A case study of 2019-nCOV cases in Argentina with the real data based on daily cases from March 03, 2020 to March 29, 2021 using classical and fractional derivatives

Fractional order mathematical model for B.1.1.529 SARS-Cov-2 Omicron variant with quarantine and vaccination

In this paper, a fractional order nonlinear model for Omicron, known as B.1.1.529 SARS-Cov-2 variant, is proposed. The COVID-19 vaccine and quarantine are inserted to ensure the safety of host population in the model. The fundamentals of positivity and boundedness of the model solution are simulated. The reproduction number is estimated to determine whether or not the epidemic will spread further in Tamilnadu, India. Real Omicron variant pandemic data from Tamilnadu, India, are validated. The fractional-order generalization of the proposed model, along with real data-based numerical simulations, is the novelty of this study.

Usefulness of High-Resolution Computed Tomography in Early Diagnosis of Patients with Suspected COVID-19

BACKGROUND

Diagnosis of coronavirus disease 2019 (COVID-19) is mainly based on molecular testing. General population studies have shown that chest Computed Tomography (CT) can also be useful.

OBJECTIVE

The study aims to examine the usefulness of high-resolution chest CT for early diagnosis of patients with suspected COVID-19.

DESIGN AND SETTING

This is a cross-sectional study from May 1, 2020, to August 31, 2021, at the COVID Hospital, Mexico City.

METHODS

This study examined the clinical, high-resolution chest CT imaging, and laboratory data of 160 patients who were suspected to have COVID-19. Patients with positive Reverse Transcription- Polymerase Chain Reaction (RT-PCR) testing and those with negative RT-PCR testing but clinical data compatible with COVID-19 and positive antibody testing were considered to have COVID-19 (positive). Sensitivity and specificity of CT for diagnosis of COVID-19 were calculated. p < 0.05 was considered significant.

RESULTS

Median age of 160 study patients was 58 years. The proportion of patients with groundglass pattern was significantly higher in patients with COVID-19 than in those without COVID (65.1% versus 0%; P = 0.005). COVID-19 was ruled out in sixteen (11.1%). Only four of the 132 patients diagnosed with COVID-19 (3.0%) did not show CT alterations (p < 0.001). Sensitivity and specificity of CT for COVID-19 diagnosis were 96.7% and 42.8%, respectively.

CONCLUSIONS

Chest CT can identify patients with COVID-19, as characteristic disease patterns are observed on CT in the early disease stage.

Clinical Characterizations and Radiological Findings of COVID-19: A 4 Case Report

BACKGROUND

Coronavirus disease 2019 (COVID-19, previously known as novel coronavirus [2019-nCoV]), first reported in China, has now been declared a global health emergency by World Health Organization. The clinical severity ranges from asymptomatic individuals to death. Here, we report clinical features and radiological changes of a cured family cluster infected with COVID-19.

CASE PRESENTATION

In this report, we enrolled a family of 4 members who were admitted to our hospital in January 2020. We performed a detailed analysis of each patient's records. All patients underwent chest computed tomography (CT) examination with 120 kilovolts peak and 150 kilovolt-ampere. Realtime polymerase chain reaction (RT-PCR) examinations for severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) nucleic acid were done using nasopharyngeal swabs.

CONCLUSION

In the family members infected with COVID-19 who were accompanied by other diseases or had low immunity, the pneumonia was prone to be aggravated.

A case study of 2019-nCoV in Russia using integer and fractional order derivatives

In this article, we define a mathematical model to analyze the outbreaks of the most deadly disease of the decade named 2019-nCoV by using integer and fractional order derivatives. For the case study, the real data of Russia is taken to perform novel parameter estimation by using the Trust Region Reflective (TRR) algorithm. First, we define an integer order model and then generalize it by using fractional derivatives. A novel optimal control problem is derived to see the impact of possible preventive measures against the spread of 2019-nCoV. We implement the forward-backward sweep method to numerically solve our proposed model and control problem. A number of graphs have been plotted to see the impact of the proposed control practically. The Russian data-based parameter estimation along with the proposal of a mathematical model in the sense of Caputo fractional derivative that contains the memory term in the system are the main novel features of this study.

Combining epidemiology and economics to assess control of a viral endemic animal disease: Porcine Reproductive and Respiratory Syndrome (PRRS)

Porcine reproductive and respiratory syndrome (PRRS) is an extremely contagious disease that causes great damage to the U.S. pork industry. PRRS is not subject to official control in the U.S., but most producers adopt control strategies, including vaccination. However, the PRRS virus mutates frequently, facilitating its ability to infect even vaccinated animals. In this paper we analyze how increased vaccination on sow farms reduces PRRS losses and when vaccination is profitable. We develop a SIR model to simulate the spread of an outbreak between and within swine farms located in a region of Minnesota. Then, we estimate economic losses due to PRRS and calculate the benefits of vaccination. We find that increased vaccination of sow farms increases the private profitability of vaccination, and also transmits positive externalities to farms that do not vaccinate. Although vaccination reduces industry losses, a low to moderate vaccine efficacy implies that large PRRS losses remain, even on vaccinated farms. Our approach provides useful insight into the dynamics of an endemic animal disease and the benefits of different vaccination regimens.

Modeling the multifractal dynamics of COVID-19 pandemic

To describe the COVID-19 pandemic, we propose to use a mathematical model of multifractal dynamics, which is alternative to other models and free of their shortcomings. It is based on the fractal properties of pandemics only and allows describing their time behavior using no hypotheses and assumptions about the structure of the disease process. The model is applied to describe the dynamics of the COVID-19 pandemic from day 1 to day 699 from the beginning of the pandemic. The calculated parameters of the model accurately determine the parameters of the trend and the large jump in daily diseases in this time interval. Within the framework of this model and finite-difference parametric nonlinear equations of the reduced SIR (Susceptible-Infected-Removed) model, the fractal dimensions of various segments of daily incidence in the world and variations in the main reproduction number of COVID-19 were calculated based on the data of COVID-19 world statistics.

Agent-based epidemiological modeling of COVID-19 in localized environments

Epidemiological modeling is used, under certain assumptions, to represent the spread of a disease within a population. Information generated by these models can then be applied to inform public health practices and mitigate risk. To provide useful and actionable preparedness information to administrators and policy makers, epidemiological models must be formulated to model highly localized environments such as office buildings, campuses, or long-term care facilities. In this paper, a highly configurable agent-based simulation (ABS) framework designed for localized environments is proposed. This ABS provides information about risk and the effects of both pharmacological and non-pharmacological interventions, as well as detailed control over the rapidly evolving epidemiological characteristics of COVID-19. Simulation results can inform decisions made by facility administrators and be used as inputs for a complementary decision support system. The application of our ABS to our research lab environment as a proof of concept demonstrates the configurability and insights achievable with this form of modeling, with future work focused on extensibility and integration with decision support.

Effects of greenhouse gases and hypoxia on the population of aquatic species: a fractional mathematical model

Study of ecosystems has always been an interesting topic in the view of real-world dynamics. In this paper, we propose a fractional-order nonlinear mathematical model to describe the prelude of deteriorating quality of water cause of greenhouse gases on the population of aquatic animals. In the proposed system, we recall that greenhouse gases raise the temperature of water, and because of this reason, the dissolved oxygen level goes down, and also the rate of circulation of disintegrated oxygen by the aquatic animals rises, which causes a decrement in the density of aquatic species. We use a generalized form of the Caputo fractional derivative to describe the dynamics of the proposed problem. We also investigate equilibrium points of the given fractional-order model and discuss the asymptotic stability of the equilibria of the proposed autonomous model. We recall some important results to prove the existence of a unique solution of the model. For finding the numerical solution of the established fractional-order system, we apply a generalized predictor-corrector technique in the sense of proposed derivative and also justify the stability of the method. To express the novelty of the simulated results, we perform a number of graphs at various fractional-order cases. The given study is fully novel and useful for understanding the proposed real-world phenomena.

A new study on two different vaccinated fractional-order COVID-19 models via numerical algorithms

The main purpose of this paper is to provide new vaccinated models of COVID-19 in the sense of Caputo-Fabrizio and new generalized Caputo-type fractional derivatives. The formulation of the given models is presented including an exhaustive study of the model dynamics such as positivity, boundedness of the solutions and local stability analysis. Furthermore, the unique solution existence for the proposed fractional order models is discussed via fixed point theory. Numerical solutions are also derived by using two-steps Adams-Bashforth algorithm for Caputo-Fabrizio operator, and modified Predictor-Corrector method for generalised Caputo fractional derivative. Our analysis allow to show that the given fractional-order models exemplify the dynamics of COVID-19 much better than the classical ones. Also, the analysis on the convergence and stability for the proposed methods are performed. By this study, we see that how the vaccine availability plays an important role in the control of COVID-19 infection.

A study on the dynamics of alkali–silica chemical reaction by using Caputo fractional derivative

In this paper, we propose a mathematical study to simulate the dynamics of alkali–silica reaction (ASR) by using the Caputo fractional derivative. We solve a non-linear fractional-order system containing six differential equations to understand the ASR. For proving the existence of a unique solution, we use some recent novel properties of Mittag–Leffler function along with the fixed point theory. The stability of the proposed system is also proved by using Ulam–Hyers technique. For deriving the fractional-order numerical solution, we use the well-known Adams–Bashforth–Moulton scheme along with its stability. Graphs are plotted to understand the given chemical reaction practically. The main reason to use the Caputo-type fractional model for solving the ASR system is to propose a novel mathematical formulation through which the ASR mechanism can be efficiently explored. This paper clearly shows the importance of fractional derivatives in the study of chemical reactions.