Search Results (77)

This study explores the viral dynamics of SARS-CoV-2 infection within host cells by incorporating the pharmacological effects of andrographolide—a bioactive compound extracted from Andrographis paniculata, renowned for its antiviral, anti-inflammatory, and immunomodulatory properties. Through the application of mathematical modeling, the interactions among the virus, host cells, and immune responses are simulated to provide a comprehensive analysis of viral behavior over time. Two distinct models were employed to assess the impact of varying andrographolide dosages on viral load, target cell populations, and immune responses. One model revealed a clear dose–response relationship, whereas the other indicated that additional biological or pharmacological factors may modulate drug efficacy. Both models demonstrated stability, with basic reproductive numbers (R₀) suggesting the potential for viral propagation in the absence of effective therapeutic interventions. This study emphasizes the significance of understanding the pharmacokinetics (PK) and pharmacodynamics (PD) of andrographolide to optimize its therapeutic potential. The findings also underscore the necessity for further investigation into the compound’s absorption, distribution, metabolism, and excretion (ADME) characteristics, as well as its prospective applications in the treatment of not only COVID-19 but also other viral infections. Overall, the results lay a foundational framework for future experimental research and clinical trials aimed at refining andrographolide dosing regimens and improving patient outcomes. Full article

Understanding the effectiveness of different quarantine strategies is crucial for controlling the spread of COVID-19, particularly in regions with limited data. This study presents a SCIRD-inspired model to simulate the transmission dynamics of COVID-19 in medium-sized cities and their surrounding satellite towns. Unlike previous works that focus primarily on large urban centers or homogeneous populations, our approach incorporates intercity mobility and evaluates the impact of spatially differentiated interventions. By analyzing lockdown strategies implemented during the first year of the pandemic, we demonstrate that short, localized lockdowns are highly effective in reducing virus propagation, while intermittent restrictions balance public health concerns with socioeconomic demands. A key contribution of this study is the validation of the epidemic model using real-world data from the 2021 lockdown that occurred in a medium-sized city, confirming its predictive accuracy and adaptability to different contexts. Additionally, we provide a detailed analysis of how mobility patterns between municipalities influence infection spread, offering a more comprehensive mathematical framework for decision-making. These findings advance the understanding of epidemic control in regions with sparse data and provide evidence-based insights to inform public health policies in similar contexts. Full article

The aim of this paper is to investigate the qualitative behavior of a mathematical model of the COVID-19 pandemic. The constructed SAIRS-type mathematical model is based on nonlinear delay differential equations. The discrete-time delay is introduced in the model in order to take into account the latent stage where the individuals already have the virus but cannot yet infect others. This aspect is a crucial part of this work since other models assume exponential transition for this stage, which can be unrealistic. We study the qualitative dynamics of the model by performing global and local stability analysis. We compute the basic reproduction number ${\mathcal{R}}_0^d$, which depends on the time delay and determines the stability of the two steady states. We also compare the qualitative dynamics of the delayed model with the model without time delay. For global stability, we design two suitable Lyapunov functions that show that under some scenarios the disease persists whenever ${\mathcal{R}}_0^d>1$. Otherwise, the solution approaches the disease-free equilibrium point. We present a few numerical examples that support the theoretical analysis and the methodology. Finally, a discussion about the main results and future directions of research is presented. Full article

A novel time-dependent deterministic SEIRS model, extended with vaccination, hospitalization, and vital dynamics, is introduced. Time-varying basic and effective reproduction numbers associated with this model are defined, which are crucial metrics in understanding epidemic dynamics. Furthermore, a parameter identification approach has been used to develop a numerical method to compute these numbers for long-term epidemics. We analyze the actual COVID-19 data from the USA, Italy, and Bulgaria to solve appropriate inverse problems and gain an understanding of the time evolution behavior of the basic and effective reproduction numbers. Moreover, an insightful comparison of key coronavirus data and epidemiological parameters across these countries has been conducted. For this purpose, while the basic and effective reproduction numbers provide insights into the virus transmission potential, we propose data-driven criteria for assessing the actual realization of the transmission potential of the SARS-CoV-2 virus and the effectiveness of the applied restrictive measures. To obtain these results, we conduct a mathematical analysis to demonstrate various biological properties of the new differential model, including non-negativity, boundedness, existence, and uniqueness of the solution. The new model and the associated numerical simulation tools proposed herein could be applied to COVID-19 data in any country worldwide and hold a promising potential for the transmission capacity and impact of the virus. Full article

The COVID-19 pandemic has underscored the pivotal role of vaccines in mitigating the devastating impact of the virus. In Thailand, the vaccination campaign against SARS-CoV-2 began on 28 February 2021, initially prioritizing healthcare professionals before expanding into a nationwide effort on 7 June 2021. This study employs a mathematical model of COVID-19 transmission with vaccination to analyze the impact of Thailand’s COVID-19 vaccination program from 1 March 2021 to 31 December 2022. We specifically assess the potential loss of lives and occurrence of severe infections across various age groups in a hypothetical scenario where vaccines were not administered. By fitting our model with officially reported COVID-19 death data, our analysis reveals that vaccination efforts prevented a total of 300,234 deaths (95% confidence interval: 295,938–304,349) and averted 1.60 million severe COVID-19 infections (95% confidence interval: 1.54–1.65 million). Notably, the elderly population over 80 years old benefited the most from vaccination, with an estimated 84,518 lives saved, constituting 4.28% of this age group. Furthermore, individuals aged between 70 and 74 years experienced the highest reduction in severe infections, with vaccination potentially preventing 8.35% of this age bracket from developing severe COVID-19. Full article

COVID-19 is an enveloped virus with a single-stranded $RNA$ genome. The surface of the virus contains spike proteins, which enable the virus to attach to host cells and enter the interior of the cells. After entering the cell, the virus exploits the host cell’s mechanisms for replication and dissemination. Since the end of 2019, COVID-19 has spread rapidly around the world, leading to a large-scale epidemic. In response to the COVID-19 pandemic, the global scientific community quickly launched vaccine research and development. Vaccination is regarded as a crucial strategy for controlling viral transmission and mitigating severe cases. In this paper, we propose a novel mathematical model for COVID-19 infection incorporating vaccine-induced immunization failure. As a cornerstone of infectious disease prevention measures, vaccination stands as the most effective and efficient strategy for curtailing disease transmission. Nevertheless, even with vaccination, the occurrence of vaccine immunization failure is not uncommon. This necessitates a comprehensive understanding and consideration of vaccine effectiveness in epidemiological models and public health strategies. In this paper, the basic regeneration number is calculated by the next generation matrix method, and the local and global asymptotic stability of disease-free equilibrium point and endemic equilibrium point are proven by methods such as the Routh–Hurwitz criterion and Lyapunov functions. Additionally, we conduct fractional-order numerical simulations to verify that order $0.86$ provides the best fit with COVID-19 data. This study sheds light on the roles of immunization failure and fractional-order control. Full article

The COVID-19 pandemic has not only brought a virus to the public, but also spawned a large number of rumors. The Internet has made it very convenient for media websites to record and spread rumors, while the official government, as the subject of rumor control, can release rumor-refutation information to reduce the harm of rumors. Therefore, this study took into account information-carrying variables, such as media websites and official governments, and expanded the classic ISR rumor propagation model into a five-dimensional, two-level rumor propagation model that interacts between the main body layer and the information layer. Based on the constructed model, the mean field equation was obtained. Through mathematical analysis, the equilibrium point and the basic reproduction number of rumors were calculated. At the same time, stability analysis was conducted using the Routh Hurwitz stability criterion. Finally, a numerical simulation verified that when the basic regeneration number was less than 1, rumors disappeared in the system; when the basic regeneration number was greater than 1, rumors continued to exist in the system and rumors erupted. The executive power of the official government to dispel rumors, that is, the effectiveness of the government, played a decisive role in suppressing the spread of rumors. Full article

The relationship between COVID-19 infections and environmental contaminants provides insight into how environmental factors can influence the spread of infectious diseases. By integrating epidemiological and environmental variables into a mathematical framework, the interaction between virus spread and the environment can be determined. The aim of this study was to evaluate the impact of atmospheric contaminants on the increase in COVID-19 infections in the city of Quito through the application of statistical tests. The data on infections and deaths allowed to identify the periods of greatest contagion and their relationship with the contaminants O₃, SO₂, CO, PM_2.5, and PM₁₀. A validated database was used, and statistical analysis was applied through five models based on simple linear regression. The models showed a significant relationship between SO₂ and the increase in infections. In addition, a moderate correlation was shown with PM_2.5, O₃, and CO, and a low relationship was shown for PM₁₀. These findings highlight the importance of having policies that guarantee air quality as a key factor in maintaining people’s health and preventing the proliferation of viral and infectious diseases. Full article

The COVID-19 pandemic has presented a complex situation that requires a balance between control measures like lockdowns and easing restrictions. Control measures can limit the spread of the virus but can also cause economic and social issues. Easing restrictions can support economic recovery but may increase the risk of virus transmission. Mathematical approaches can help address these trade-offs by modeling the interactions between factors such as virus transmission rates, public health interventions, and economic and social impacts. A study using a susceptible-infected-susceptible (SIS) model with modified discrete time was conducted to determine the cost of handling COVID-19. The results showed that, without government intervention, the number of patients rejected by health facilities and the cost of handling a pandemic increased significantly. Lockdown intervention provided the least number of rejected patients compared to social distancing, but the costs of handling the pandemic in the lockdown scenario remained higher than those of social distancing. This research demonstrates that mathematical approaches can help identify critical junctures in a pandemic, such as limited health system capacity or high transmission rates, that require rapid response and appropriate action. By using mathematical analysis, decision-makers can develop more effective and responsive strategies, considering the various factors involved in the virus’s spread and its impact on society and the economy. Full article

After the coronavirus disease 2019 (COVID-19) outbreak erupted, it swiftly spread globally and triggered a severe public health crisis in 2019. To contain the virus’s spread, several countries implemented various lockdown measures. As the governments faced this unprecedented challenge, understanding the impact of lockdown policies became paramount. The goal of addressing the pandemic crisis is to devise prudent policies that strike a balance between safeguarding lives and maintaining economic stability. Traditional mathematical and statistical models for studying virus transmission only offer macro-level predictions of epidemic development and often overlook individual variations’ impact, therefore failing to reflect the role of government decisions. To address this challenge, we propose an integrated framework that combines agent-based modeling (ABM) and deep Q-network (DQN) techniques. This framework enables a more comprehensive analysis and optimization of epidemic control strategies while considering real human behavior. We construct a pandemic simulator based on the ABM method, accurately simulating agents’ daily activities, interactions, and the dynamic spread of the virus. Additionally, we employ a data-driven approach and adjust the model through real statistical data to enhance its effectiveness. Subsequently, we integrated ABM into a decision-making framework using reinforcement learning techniques to explore the most effective strategies. In experiments, we validated the model’s effectiveness by simulating virus transmission across different countries globally. In this model, we obtained decision outcomes when governments focused on various factors. Our research findings indicate that our model serves as a valuable tool for decision-makers, enabling them to formulate prudent and rational policies. Full article

The threat posed by the COVID-19 pandemic has been accompanied by an epidemic of misinformation, causing confusion and mistrust among the public. Misinformation about COVID-19 whether intentional or unintentional takes many forms, including conspiracy theories, false treatments, and inaccurate information about the origins and spread of the virus. Though the pandemic has brought to light the significant impact of misinformation on public health, mathematical modeling emerged as a valuable tool for understanding the spread of COVID-19 and the impact of public health interventions. However, there has been limited research on the mathematical modeling of the spread of misinformation related to COVID-19. In this paper, we present a mathematical model of the spread of misinformation related to COVID-19. The model highlights the challenges posed by misinformation, in that rather than focusing only on the reproduction number that drives new infections, there is an additional threshold parameter that drives the spread of misinformation. The equilibria of the model are analyzed for both local and global stability, and numerical simulations are presented. We also discuss the model’s potential to develop effective strategies for combating misinformation related to COVID-19. Full article

COVID-19 is an airborne disease, with the vast majority of infections occurring indoors. In comparison, little transmission occurs outdoors. Here, we investigate the airborne transmission pathways that differentiate the indoors from outdoors and conclude that profound differences exist, which help to explain why SARS-CoV-2 transmission is much more prevalent indoors. Near- and far-field transmission pathways are discussed along with factors that affect infection risk, with aerosol concentration, air entrainment, thermal plumes, and occupancy duration all identified as being influential. In particular, we present the fundamental equations that underpin the Wells–Riley model and show the mathematical relationship between inhaled virus particles and quanta of infection. A simple model is also presented for assessing infection risk in spaces with incomplete air mixing. Transmission risk is assessed in terms of aerosol concentration using simple 1D equations, followed by a description of thermal plume–ceiling interactions. With respect to this, we present new experimental results using Schlieren visualisation and computational fluid dynamics (CFD) based on the Eulerian–Lagrangian approach. Pathways of airborne infection are discussed, with the key differences identified between indoors and outdoors. In particular, the contribution of thermal and exhalation plumes is evaluated, and the presence of a near-field/far-field feedback loop is postulated, which is absent outdoors. Full article

The COVID-19 pandemic has had a significant impact on countries worldwide, including the United Kingdom (UK). The UK has faced numerous challenges, but its response, including the rapid vaccination campaign, has been noteworthy. While progress has been made, the study of the pandemic is important to enable us to properly prepare for future epidemics. Collaboration, vigilance, and continued adherence to public health measures will be crucial in navigating the path to recovery and building resilience for the future. In this article, we propose an overview of the COVID-19 situation in the UK using both mathematical (a nonlinear differential equation model) and statistical (time series modeling on a moving window) models on the transmission dynamics of the COVID-19 virus from the beginning of the pandemic up until July 2022. This is achieved by integrating a hybrid model and daily empirical case and death data from the UK. We partition this dataset into before and after vaccination started in the UK to understand the influence of vaccination on disease dynamics. We used the mathematical model to present some mathematical analyses and the calculation of the basic reproduction number ($R_0$). Following the sensitivity analysis index, we deduce that an increase in the rate of vaccination will decrease $R_0$. Also, the model was fitted to the data from the UK to validate the mathematical model with real data, and we used the data to calculate time-varying $R_0$. The homotopy perturbation method (HPM) was used for the numerical simulation to demonstrate the dynamics of the disease with varying parameters and the importance of vaccination. Furthermore, we used statistical modeling to validate our model by performing principal component analysis (PCA) to predict the evolution of the spread of the COVID-19 outbreak in the UK on some statistical predictor indicators from time series modeling on a 14-day moving window for detecting which of these indicators capture the dynamics of the disease spread across the epidemic curve. The results of the PCA, the index of dispersion, the fitted mathematical model, and the mathematical model simulation are all in agreement with the dynamics of the disease in the UK before and after vaccination started. Conclusively, our approach has been able to capture the dynamics of the pandemic at different phases of the disease outbreak, and the result presented will be useful to understand the evolution of the disease in the UK and future and emerging epidemics. Full article

The severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is responsible for coronavirus disease-19 (COVID-19). This virus has caused a global pandemic, marked by several mutations leading to multiple waves of infection. This paper proposes a comprehensive and integrative mathematical approach to the third wave of COVID-19 (Omicron) in the Kingdom of Saudi Arabia (KSA) for the period between 16 December 2022 and 8 February 2023. It may help to implement a better response in the next waves. For this purpose, in this article, we generate a new mathematical transmission model for coronavirus, particularly during the third wave in the KSA caused by the Omicron variant, factoring in the impact of vaccination. We developed this model using a fractal-fractional derivative approach. It categorizes the total population into six segments: susceptible, vaccinated, exposed, asymptomatic infected, symptomatic infected, and recovered individuals. The conventional least-squares method is used for estimating the model parameters. The Perov fixed point theorem is utilized to demonstrate the solution’s uniqueness and existence. Moreover, we investigate the Ulam–Hyers stability of this fractal–fractional model. Our numerical approach involves a two-step Newton polynomial approximation. We present simulation results that vary according to the fractional orders ($\gamma$) and fractal dimensions ($\theta$), providing detailed analysis and discussion. Our graphical analysis shows that the fractal-fractional derivative model offers more biologically realistic results than traditional integer-order and other fractional models. Full article

This work is a response to the appeal of various international health organizations and the Automatic Control Community for collaboration in addressing Coronavirus/COVID-19 challenges during the initial stages of the pandemic. Specifically, this study presents scientific evidence supporting the efficacy of three primary non-pharmacological strategies for pandemic mitigation. We propose a control system to aid in formulating a public decision policy aimed at managing the spread of COVID-19 caused by the SARS-CoV-2 virus, commonly known as coronavirus. The primary objective is to prevent overwhelming healthcare systems by averting the saturation of intensive care units (ICUs). In the context of COVID-19, understanding the peak infection rate and its time delay is crucial for preparing healthcare infrastructure and ensuring an adequate supply of intensive care units equipped with automatic ventilators. While it is widely recognized that public policies encompassing confinement and social distancing can flatten the epidemiological curve and provide time to bolster healthcare resources, there is a dearth of studies examining this pivotal issue from the perspective of control system theory. In this study, we introduce a control system founded on three prevailing non-pharmacological tools for epidemic and pandemic mitigation: social distancing, confinement, and population-wide testing and isolation in regions experiencing community transmission. Our analysis and control system design rely on the susceptible-exposed–infected–recovered–deceased (SEIRD) mathematical model, which describes the temporal dynamics of a pandemic, tailored in this research to account for the temporal and spatial characteristics of SARS-CoV-2 behavior. This model incorporates the influence of conducting tests with subsequent population isolation. An On–off control strategy is analyzed, and a proportional–integral–derivative (PID) controller is proposed to generate a sequence of public policy decisions. The proposed control system employs the required number of critical beds and ICUs as feedback signals and compares these with the available bed capacity to generate an error signal, which is utilized as input for the PID controller. The control actions outlined involve five phases of “Social Distancing and Confinement” (SD&C) to be implemented by governmental authorities. Consequently, the control system generates a policy sequence for SD&C, with applications occurring on a weekly or biweekly basis. The simulation results underscore the favorable impact of these three mitigation strategies against the coronavirus, illustrating their efficacy in controlling the outbreak and thereby mitigating the risk of healthcare system collapse. Full article