by the maximum posterior estimator under Bayesian probability. The data analysis confirms the existence of user preferences leaning towards less healthy meals in two public datasets. A comprehensive experiment demonstrates that our CateRec effectively boosts healthiness exposure in terms of mean healthiness score and ranking exposure while being comparable to the state-of-the-art model in terms of recommendation accuracy.

Global stability and optimal control of an age-structured SVEIR epidemic model with waning immunity and relapses.

The efficacy of vaccination, incomplete treatment and disease relapse are critical challenges that must be faced to prevent and control the spread of infectious diseases. Age heterogeneity is also a crucial factor for this study. In this paper, we investigate a new age-structured SVEIR epidemic model with the nonlinear incidence rate, waning immunity, incomplete treatment and relapse. Next, the asymptotic smoothness, the uniform persistence and the existence of interior global attractor of the solution semi-flow generated by the system are given. We define the basic reproduction number and prove the existence of the equilibria of the model. And we study the global asymptotic stability of the equilibria. Then the parameters of the model are estimated using tuberculosis data in China. The sensitivity analysis of is derived by the Partial Rank Correlation Coefficient method. These main theoretical results are applied to analyze and predict the trend of tuberculosis prevalence in China. Finally, the optimal control problem of the model is discussed. We choose to take strengthening treatment and controlling relapse as the control parameters. The necessary condition for optimal control is established.

Assessing the impact of immunotherapy on oncolytic virotherapy in the treatment of cancer

AbstractCombined oncolytic virotherapy and immunotherapy are novel treatment protocols that represent a promising and advantageous strategy for various cancers, surpassing conventional anti-cancer treatments. This is due to the reduced toxicity associated with traditional cancer therapies. We present a mathematical model that describes the interactions between tumor cells, the immune response, and the combined application of virotherapy and interleukin-2 (IL-2). A stability analysis of the model for both the tumor and tumor-free states is discussed. To gain insight into the impact of model parameters on tumor cell growth and inhibition, we perform a sensitivity analysis using Latin hypercube sampling to compute partial rank correlation coefficient values and their associated p-values. Furthermore, we perform optimal control techniques using the Pontryagin maximum principle to minimize tumor burden and determine the most effective protocol for the administered treatment. We numerically demonstrate the ability of combined virotherapy and IL-2 to eliminate tumors.

Agent-based model demonstrates the impact of nonlinear, complex interactions between cytokinces on muscle regeneration.

Muscle regeneration is a complex process due to dynamic and multiscale biochemical and cellular interactions, making it difficult to identify microenvironmental conditions that are beneficial to muscle recovery from injury using experimental approaches alone. To understand the degree to which individual cellular behaviors impact endogenous mechanisms of muscle recovery, we developed an agent-based model (ABM) using the Cellular-Potts framework to simulate the dynamic microenvironment of a cross-section of murine skeletal muscle tissue. We referenced more than 100 published studies to define over 100 parameters and rules that dictate the behavior of muscle fibers, satellite stem cells (SSCs), fibroblasts, neutrophils, macrophages, microvessels, and lymphatic vessels, as well as their interactions with each other and the microenvironment. We utilized parameter density estimation to calibrate the model to temporal biological datasets describing cross-sectional area (CSA) recovery, SSC, and fibroblast cell counts at multiple timepoints following injury. The calibrated model was validated by comparison of other model outputs (macrophage, neutrophil, and capillaries counts) to experimental observations. Predictions for eight model perturbations that varied cell or cytokine input conditions were compared to published experimental studies to validate model predictive capabilities. We used Latin hypercube sampling and partial rank correlation coefficient to identify in silico perturbations of cytokine diffusion coefficients and decay rates to enhance CSA recovery. This analysis suggests that combined alterations of specific cytokine decay and diffusion parameters result in greater fibroblast and SSC proliferation compared to individual perturbations with a 13% increase in CSA recovery compared to unaltered regeneration at 28 days. These results enable guided development of therapeutic strategies that similarly alter muscle physiology (i.e. converting extracellular matrix [ECM]-bound cytokines into freely diffusible forms as studied in cancer therapeutics or delivery of exogenous cytokines) during regeneration to enhance muscle recovery after injury.

Agent-based model demonstrates the impact of nonlinear, complex interactions between cytokines on muscle regeneration

Muscle regeneration is a complex process due to dynamic and multiscale biochemical and cellular interactions, making it difficult to identify microenvironmental conditions that are beneficial to muscle recovery from injury using experimental approaches alone. To understand the degree to which individual cellular behaviors impact endogenous mechanisms of muscle recovery, we developed an agent-based model (ABM) using the Cellular-Potts framework to simulate the dynamic microenvironment of a cross-section of murine skeletal muscle tissue. We referenced more than 100 published studies to define over 100 parameters and rules that dictate the behavior of muscle fibers, satellite stem cells (SSCs), fibroblasts, neutrophils, macrophages, microvessels, and lymphatic vessels, as well as their interactions with each other and the microenvironment. We utilized parameter density estimation to calibrate the model to temporal biological datasets describing cross-sectional area (CSA) recovery, SSC, and fibroblast cell counts at multiple timepoints following injury. The calibrated model was validated by comparison of other model outputs (macrophage, neutrophil, and capillaries counts) to experimental observations. Predictions for eight model perturbations that varied cell or cytokine input conditions were compared to published experimental studies to validate model predictive capabilities. We used Latin hypercube sampling and partial rank correlation coefficient to identify in silico perturbations of cytokine diffusion coefficients and decay rates to enhance CSA recovery. This analysis suggests that combined alterations of specific cytokine decay and diffusion parameters result in greater fibroblast and SSC proliferation compared to individual perturbations with a 13% increase in CSA recovery compared to unaltered regeneration at 28 days. These results enable guided development of therapeutic strategies that similarly alter muscle physiology (i.e. converting extracellular matrix [ECM]-bound cytokines into freely diffusible forms as studied in cancer therapeutics or delivery of exogenous cytokines) during regeneration to enhance muscle recovery after injury.

Improving tuberculosis control: assessing the value of medical masks and case detection-a multi-country study with cost-effectiveness analysis.

Tuberculosis (TB) remains a significant global health concern, necessitating effective control strategies. This article presents a mathematical model to evaluate the comparative effectiveness of medical mask usage and case detection in TB control. The model is constructed as a system of ordinary differential equations and incorporates crucial aspects of TB dynamics, including slow-fast progression, medical mask use, case detection, treatment interventions and differentiation between symptomatic and asymptomatic cases. A key objective of TB control is to ensure that the reproduction number, , remains below unity to achieve TB elimination or persistence if exceeds 1. Our mathematical analysis reveals the presence of a transcritical bifurcation when the signifies a critical juncture in TB control strategies. These results confirm that the effectiveness of case detection in diminishing the endemic population of symptomatic individuals within a TB-endemic equilibrium depends on exceeding a critical threshold value. Furthermore, our model is calibrated using TB yearly case incidence data per 100 000 population from Indonesia, India, Lesotho and Angola. We employed the bootstrap resampling residual approach to assess the uncertainty inherent in our parameter estimates which provides a comprehensive distribution of the parameter values. Despite a declining trend in new incidence, these four countries exhibit a reproduction number greater than 1, indicating persistent TB cases in the presence of ongoing TB control programmes. We employ the partial rank correlation coefficient in conjunction with the Latin hypercube sampling method to conduct a global sensitivity analysis of the parameter for each fitted parameter in every country. We find that the medical mask use is more sensitive to reduce compared with the case detection implementation. To further gain insight into the necessary control strategy, we formulated an optimal control and studied the cost-effectiveness analysis of our model to investigate the impact of case detection and medical mask use as control measures in TB spread. Cost-effectiveness analysis demonstrates that combining these interventions emerges as the most cost-effective strategy for TB control. Our findings highlight the critical importance of medical masks and their efficacy coupled with case detection in shaping TB control dynamics, elucidating the primary parameter of concern for managing the control reproduction number. We envisage our findings to have implications and be vital for TB control if implemented by policymakers and healthcare practitioners involved in TB control efforts.

Stability and backward bifurcation for an HIV model with macrophages and CD4+T cells with latent reservoirs

Human immunodeficiency virus (HIV) primarily attacks CD4+ T cells but can also attack macrophage and dendritic cells leading to AIDS disease. Antiretroviral therapies are unavoidable to treat patients with HIV. However, the existing therapies failed in eliminating viral particles in infected patients. The establishment of a latency state in these patients could play a major role in this failure. To better understand the impact of different drug therapies on HIV dynamics, we propose an in-host model describing the dynamics of HIV and its interaction with both CD4+T and macrophage cells. This model incorporates the CD4+T latent reservoir as well. Results on the positivity, boundedness, and stability of solutions are shown. Furthermore, the basic reproduction number R0 is obtained using the next generation-matrix method. It is shown that the model is locally asymptotically stable at disease-free equilibrium (DFE) when the basic reproduction number R0<1. Moreover, the model exhibits either forward or backward bifurcation when R0=1. The global asymptotic stability of equilibria is investigated using suitable Lyapunov functions. To study the impact of our model parameters on the model dynamics, a sensitivity analysis is performed using the partial rank correlation coefficient method and the Latin hypercube sampling. Finally, numerical simulations are carried out to assess several drug therapy strategies to reduce HIV infection and improve health outcomes for HIV infected patients.

De-escalation of dual antiplatelet therapy for patients with acute coronary syndrome after percutaneous coronary intervention: a systematic review and network meta-analysis

ObjectivesTo compare dual antiplatelet therapy (DAPT) de-escalation with five alternative DAPT strategies in patients with acute coronary syndrome (ACS) undergoing percutaneous coronary intervention (PCI).DesignWe conducted a systematic review and network...

Comparative analysis of a fractional co-infection model using nonstandard finite difference and two-step Lagrange polynomial methods

In this work, Caputo fractional model for co-dynamics of two-strains (Alpha and Delta variants) of SARS-CoV-2 and tuberculosis (TB) is formulated. We investigates the basic mathematical analysis, existence of unique solution, stability analysis, sensitivity analysis and simulations of the proposed model. In the basic mathematical analysis, it is proved that the model’s solutions are non-negative, bounded and locally asymptotically stable at disease free equilibrium (DFE) point. The existence of unique solution is proved by using Banach fixed point theorem (BFPT). Stability analysis is carried out by employing Hyers–Ulam stability criteria. Sensitivity analysis is performed to assess the impact of the model parameters on the general dynamics of the model by implementing partial rank correlation coefficient (PRCC) technique. Simulations of the proposed model obtained from non-standard finite difference scheme (NSFDs) are compared with the simulations obtained from two-step Lagrange polynomial method (TLPM). It is concluded that NSFDs gives more accurate and realistic results than TLPM. To assess some control measures necessary for reducing the co-spread of both diseases, comparative simulations are carried out for the infected classes. Also, numerical assessments showed that preventive efforts against SARS-CoV-2 variants could results in the reduction of TB prevalence and the co-infection of both diseases.