The modeling and analysis of the COVID-19 pandemic with vaccination and treatment control: a case study of Maharashtra, Delhi, Uttarakhand, Sikkim, and Russia in the light of pharmaceutical and non-pharmaceutical approaches

Optimal control analysis on the spread of COVID-19: Impact of contact transmission and environmental contamination

The study investigates the intricate dynamics of SARS-CoV-2 transmission, with a particular focus on both close-contact interactions and environmental factors. Using advanced mathematical modeling and epidemiological analysis, explored the effects of these transmission pathways on the spread of COVID-19. The equilibrium points for both disease-free and endemic states are calculated and evaluated to determine their global stability. Additionally, the basic reproduction number (R0) is derived to quantify the transmission potential of the virus. To ensure model accuracy, numerical simulations are performed using MATLAB, utilizing daily COVID-19 case data from India. Parameter values are sourced from existing literature, with certain parameters estimated through fitting the model to observed data. Crucially, the model incorporates environmental transmission factors, such as surface contamination and airborne spread. The inclusion of these factors provides a more comprehensive understanding of the virus's spread, demonstrating the importance of interventions like use of face masks, environmental sanitization, vaccine efficacy, availability of treatment resources underappreciated when focusing solely on direct human contact. A sensitivity analysis is conducted to assess the impact of different parameters on R0, with results visualized through heat maps to identify the most influential factors. Furthermore, Pontryagin's maximum principle is employed to develop an optimal control model, enabling the formulation of effective intervention strategies. By analysing both interpersonal and environmental transmission mechanisms, this study offers a more holistic framework for understanding SARS-CoV-2 transmission. The insights gained are critical for informing public health strategies, emphasizing the necessity of addressing both direct contact and environmental sources of infection to more effectively manage current and future outbreaks.

Mathematical model for understanding the relationship between diabetes and novel coronavirus

A new model is proposed to explore interactions between diabetes and novel coronavirus. The model accounted for both the omicron variant and variants varying from omicron. The model investigated compartments such as hospitalization, diabetes, co-infection, omicron variant, and quarantine. Additionally, the impact of different vaccination doses is assessed. Sensitivity analysis is carried out to determine disease prevalence and control options, emphasizing the significance of knowing epidemics and their characteristics. The model is validated using actual data from Japan. The parameters are fitted with the help of "Least Square Curve Fitting" method to describe the dynamic behavior of the proposed model. Simulation results and theoretical findings demonstrate the dynamic behavior of novel coronavirus and diabetes mellitus (DM). Biological illustrations that illustrate impact of model parameters are evaluated. Furthermore, effect of vaccine efficacy and vaccination rates for the vaccine's first, second, and booster doses is conducted. The impact of various preventive measures, such as hospitalization rate, quarantine or self-isolation rate, vaccine dose-1, dose-2, and booster dose, is considered for diabetic individuals in contact with symptomatic or asymptomatic COVID-19 infectious people in the proposed model. The findings demonstrate the significance of vaccine doses on people with diabetes and individuals infectious with omicron variant. The proposed work helps with subsequent prevention efforts and the design of a vaccination policy to mitigate the effect of the novel coronavirus.

Dual-strain dynamics of COVID-19 variants in India: Modeling, analysis, and implications for pandemic control

This study introduces a detailed compartmental model developed to understand the complex dynamics of COVID-19 transmission, focusing on the Delta and Omicron variants in India. The model tracks disease progression through different population compartments, considering factors like vaccination, time-dependent transmission, economic burden and COVID-19 death rates, loss of vaccine-induced immunity, and the transition of asymptomatic cases to recovery. The model is validated against established epidemiological knowledge and real-world data, emphasizing dynamic parameterization and accurate representation of immunity dynamics. The basic reproduction number for both variants is calculated, and sensitivity analysis for various parameters is conducted. Time-dependent parameters are estimated using the discrete inverse method. The study also explores the economic burden, impact of different types of masks, vaccine efficacy, and vaccine-induced immunity through numerical analysis.

A six-compartment model for COVID-19 with transmission dynamics and public health strategies

The global crisis of the COVID-19 pandemic has highlighted the need for mathematical models to inform public health strategies. The present study introduces a novel six-compartment epidemiological model that uniquely incorporates a higher isolation rate for unreported symptomatic cases of COVID-19 compared to reported cases, aiming to enhance prediction accuracy and address the challenge of initial underreporting. Additionally, we employ optimal control theory to assess the cost-effectiveness of interventions and adapt these strategies to specific epidemiological scenarios, such as varying transmission rates and the presence of asymptomatic carriers. By applying this model to COVID-19 data from India (30 January 2020 to 24 November 2020), chosen to capture the initial outbreak and subsequent waves, we calculate a basic reproduction number of 2.147, indicating the high transmissibility of the virus during this period in India. A sensitivity analysis reveals the critical impact of detection rates and isolation measures on disease progression, showing the robustness of our model in estimating the basic reproduction number. Through optimal control simulations, we demonstrate that increasing isolation rates for unreported cases and enhancing detection reduces the spread of COVID-19. Furthermore, our cost-effectiveness analysis establishes that a combined strategy of isolation and treatment is both more effective and economically viable. This research offers novel insights into the efficacy of non-pharmaceutical interventions, providing a tool for strategizing public health interventions and advancing our understanding of infectious disease dynamics.

Predictive models for health outcomes due to SARS-CoV-2, including the effect of vaccination: a systematic review

BACKGROUND

The interaction between modelers and policymakers is becoming more common due to the increase in computing speed seen in recent decades. The recent pandemic caused by the SARS-CoV-2 virus was no exception. Thus, this study aims to identify and assess epidemiological mathematical models of SARS-CoV-2 applied to real-world data, including immunization for coronavirus 2019 (COVID-19).

METHODOLOGY

PubMed, JSTOR, medRxiv, LILACS, EconLit, and other databases were searched for studies employing epidemiological mathematical models of SARS-CoV-2 applied to real-world data. We summarized the information qualitatively, and each article included was assessed for bias risk using the Joanna Briggs Institute (JBI) and PROBAST checklist tool. The PROSPERO registration number is CRD42022344542.

FINDINGS

In total, 5646 articles were retrieved, of which 411 were included. Most of the information was published in 2021. The countries with the highest number of studies were the United States, Canada, China, and the United Kingdom; no studies were found in low-income countries. The SEIR model (susceptible, exposed, infectious, and recovered) was the most frequently used approach, followed by agent-based modeling. Moreover, the most commonly used software were R, Matlab, and Python, with the most recurring health outcomes being death and recovery. According to the JBI assessment, 61.4% of articles were considered to have a low risk of bias.

INTERPRETATION

The utilization of mathematical models increased following the onset of the SARS-CoV-2 pandemic. Stakeholders have begun to incorporate these analytical tools more extensively into public policy, enabling the construction of various scenarios for public health. This contribution adds value to informed decision-making. Therefore, understanding their advancements, strengths, and limitations is essential.

Dynamics of the COVID-19 pandemic: nonlinear approaches on the modelling, prediction and control

This special issue contains 35 regular articles on the analysis and dynamics of COVID-19 with several applications. Some analyses are on the construction of mathematical models representing the dynamics of COVID-19, and some are on the estimations and predictions of the disease, a few with possible applications. The various contributions report important, timely, and promising results, such as the effects of several waves, deep learning-based COVID-19 classifications, and multivariate time series with applications.

A time-delayed model for the spread of COVID-19 with vaccination

A mathematical model is presented in this paper to investigate the effects of time delay in vaccine production on COVID-19 spread. The model is analyzed qualitatively and numerically. The qualitative analysis indicates that the system variables are non-negative, bounded, and biologically meaningful. Moreover, the model has produced two equilibrium points: the free equilibrium point, which can exist without conditions, and the endemic equilibrium point, which can exist if the control reproduction number, [Formula: see text], is not less than one. In addition, the local stability of the equilibrium points is investigated and agrees with the numerical analysis results. Finally, a sensitivity analysis is conducted for [Formula: see text]. In particular, we examine the effect of the vaccine's time delay, vaccine rate, and vaccine efficiency on the model dynamics.

How do the contaminated environment influence the transmission dynamics of COVID-19 pandemic?

COVID-19 is an infectious disease caused by the SARS-CoV-2 virus that first appeared in Wuhan city and then globally. The COVID-19 pandemic exudes public health and socio-economic burden globally. Mathematical modeling plays a significant role to comprehend the transmission dynamics and controlling factors of rapid spread of the disease. Researchers focus on the human-to-human transmission of the virus but the SARS-CoV-2 virus also contaminates the environment. In this study we proposed a nonlinear mathematical model for the COVID-19 pandemic to analyze the transmission dynamics of the disease in India. We have also incorporated the environment contamination by the infected individuals as the population density is very high in India. The model is fitted and parameterized using daily new infection data from India. Analytical study of the proposed COVID-19 model, including feasibility of critical points and their stability reveals that the infection-free steady state is stable if the basic reproduction number is less than unity otherwise the system shows significant outbreak. Numerical illustrations demonstrates that if the rate of environment contamination increased then the number of infected persons also increased. But if the environment is disinfected by sanitization then the number of infected persons cannot drastically increase.

Response of vaccination on community transmission of COVID-19: a dynamical approach

Due to the severity of COVID-19, vaccination campaigns have been or are underway in most parts of the world. In the current circumstances, it is obligatory to examine the response of vaccination on transmission of the SARS-CoV-2 virus when there are many vaccines available. Considering the importance of vaccination, a dynamic model has been proposed to provide an insight in the same direction. A mathematical model has been developed where six population compartments viz. susceptible, infected, vaccinated, home-isolated, hospitalized and recovered population are considered. Moreover, two novel parameters are included in the model to ascertain the effectiveness and speed of the vaccination campaign. Reproduction number and local stability of both the disease-free and endemic equilibrium points are studied to examine the nature of population dynamics. Graphical results for the community stage of COVID-19 infection are simulated and compared with real data to ascertain the validity of our model. The data is then studied to understand the impact of vaccination. These numerical results evidently demonstrate that home isolation and hospitalization should continue for the infected people until the transmission of the virus from person to person reduces sufficiently after completely vaccinating every nation. This model also recommends that all type of prevention measures should still be taken to avoid any type of critical situation due to infection and also reduce the death rate.

Estimation of the basic reproduction number of COVID-19 from the incubation period distribution

The estimates of the future course of spreading of the SARS-CoV-2 virus are frequently based on Markovian models in which the duration of residence in any compartment is exponentially distributed. Accordingly, the basic reproduction number R 0 is also determined from formulae where it is related to the parameters of such models. The observations show that the start of infectivity of an individual appears nearly at the same time as the onset of symptoms, while the distribution of the incubation period is not an exponential. Therefore, we propose a method for estimation of R 0 for COVID-19 based on the empirical incubation period distribution and assumed very short infectivity period that lasts only few days around the onset of symptoms. We illustrate this venerable approach to estimate R 0 for six major European countries in the first wave of the epidemic. The calculations show that even if the infectivity starts 2 days before the onset of symptoms and stops instantly when they appear (immediate isolation), the value of R 0 is larger than that from the classical, SIR model. For more realistic cases, when only individuals with mild symptoms spread the virus for few days after onset of symptoms, the respective values are even larger. This implies that calculations of R 0 and other characteristics of spreading of COVID-19 based on the classical, Markovian approaches should be taken very cautiously.

COVID-19: respiratory disease diagnosis with regularized deep convolutional neural network using human respiratory sounds

Human respiratory sound auscultation (HRSA) parameters have been the real choice for detecting human respiratory diseases in the last few years. It is a challenging task to extract the respiratory sound features from the breath, voice, and cough sounds. The existing methods failed to extract the sound features to diagnose respiratory diseases. We proposed and evaluated a new regularized deep convolutional neural network (RDCNN) architecture to accept COVID-19 sound data and essential sound features. The proposed architecture is trained with the COVID-19 sound data sets and gives a better learning curve than any other state-of-the-art model. We examine the performance of RDCNN with Max-Pooling (Model-1) and without Max-Pooling (Model-2) functions. In this work, we observed that RDCNN model performance with three sound feature extraction methods [Soft-Mel frequency channel, Log-Mel frequency spectrum, and Modified Mel-frequency Cepstral Coefficient (MMFCC) spectrum] for COVID-19 sound data sets (KDD-data, ComParE2021-CCS-CSS-Data, and NeurlPs2021-data). To amplify the models' performance, we applied the augmentation technique along with regularization. We have also carried out this work to estimate the mutation of SARS-CoV-2 in the five waves using prognostic models (fractal-based). The proposed model achieves state-of-the-art performance on the COVID-19 sound data set to identify COVID-19 disease symptoms. The model's learnable parameter gradients have vanished in the intermediate layers while optimizing the prediction error which is addressed with our proposed RDCNN model. Our experiments suggested that 3 × 3 kernel size for regularized deep CNN (without max-pooling) shows 2-3% better classification accuracy compared to RDCNN with max-pooling. The experimental results suggest that this new approach may achieve the finest results on respiratory diseases.