Next Generation Matrix Method Research Articles

Modelling the Time-varying Transmission of Wild Poliovirus in Pakistan

Aims/Objectives: The efforts to eradicate the wild poliovirus since 1988 have successfully reduced its global prevalence by 99%. However, as of 2024, Pakistan and Afghanistan remain the only two endemic countries facing the virus transmission. This study employs a transmission dynamic model to understand the persistence of wild poliovirus type 1 (WPV1) in Pakistan. Study Design: An ordinary differential equations-based deterministic type of mathematical model was developed. Place and Duration of Study: Department of Epidemiology and Public Health and Institute of Microbiology, University of Agriculture Faisalabad, March 2023 to August 2023. Methodology: We included the number of reported polio cases and the proportion of missed children by supplementary immunization activities (SIAs) across the country from 2017-2022. The model considered both human-human and environment-human virus transmission through sewage contamination and these are represented by time-dependent transmission rate parameters. The parameter estimation was done by model fitting to the reported data of WPV1 cases. The model simulations then predicted the future polio infections in Pakistan. Results: Our analysis identified that the asymptomatic infectious population missed by the SIAs is the major contributor to disease persistence in the country. Moreover, the environment can contribute to virus transmission in areas with poor WASH infrastructure and under-immunized populations. The estimated basic reproduction number through the next-generation matrix method was 1.61 while the estimated effective reproduction number was 0.12. The model showed a better predictive ability than constant transmission rate models. The numerical simulations considering the reduction in the virus-shedding rate by the asymptomatic population resulted in an 85% reduction in future polio cases in Pakistan. Conclusion: The results suggest that endemic virus transmission will continue subject to the current higher vaccination coverage across the country. The model can be further utilized to guide eradication efforts for targeted allocation of preemptive measures.

Impact of Yoga Awareness on Transmission Dynamics of Communicable Diseases: SIR Model Analysis

Communicable diseases are major health problems that affect the whole economy of the na-tion. So it becomes the prime agenda of developed and developing countries to educate peo-ple about disease dynamics and control strategies. Due to changes in people’s living styles, disease treatment modality has been changed. So, we have introduced Yoga awareness as control strategy which includes Ahar, Vihar, Achar and Vichar. They are means for achiev-ing the physical, mental, social and spiritual well-being. Our main aim is to model the role of Yoga awareness in controlling the disease dynamics. It maintains the physical fitness of practitioners and improve the whole metabolism system of the human body. In this work, the previous SIR model is modified by incorporating a new awareness transmission rate β 1 to the existing model. Real life situation data of Yoga aware and aware infected individuals were col-lected from different Yoga centers of Sudurpashchim province, Nepal and analyzed by using mathematical techniques. Stability analysis of governing by ordinary differential equations showed that model is stable. Yoga awareness reproduction number Ra was calculated by next-generation matrix method. Sensitivity analysis of Ra and concerning parameters indicate that Ra decreases with an increase in Yoga awareness coverage level. Also, the recovery rate has the opposite relation with Ra which indicates that the recovery period also decreases with an increase in awareness coverage. Local and global stability analysis showed that disease-free equilibrium exists when Ra < 1 and endemic equilibrium exists when Ra > 1. Numerical simulations also support the analytical results and suggest that Yoga awareness has a positive influence on controlling disease d ynamics. The increase in the coverage of awareness leads to reduced susceptibility and infectivity. So propagation of disease can be controlled by Yoga awareness.

Study on SEAI Model of COVID-19 Based on Asymptomatic Infection

In this paper, an SEAI epidemic model with asymptomatic infection is studied under the background of mass transmission of COVID-19. First, we use the next-generation matrix method to obtain the basic reproductive number R0 and calculate the equilibrium point. Secondly, when R0<1, the local asymptotic stability of the disease-free equilibrium is proved by Hurwitz criterion, and the global asymptotic stability of the disease-free equilibrium is proved by constructing the Lyapunov function. When R0>1, the system has a unique endemic equilibrium point and is locally asymptotically stable, and it is also proved that the system is uniformly persistent. Then, the application of optimal control theory is carried out, and the expression of the optimal control solution is obtained. Finally, in order to verify the correctness of the theory, the stability of the equilibrium point is numerically simulated and the sensitivity of the parameters of R0 is analyzed. We also simulated the comparison of the number of asymptomatic infected people and symptomatic infected people before and after adopting the optimal control strategy. This shows that the infection of asymptomatic people cannot be underestimated in the spread of COVID-19 virus, and an isolation strategy should be adopted to control the spread speed of the disease.

Analyzing Global Stability of M-Pox Disease Dynamics: Mathematical Insights into Detection and Treatment Strategies

In this research, a mathematical model is constructed to scrutinize the transmission patterns of monkeypox (mpox), with a specific emphasis on integrating the early detection of infected undetected individuals to curb its transmission. This research takes into account a range of factors influencing the propagation of monkeypox, encompassing population demographics, contact dynamics, and the efficacy of early detection of unidentified infected individuals. Employing the next-generation matrix method, the basic reproduction number (R0) is computed, revealing that the disease-free equilibrium state is locally asymptotically stable when (R0<1). This suggests that containment of monkeypox is achievable within a human populace where (R0) remains below one (1), yet it transitions to an endemic state when (R0) exceeds this critical value one (1). Furthermore, a sensitivity analysis is conducted to evaluate the robustness of our findings to variations in model parameters. Utilizing numerical simulations conducted via MAPLE 18, we demonstrate the significance of prompt identification and immediate intervention for infected individuals who may otherwise go undetected, in effectively diminishing the dynamic propagation of monkeypox. The results underscore the pivotal role of early detection in mitigating monkeypox outbreaks and curtailing transmission rates.

Mathematical Modelling of COVID-19 with Vaccination, Quarantine and Non-Pharmaceutical Interventions

This study formulated and analyzed a deterministic mathematical model of ten compartments for the transmission dynamics of COVID-19 infection using a system of non-linear ordinary differential equations. The system has disease-free and endemic equilibrium points. The basic reproduction number was obtained using the next-generation matrix method and the stability of the equilibrium points were analyzed. From the qualitative analysis, the disease-free equilibrium point is both locally and globally asymptotically stable. Finally, numerical simulations of the model were carried out using MATLAB R2021a. Based on the result obtained, it was concluded that the implementation of vaccination, non-pharmaceutical intervention as well as contact tracing and quarantine can lead to effective control or elimination of the COVID-19 pandemic. And hence, we recommend that the responsible agencies should create a way of enlightening the public on the need of being vaccinated for COVID-19 so as to prevent themselves from getting infected; also, adequate and effective implementation of vaccination and non-pharmaceutical interventions is required in order to prevent or curtail the COVID-19 infection completely. COVID-19, Non-pharmaceutical intervention, Quarantine, Stability analysis, Vaccination

A Mathematical Model for Transmission of Taeniasis and Neurocysticercosis

In this study, we present a mathematical model for the codynamics of taeniasis and neurocysticercosis and rigorously analyze it. To understand the underlying dynamics of the proposed model, basic system properties such as the positivity and boundedness of solutions are investigated through the completing differential process. The basic reproduction number was calculated using the next-generation matrix method, and the analysis showed that when R0<1, the disease in the community eventually dies out, and when R0>1, the diseases persist. Local stability of the equilibria was analyzed using the Jacobian matrix, and Lyapunov function techniques were used to determine the global analysis, which showed that the endemic equilibrium point was globally stable when R0>1. On the other hand, the disease-free equilibrium was determined to be globally stable when R0<1. To identify the most influential parameters of the proposed model, partial correlation coefficient techniques were used. The numerical results depict that the model aligns well with the transmission dynamics, which goes through two populations: humans and pigs, whereby the model system stabilizes after some time, showing the validity of the proposed model. Furthermore, the simulations of the proposed model revealed that the shedding habit of infected humans with taeniasis and the bad cooking habit or eating of raw or undercooked pork products have a higher impact on the spread of neurocysticercosis and taeniasis in the community. Hence, this study proposes that in order to control taeniasis and neurocysticercosis, effective disease control measures should primarily prioritize hygienic behaviour and proper cooking of pork meat to the required temperature.

Analysis of a patch epidemic model incorporating population migration and entry–exit screening

This paper presents an SIQR patch model that combines population migration and entry–exit screening. The threshold for disease extinction is determined using the next-generation matrix method. By constructing the Lyapunov function, the global asymptotic stability of the disease-free equilibrium is demonstrated when R0 < 1. The local asymptotic stability of the endemic equilibrium is shown using the Hurwitz criterion, and it is found that the disease is uniformly persistent when R0 > 1. The influence of screening and migration on disease dynamics is discussed via numerical simulations. Our findings highlight the significance of the detection rate as a vital index in disease transmission and emphasize the effectiveness of screening strategies in preventing outbreaks. Therefore, during an outbreak, it is recommended to establish checkpoints in regions with high mobility to identify and isolate potentially infected individuals, thereby reducing the widespread dissemination of the pandemic.

Fractional view analysis of sexual transmitted human papilloma virus infection for public health

The infection of human papilloma virus (HPV) poses a global public health challenge, particularly in regions with limited access to health care and preventive measures, contributing to health disparities and increased disease burden. In this research work, we present a new model to explore the transmission dynamics of HPV infection, incorporating the impact of vaccination through the Atangana–Baleanu derivative. We establish the positivity and uniqueness of the solution for the proposed model HPV infection. The threshold parameter is determined through the next-generation matrix method, symbolized by R0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathcal {R}}_0$$\\end{document}. Moreover, we investigate the local asymptotic stability of the infection-free steady-state of the system. The existence of the solutions of the recommended model is determined through fixed-point theory. A numerical scheme is presented to visualize the dynamical behavior of the system with variation of input factors. We have shown the impact of input parameters on the dynamics of the system through numerical simulations. The findings of our investigation delineated the principal parameters exerting significant influence for the control and prevention of HPV infection.

Mathematical Modeling of Coccidiosis Dynamics in Chickens with Some Control Strategies

Coccidiosis is an infectious disease caused by the Eimeria species. The species can infect a bird’s digestive system, severely slow down its growth, and is a serious economic burden for chickens. A mathematical model for the transmission dynamics of coccidiosis disease in chickens in the presence of control interventions has been formulated and analyzed to gain insights into the dynamics of the disease in the population. Three control interventions, namely vaccination, sanitation, and treatment, are implemented. The study intends to assess the effects of these control interventions in coccidiosis transmission dynamics. Using the theory of differential equations, the invariant set of the model was derived, and the model’s solution was found to be mathematically and biologically significant. Analytical methods are employed to establish equilibrium solutions and investigate the stability of the model system’s equilibria, while numerical simulations illustrate the analytical results. The effective reproduction number is obtained using the next-generation matrix method, and the local stability of the equilibria of the model is established. The disease-free equilibrium is proved to be locally stable when the effective reproduction number is less than unity. Also, the nature of the bifurcation and its implications for disease prevention are investigated through the application of the center manifold theory. On the other hand, sensitivity analysis is carried out to investigate the parameters that impact the transmission of coccidiosis disease using the normalized forward sensitivity index. The parameters that have a greater influence on the effective reproduction number should be targeted for control purposes to lessen the spread of disease. Furthermore, numerical simulation is performed to investigate the contribution of each control intervention.

Prediction and decision making in corona virus using fuzzy mathematical model

During the period of 2019–20, forecasting was of utmost priority for health care planning and to combat COVID-19 pandemic. Almost everyone’s life has been greatly impacted by COVID-19. Understanding how the disease spreads is crucial to know how the disease behaves dynamically. The aim of the research is to construct an SEI Q1Q2 R model for COVID-19 with fuzzy parameters. The fuzzy parameters are the transmission rate, the infection rate, the recovery rate and the death rate. We compute the basic reproduction number, using next-generation matrix method, which will be used further to study the model’s prediction. The COVID-free and endemic equilibrium points attain local and global stability when R0 < 1. A sensitivity analysis of the reproduction number against its internal parameter has been done. The results of this model showed that intervention measures. The numerical simulation along with graphical representations at COVID-free and endemic points are shown. The SEIQ1Q2R model is a successful model to analyse the spreading and controlling the epidemics like COVID-19.

Mathematical analysis and simulation of COVID-19 model with booster dose vaccination strategy in Bangladesh

The control of COVID-19 transmission remains a crucial issue despite the administration of multiple doses of vaccines, given the ongoing emergence of new variants. This study proposes a mathematical model of COVID-19 with multiple doses of vaccinations. We find disease-free equilibrium (DFE) and disease-endemic equilibrium (DEE) and perform their stability analysis to explore in which parameters space the disease will be fade-out or persists in the population. This study derives mathematical expressions for the basic reproductive numbers (R0) using the Next-Generation Matrix method. Using surface and contour plots, we brought to light the exciting consequences of disease transmission rate and other parameter values on the basic reproduction number (R0). It demonstrates that the disease-free equilibrium point is locally stable when R0 < 1, whereas the disease-endemic equilibrium point is locally stable for R0 > 1. We also perform bifurcation analysis to demonstrate in which conditions the disease will be stable or unstable when R0 = 1. Numerical simulations show that increasing first dose vaccination rate is more effective than second and booster doses vaccination rate for reducing the number of asymptomatic and symptomatic cases in Bangladesh. We use COVID-19 incidence data from WHO between January and December 2022 and estimate parameters using the least-squares technique. We perform the sensitivity index of symptomatic and asymptomatic cases to identify the most significant parameter for disease outbreaks and found that transmission rate had the highest impact on disease prevalence. This research provides insight to prevent and control of COVID-19 transmission with booster-dose vaccination in Bangladesh.

Optimal control strategies on HIV/AIDS and pneumonia co-infection with mathematical modelling approach

In this paper, a compartmental model on the co-infection of pneumonia and HIV/AIDS with optimal control strategies was formulated using the system of ordinary differential equations. Using qualitative methods, we have analysed the mono-infection and HIV/AIDS and pneumonia co-infection models. We have computed effective reproduction numbers by applying the next-generation matrix method, applying Castillo Chavez criteria the models disease-free equilibrium points global stabilities were shown, while we have used the Centre manifold criteria to determine that the pneumonia infection and pneumonia and HIV/AIDS co-infection exhibit the phenomenon of backward bifurcation whenever the corresponding effective reproduction number is less than unity. We carried out the numerical simulations to investigate the behaviour of the co-infection model solutions. Furthermore, we have investigated various optimal control strategies to predict the best control strategy to minimize and possibly to eradicate the HIV/AIDS and pneumonia co-infection from the community.

Optimal Control Strategy of a Mathematical Model for the Fifth Wave of COVID-19 Outbreak (Omicron) in Thailand

The world has been fighting against the COVID-19 Coronavirus which seems to be constantly mutating. The present wave of COVID-19 illness is caused by the Omicron variant of the coronavirus. The vaccines against the five variants (α, β, γ, δ, and ω) have been quickly developed using mRNA technology. The efficacy of the vaccine developed for one of the strains is not the same as the efficacy of the vaccine developed for the other strains. In this study, a mathematical model of the spread of COVID-19 was made by considering asymptomatic population, symptomatic population, two infected populations and quarantined population. An analysis of basic reproduction numbers was made using the next-generation matrix method. Global asymptotic stability analysis was made using the Lyapunov theory to measure stability, showing an equilibrium point’s stability, and examining the model with the fact of COVID-19 spread in Thailand. Moreover, an analysis of the sensitivity values of the basic reproduction numbers was made to verify the parameters affecting the spread. It was found that the most common parameter affecting the spread was the initial number in the population. Optimal control problems and social distancing strategies in conjunction with mask-wearing and vaccination control strategies were determined to find strategies to give better control of the spread of disease. Lagrangian and Hamiltonian functions were employed to determine the objective function. Pontryagin’s maximum principle was employed to verify the existence of the optimal control. According to the study, the use of social distancing in conjunction with mask-wearing and vaccination control strategies was able to achieve optimal control rather than controlling just one or another.

Synchronization Studies of Hindmarsh–Rose Neuron Networks: Unraveling the Influence of connection induced memristive synapse

This study focuses on the synchronization analysis of Hindmarsh–Rose neurons coupled through a common memristor (coupled mHRN). Initially, we thoroughly examine the synchronization of two mHRNs coupled via a common memristor before exploring synchronization in a network of mHRNs. The stability of the proposed model is analyzed in three cases, demonstrating the existence of a single equilibrium point whose stability is influenced by external stimuli. The stable and unstable regions are investigated using eigenvalues. Through bifurcation analysis and the determination of maximum Lyapunov exponents, we identify chaotic and hyperchaotic trajectories. Additionally, using the next-generation matrix method, we calculate the chaotic number C0, demonstrating the influence of coupling strength on the chaotic and hyperchaotic behavior of the system. The exponential stability of the synchronous mHRN is derived analytically using Lyapunov theory, and our results are verified through numerical simulations. Furthermore, we explore the impact of initial conditions and memristor synapses, as well as the coupling coefficient, on the synchronization of coupled mHRN. Finally, we investigate a network consisting of n number of mHRNs and observe various collective behaviors, including incoherent, coherent, traveling patterns, traveling wave chimeras, and imperfect chimeras, which are determined by the memristor coupling coefficient.

Competitive information propagation considering local-global prevalence on multi-layer interconnected networks

The popularity of online social networks (OSNs) promotes the co-propagation of multiple types of information. And there exist inevitably competitive interactions between these information, which will significantly affect the spreading trend of each information. Besides, the coupled topology of multi-layer interconnects exhibited in OSNs will also increase the research complexity of information propagation dynamics. To effectively address these challenges, we propose a novel competitive information propagation model on multi-layer interconnected networks, where the tendency of an individual to become a positive or negative spreader depends on the weighted consideration of local and global prevalence. Then the basic reproduction number is calculated via next-generation matrix method. And under the critical conditions of the basic reproduction number, the asymptotic stability of information-free and information-endemic equilibria is theoretically proven through Lyapunov stability theory. Besides, an optimal control problem involving two heterogeneous controls is formulated, aiming at achieving the best suppression performance of negative information with the minimum control cost. According to Cesari theorem and Pontryagin minimum principle, the existence and analytical formulation of optimal solutions are derived. Extensive numerical experiments are conducted to prove the correctness of our theoretical results, and evaluate the effectiveness of our proposed control strategies. This study can provide useful insights into the modeling and control of multiple information propagation considering multi-layer network topology and individual adaptive behavior.

Investigating the fractional dynamics and sensitivity of an epidemic model with nonlinear convex rate

The current study analyzes a fractional compartmental epidemic model for the transmission of infectious disease in a community. This study uses the Caputo derivative as well as Atangana–Baleanu derivative to consider a SIR fractional epidemic model with a convex incidence rate. We demonstrate the existence and uniqueness of solutions by using the idea of fixed-point theory. Comprehensive mathematical approaches show the physical properties of solutions, such as non-negativity and boundedness. The basic reproduction number is evaluated using the next-generation matrix method, determining whether the infection will spread in society. The stability analysis is performed with phase portraits, which show that the infection-free and infection-present steady states of the considered model are locally and globally asymptotically stable. The sensitivity of the basic reproduction number is carried out through 3D graphs, which indicate the most sensitive and impactful parameters. Finally, for the numerical solution of the underlying model, a numerical technique is applied and these solutions evaluate the theoretical results through numerical simulations. Numerical simulations that aim to decrease the fractional parameter and convex incidence rate can bring about a significant change in infected individuals.

Modeling the effect of non-pharmaceutical measures and vaccination on the spread of two variants of COVID-19 in India

An RNA virus, SARS-CoV-2 is capable of mutation, and vaccines developed to combat its earlier strains are comparatively less effective against its new emerging variants of concern. Therefore, it is proposed to formulate a two-strain COVID-19 deterministic model that incorporates non-pharmaceutical preventive strategies along with an imperfect and leaky vaccine. The control reproduction number (denoted by Rc) of the model is calculated using the next-generation matrix method. Rigorous model analysis elucidates that its disease-free equilibrium (DFE) is locally asymptotically stable when Rc<1. Using the central manifold theorem, the occurrence of subcritical bifurcation is proved when the relevant conditions required for its existence hold. However, the model exhibits transcritical bifurcation when the vaccinated population does not get infected. Additionally, the DFE point of this reduced case is globally asymptotically stable when Rc is sufficiently less than 1. Moreover, the model is analyzed to reveal the presence and global asymptotic stability (using the Lyapunov function approach) of endemic equilibrium points. The introduced model is calibrated and cross-validated with observed daily and cumulative data of Delta (1 April 2021 to 30 November 2021) and Omicron variant (1 December 2021 to 15 February 2022). Data fitting depicts that competitive exclusion exists among the variants as the Omicron variant tends to extinct other variants prevalent in that duration within a restricted timeframe. The model is examined, using the known and calibrated parameter values corresponding to the Omicron variant, to examine the impression of vaccination, quarantine, isolation, and lockdown on the prevalence of illness in India. The impact of fluctuations in vaccine and infection-induced immunities on daily and cumulative cases is studied. It is observed that vaccine-derived immunity exerts a greater influence on the current wave of the pandemic as compared to subsequent waves while natural infection immunity has a significant impact on future waves of the pandemic. Furthermore, there is a possibility of a future wave of the Omicron variant but with a relatively low peak. The minimum percentage of vaccinated people required to reach community-wide herd immunity has been estimated with respect to vaccine efficacy and various non-pharmaceutical control parameters.

Dynamics of a nonlinear epidemic transmission model incorporating a class of hospitalized individuals: a qualitative analysis and simulation

This study aims to develop a novel mathematical epidemic compartmental model that includes a compartment or class for individuals who become infected and experience severe illness due to the infection. These individuals require hospitalization and the use of specialized medical equipment, such as ventilators, ICU beds, etc, during an outbreak. This compartment is referred to as the ‘hospitalized population compartment’ throughout this study. Additionally, the model incorporates a saturated incidence rate for new infection cases and the hospitalization rate for individuals severely affected by the infection, intending to create a more realistic scenario of the dynamics of disease transmission. The model is developed by integrating a compartment for hospitalized individuals into the standard susceptible-infected-recovered compartmental model and is subsequently mathematically analyzed for qualitative behavior. In this model, the saturated hospitalization rate reflects that the number of severely infected individuals who can be hospitalized is limited at any given time due to constraints in sufficient hospital infrastructure availability. The incidence rate of susceptibles becoming infected is modeled using the Holling Type II functional form, which incorporates inhibitory effects observed within the population. The study analyzes the mathematical model for two types of equilibria: the disease-free equilibrium (DFE) and the endemic equilibrium (EE). To investigate the stability of both equilibria, the basic reproduction number, , is calculated using the next-generation matrix method. The findings indicate that when , the DFE is locally asymptotically stable. Conversely, when , the DFE becomes unstable, leading to the emergence of a positive EE. Additionally, the study explores the occurrence of forward and backward transcritical bifurcations under specific conditions when . Furthermore, the study delves into both the local and global stability behaviors of the EE. Numerical simulations of the model are also performed to support the theoretical findings.

Dynamical analysis of a nonlinear fractional cervical cancer epidemic model with the nonstandard finite difference method

In this paper, we analyze the fractional compartmental model in the sense of Caputo derivative for the dynamics of the novel human papillomavirus, which causes cervical cancer. We study and investigate the dynamical analysis of a nonlinear fractional-order cervical cancer epidemic model with the nonstandard finite difference method. The newly proposed nonlinear fractional model is an extension of an integer-order cervical cancer mathematical model. We demonstrate the solution's existence, uniqueness, non-negativity, and boundedness by utilizing fundamental concepts of the fixed-point theory. The basic reproduction number, which analyzes whether or not the infection spreads to the population, is computed using the next-generation matrix method. We investigate the local and global asymptotic stability of the derived cervical-free and cervical-present equilibrium points and discuss the sensitivity of the basic reproduction number, which depends on the parameters of the proposed model. Furthermore, a mathematical simulation of the suggested continuous model is performed to evaluate the reported theoretical results using the nonstandard finite difference method. The acquired results are displayed, which show that a fractional parameter plays a pivotal role in controlling the cervical cancer.

Modeling the dynamics of COVID-19 in the presence of Delta and Omicron variants with vaccination and non-pharmaceutical interventions

Since its inception in December 2019, many safe and effective vaccines have been invented and approved for use against COVID-19 along with various non-pharmaceutical interventions. But the emergence of numerous SARS-CoV-2 variants has put the effectiveness of these vaccines, and other intervention measures under threat. So it is important to understand the dynamics of COVID-19 in the presence of its variants of concern (VOC) in controlling the spread of the disease. To address these situations and to find a way out of this problem, a new mathematical model consisting of a system of non-linear differential equations considering the original COVID-19 strain with its two variants of concern (Delta and Omicron) has been proposed and formulated in this paper. We then analyzed the proposed model to study the transmission dynamics of this multi-strain model and to investigate the consequences of the emergence of multiple new SARS-CoV-2 variants which are more transmissible than the previous ones. The control reproduction number, an important threshold parameter, is then calculated using the next-generation matrix method. Further, we presented the discussion about the stability of the model equilibrium. It is shown that the disease-free equilibrium (DFE) of the model is locally asymptotic stable when the control reproduction is less than unity. It is also shown that the model has a unique endemic equilibrium (EEP) which is locally asymptotic stable when the control reproduction number is greater than unity. Using the Center Manifold theory it is shown that the model also exhibits the backward bifurcation phenomenon when the control reproduction number is less than unity. Again without considering the re-infection of the recovered individuals, it is proved that the disease-free equilibrium is globally asymptotically stable when the reproduction threshold is less than unity. Finally, numerical simulations are performed to verify the analytic results and to show the impact of multiple new SARS-CoV-2 variants in the population which are more contagious than the previous variants. Global uncertainty and sensitivity analysis has been done to identify which parameters have a greater impact on disease dynamics and control disease transmission. Numerical simulation suggests that the emergence of new variants of concern increases COVID-19 infection and related deaths. It also reveals that a combination of non-pharmaceutical interventions with vaccination programs of new more effective vaccines should be continued to control the disease outbreak. This study also suggests that more doses of vaccine should provide to combat new and deadly variants like Delta and Omicron.