Application of Fractional SIQRV Model for SARS-CoV-2 and Stability Analysis

Throughout history, infectious diseases have been the cause of outbreaks and the deaths of people. It is crucial for endemic disease management to be able to forecast the number of infections at a given moment and the frequency of new infections so that the appropriate precautions can be taken. The COVID-19 pandemic has highlighted the value of mathematical modeling of pandemics. The susceptible–infected–quarantined–recovered–vaccinated (SIQRV) epidemic model was used in this work. Symmetrical aspects of the proposed dynamic model, disease-free equilibrium, and stability were analyzed. The symmetry of the population size over time allows the model to find stable equilibrium points for any parameter value and initial conditions. The assumption of the strong symmetry of the initial conditions and parameter values plays a key role in the analysis of the fractional SIQRV model. In order to combat the pandemic nature of the disease, control the disease in the population, and increase the possibility of eradicating the disease, effective control measures include quarantine and immunization. Fractional derivatives are used in the Caputo sense. In the model, vaccination and quarantine are two important applications for managing the spread of the pandemic. Although some of the individuals who were vaccinated with the same type and equal dose of vaccine gained strong immunity thanks to the vaccine, the vaccine could not give sufficient immunity to the other part of the population. This is thought to be related the structural characteristics of individuals. Thus, although some of the individuals vaccinated with the same strategy are protected against the virus for a long time, others may become infected soon after vaccination. Appropriate parameters were used in the model to reflect this situation. In order to validate the model, the model was run by taking the COVID-19 data of Türkiye about a year ago, and the official data on the date of this study were successfully obtained. In addition to the stability analysis of the model, numerical solutions were obtained using the fractional Euler method. © 2023 by the authors.

Trends in Biomathematics: Stability and Oscillations in Environmental, Social, and Biological Models: Selected Works from the BIOMAT Consortium Lectures, Rio de Janeiro, Brazil, 2021

This contributed volume convenes selected, peer-reviewed works presented at the BIOMAT 2021 International Symposium, which was virtually held on November 1-5, 2021, with its organization staff based in Rio de Janeiro, Brazil. In this volume the reader will find applications of mathematical modeling on health, ecology, and social interactions, addressing topics like probability distributions of mutations in different cancer cell types;oscillations in biological systems;modeling of marine ecosystems;mathematical modeling of organs and tissues at the cellular level;as well as studies on novel challenges related to COVID-19, including the mathematical analysis of a pandemic model targeting effective vaccination strategy and the modeling of the role of media coverage on mitigating the spread of infectious diseases. Held every year since 2001, the BIOMAT International Symposium gathers together, in a single conference, researchers from Mathematics, Physics, Biology, and affine fields to promote the interdisciplinary exchange of results, ideas and techniques, promoting truly international cooperation for problem discussion. BIOMAT volumes published from 2017 to 2020 are also available by Springer. © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2022.

A Study on Optimal Control of a COVID-19 Transmission Model with the Significance of Early Screening and Testing Measures

In this paper, we present a deterministic SEQIR mathematical model that describes the transmission dynamics of COVID-19 that also in-cludes testing procedures in the quarantine stage. The reproduction number R0 is derived with some properties of the model. The stabil-ity of equilibrium points is analyzed. An objective function is pro-posed and optimal control strategies are derived using Pontryagin's Maximum Principle. The existence and uniqueness of an optimal-ity system are demonstrated. Numerical simulations are presented in different scenarios with the control interventions early screening, prevention measures of COVID-19, and following a healthy lifestyle. The main objective of the paper is to eradicate the disease in exposed stage. The chosen control variables helps us to reduce the exposed population. (c) 2023 L&H Scientific Publishing, LLC. All rights reserved.

THEORETICAL MODELLING OF THE EPIDEMIC COVID-2019 IN AZERBAIJAN.

A mathematical model of the coronavirus COVID-2019 epidemic in Azerbaijan is proposed. Analysis of the proposed mathematical model shows that the dynamic behavior of the epidemic is quite sensitive to parameters (rate constant of stages), which reflect different measures against the epidemic. This fact suggests that the lifting of all restrictive measures can aggravate the situation with COVID-19 in the republic and one should not expect the complete disappearance of the Covid-19 coronavirus in Azerbaijan.Copyright © 2023 Ministry of Health. All rights reserved.

A fractional mathematical model with nonlinear partial differential equations for transmission dynamics of severe acute respiratory syndrome coronavirus 2 infection.

This study presents a fractional mathematical model based on nonlinear Partial Differential Equations (PDEs) of fractional variable-order derivatives for the host populations experiencing transmission and evolution of the Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) pandemic. Five host population groups have been considered, the Susceptible, Exposed, Infected, Recovered, and Deceased (SEIRD). The new model, not introduced before in its current formulation, is governed by nonlinear PDEs with fractional variable-order derivatives. As a result, the proposed model is not compared with other models or real scenarios. The advantage of the proposed fractional partial derivatives of variable orders is that they can model the rate of change of subpopulation for the proposed model. As an efficient tool to obtain the solution of the proposed model, a modified analytical technique based on the homotopy and Adomian decomposition methods is introduced. Then again, the present study is general and is applicable to a host population in any country.

Modeling reality with mathematics

Simulating the behavior of a human heart, predicting tomorrow's weather, optimizing the aerodynamics of a sailboat, finding the ideal cooking time for a hamburger: to solve these problems, cardiologists, meteorologists, sportsmen, and engineers can count on math help. This book will lead you to the discovery of a magical world, made up of equations, in which a huge variety of important problems for our life can find useful answers. © The Editor(s) (if applicable) and The Author(s), under exclusive licence to Springer Nature Switzerland AG 2022. All rights reserved.

Modelling and Analysis of Hospital Inventory Policies during COVID-19 Pandemic

The global coronavirus pandemic (COVID-19) started in 2020 and is still ongoing today. Among the numerous insights the community has learned from the COVID-19 pandemic is the value of robust healthcare inventory management. The main cause of many casualties around the world is the lack of medical resources for those who need them. To inhibit the spread of COVID-19, it is therefore imperative to simulate the demand for desirable medical goods at the proper time. The estimation of the incidence of infections using the right epidemiological criteria has a significant impact on the number of medical supplies required. Modeling susceptibility, exposure, infection, hospitalization, isolation, and recovery in relation to the COVID-19 pandemic is indeed crucial for the management of healthcare inventories. The goal of this research is to examine the various inventory policies such as reorder point, periodic order, and just-in-time in order to minimize the inventory management cost for medical commodities. To accomplish this, a SEIHIsRS model has been employed to comprehend the dynamics of COVID-19 and determine the hospitalized percentage of infected people. Based on this information, various situations are developed, considering the lockdown, social awareness, etc., and an appropriate inventory policy is recommended to reduce inventory management costs. It is observed that the just-in-time inventory policy is found to be the most cost-effective when there is no lockdown or only a partial lockdown. When there is a complete lockdown, the periodic order policy is the best inventory policy. The periodic order and reorder policies are cost-effective strategies to apply when social awareness is high. It has also been noticed that periodic order and reorder policies are the best inventory strategies for uncertain vaccination efficacy. This effort will assist in developing the best healthcare inventory management strategies to ensure that the right healthcare requirements are available at a minimal cost. © 2023 by the authors.

Health Care Logistics Network Design and Analysis on Pandemic Outbreaks: Insights From COVID-19.

Health care systems throughout the world are under pressure as a result of COVID-19. It is over two years since the first case was announced in China and health care providers are continuing to struggle with this fatal infectious disease in intensive care units and inpatient wards. Meanwhile, the burden of postponed routine medical procedures has become greater as the pandemic has progressed. We believe that establishing separate health care institutions for infected and non-infected patients would provide safer and better quality health care services. The aim of this study is to find the appropriate number and location of dedicated health care institutions which would only treat individuals infected by a pandemic during an outbreak. For this purpose, a decision-making framework including two multi-objective mixed-integer programming models is developed. At the strategic level, the locations of designated pandemic hospitals are optimized. At the tactical level, we determine the locations and operation durations of temporary isolation centers which treat mildly and moderately symptomatic patients. The developed framework provides assessments of the distance that infected patients travel, the routine medical services expected to be disrupted, two-way distances between new facilities (designated pandemic hospitals and isolation centers), and the infection risk in the population. To demonstrate the applicability of the suggested models, we perform a case study for the European side of Istanbul. In the base case, seven designated pandemic hospitals and four isolation centers are established. In sensitivity analyses, 23 cases are analyzed and compared to provide support to decision makers.

Topological data analysis of antibody dynamics of severe and non-severe patients with COVID-19.

The COVID-19 pandemic is a significant public health threat with unanswered questions regarding the immune system's role in the disease's severity level. Here, based on antibody kinetic data of severe and non-severe COVID-19 patients, topological data analysis (TDA) highlights that severity is not binary. However, there are differences in the shape of antibody responses that further classify COVID-19 patients into non-severe, severe, and intermediate cases of severity. Based on the results of TDA, different mathematical models were developed to represent the dynamics between the different severity groups. The best model was the one with the lowest average value of the Akaike Information Criterion for all groups of patients. Our results suggest that different immune mechanisms drive differences between the severity groups. Further inclusion of different components of the immune system will be central for a holistic way of tackling COVID-19.

Incorporation of awareness programs into a model of the spread of HIV/AIDS among people who inject drugs

Mathematical modeling techniques have been used extensively during the human immunodeficiency virus (HIV) epidemic. Drug injection causes increased HIV spread in most countries globally. The media is crucial in spreading health awareness by changing mixing behavior. The published studies show some of the ways that differential equation models can be employed to explain how media awareness programs influence the spread and containment of disease (Greenhalgh et al. Appl Math Comput. 2015;251:539–563). Here we build a differential equation model which shows how disease awareness programs can alter the HIV prevalence in a group of people who inject drugs (PWIDs). This builds on previous work by Greenhalgh and Hay (1997) and Liang et al. (2016). We have constructed a mathematical model to describe the improved model that reduces the spread of the diseases through the effect of awareness of disease on sharing needles and syringes among the PWID population. The model supposes that PWIDs clean their needles before use rather than after. We carry out a steady state analysis and examine local stability. Our discussion has been focused on two ways of studying the influence of awareness of infection levels in epidemic modeling. The key biological parameter of our model is the basic reproductive number R0$$ {R}_0 $$. R0$$ {R}_0 $$ is a crucial number which determines the behavior of the infection. We find that if R0$$ {R}_0 $$ is less than one then the disease-free steady state is the unique steady state and moreover whatever the initial fraction of infected individuals then the disease will die out as time becomes large. If R0$$ {R}_0 $$ exceeds one there is the disease-free steady state and a unique steady state with disease present. We also showed that the disease-free steady state is locally asymptotically stable if R0$$ {R}_0 $$ is less than one, neutrally stable if R0$$ {R}_0 $$ is equal to one and unstable if R0$$ {R}_0 $$ exceeds one. In the last case, when R0$$ {R}_0 $$ is greater than one the endemic steady state was locally asymptotically stable. Our analytical results are confirmed by using simulation with realistic parameter values. In nontechnical terms, the number R0$$ {R}_0 $$ is a critical value describing how the disease will spread. If R0$$ {R}_0 $$ is less than or equal to one then the disease will always die out but if R0$$ {R}_0 $$ exceeds one and disease is present the disease will sustain itself and moreover the numbers of PWIDs with disease will tend to a unique nonzero value.

Applications of mathematical modeling and simulation in COVID-19

In this chapter, we describe the use of mathematical and simulation tools applied in various aspects of the coronavirus disease 2019 pandemic through an extensive and careful review of the recently published works. We detailed the existing implementations of models dealing with (i) the spread of the disease, (ii) the prediction of new outbreaks, (iii) the existence of new variants of the virus, (iv) the effects on the at-risk population, (v) the long-term health consequences, (vi) the resource allocation for supportive staffs and clinical beds, (vii) the dynamics of transmission and how to cut the transmission chain, (viii) the impacts of travel restrictions, social distancing and early detection, (ix) the efficacy of prophylactic agents, (x) the effects of optimum interventions, (xi) the impact of existing vaccines, and (xii) the economic effects of the pandemic. © 2023 Elsevier Inc. All rights reserved.

On a Fractional Variable-Order Model of MERS-CoV

In this paper, a non-integer variable-order epidemiological model is presented to study the human-to-human transmission of Middle East respiratory syndrome coronavirus (MERS-CoV) pandemic in two areas. In the presented SISImodel, the human population is divided into two compartments;susceptible and infectious compartments. The impact of the memory which changes with time in the sense of Caputo's derivative of fractional variable-order is studied through the numerical solutions of the proposed model. The numerical solutions are obtained via predictor corrector method. Moreover, the equilibrium points and stability of the model are illustrated. © 2023 NSP Natural Sciences Publishing Cor

A mathematical model for policy of vaccinating recovered people in controlling the spread of COVID-19 outbreak

In this paper, we develop a mathematical model for the spread of COVID-19 outbreak, taking into account vaccination in susceptible and recovered populations. The model divides the population into eight classes, including susceptible, vaccinated in S class, exposed, infected asymptomatic, infected symptomatic, hospitalized, recovery, and vaccinated in recovered class. By applying a vaccine-distribution scenario, we investigate the impact of vaccines on the COVID-19 outbreak. After analyzing the equilibrium point and computing the basic reproduction number, we perform numerical simulation and sensitivity analysis to identify the most influential parameters and evaluate the impact of vaccine distribution on policies to control the spread of COVID-19. Our findings suggest that vaccine distribution can effectively suppress the spread of COVID-19, and increasing the v parameter (vaccine distribution) and α1 parameter (acceleration of detection of undetected infected individuals who have recovered) can help control the outbreak. Moreover, decreasing the contact between vulnerable and infected individuals can lower the β1 parameter, leading to R0 < 1, which indicates a disease-free population. This study contributes to understanding the impact of vaccination on the spread of COVID-19 and provides insights for policymakers in developing control strategies. © 2023 the Author(s), licensee AIMS Press.

COVID-19 dynamics in an Ohio prison.

Incarcerated individuals are a highly vulnerable population for infection with severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). Understanding the transmission of respiratory infections within prisons and between prisons and surrounding communities is a crucial component of pandemic preparedness and response. Here, we use mathematical and statistical models to analyze publicly available data on the spread of SARS-CoV-2 reported by the Ohio Department of Rehabilitation and Corrections (ODRC). Results from mass testing conducted on April 16, 2020 were analyzed together with time of first reported SARS-CoV-2 infection among Marion Correctional Institution (MCI) inmates. Extremely rapid, widespread infection of MCI inmates was reported, with nearly 80% of inmates infected within 3 weeks of the first reported inmate case. The dynamical survival analysis (DSA) framework that we use allows the derivation of explicit likelihoods based on mathematical models of transmission. We find that these data are consistent with three non-exclusive possibilities: (i) a basic reproduction number >14 with a single initially infected inmate, (ii) an initial superspreading event resulting in several hundred initially infected inmates with a reproduction number of approximately three, or (iii) earlier undetected circulation of virus among inmates prior to April. All three scenarios attest to the vulnerabilities of prisoners to COVID-19, and the inability to distinguish among these possibilities highlights the need for improved infection surveillance and reporting in prisons.

Vaccines Alone Cannot Slow the Evolution of SARS-CoV-2.

The rapid emergence of immune-evading viral variants of SARS-CoV-2 calls into question the practicality of a vaccine-only public-health strategy for managing the ongoing COVID-19 pandemic. It has been suggested that widespread vaccination is necessary to prevent the emergence of future immune-evading mutants. Here, we examined that proposition using stochastic computational models of viral transmission and mutation. Specifically, we looked at the likelihood of emergence of immune escape variants requiring multiple mutations and the impact of vaccination on this process. Our results suggest that the transmission rate of intermediate SARS-CoV-2 mutants will impact the rate at which novel immune-evading variants appear. While vaccination can lower the rate at which new variants appear, other interventions that reduce transmission can also have the same effect. Crucially, relying solely on widespread and repeated vaccination (vaccinating the entire population multiple times a year) is not sufficient to prevent the emergence of novel immune-evading strains, if transmission rates remain high within the population. Thus, vaccines alone are incapable of slowing the pace of evolution of immune evasion, and vaccinal protection against severe and fatal outcomes for COVID-19 patients is therefore not assured.

Mathematical Modeling Evaluates How Vaccinations Affected the Course of COVID-19 Disease Progression.

The regulation policies implemented, the characteristics of vaccines, and the evolution of the virus continue to play a significant role in the progression of the SARS-CoV-2 pandemic. Numerous research articles have proposed using mathematical models to predict the outcomes of different scenarios, with the aim of improving awareness and informing policy-making. In this work, we propose an expansion to the classical SEIR epidemiological model that is designed to fit the complex epidemiological data of COVID-19. The model includes compartments for vaccinated, asymptomatic, hospitalized, and deceased individuals, splitting the population into two branches based on the severity of progression. In order to investigate the impact of the vaccination program on the spread of COVID-19 in Greece, this study takes into account the realistic vaccination program implemented in Greece, which includes various vaccination rates, different dosages, and the administration of booster shots. It also examines for the first time policy scenarios at crucial time-intervention points for Greece. In particular, we explore how alterations in the vaccination rate, immunity loss, and relaxation of measures regarding the vaccinated individuals affect the dynamics of COVID-19 spread. The modeling parameters revealed an alarming increase in the death rate during the dominance of the delta variant and before the initiation of the booster shot program in Greece. The existing probability of vaccinated people becoming infected and transmitting the virus sets them as catalytic players in COVID-19 progression. Overall, the modeling observations showcase how the criticism of different intervention measures, the vaccination program, and the virus evolution has been present throughout the various stages of the pandemic. As long as immunity declines, new variants emerge, and vaccine protection in reducing transmission remains incompetent; monitoring the complex vaccine and virus evolution is critical to respond proactively in the future.

Airway obstruction in respiratory viral infections due to impaired mucociliary clearance.

Respiratory viral infections, such as SARS-CoV-2 or influenza, can lead to impaired mucociliary clearance in the bronchial tree due to increased mucus viscosity and its hyper-secretion. We develop in this work a mathematical model to study the interplay between viral infection and mucus motion. The results of numerical simulations show that infection progression can be characterized by three main stages. At the first stage, infection spreads through the most part of mucus producing airways (about 90% of the length) without significant changes in mucus velocity and thickness layer. During the second stage, when it passes through the remaining generations, mucus viscosity increases, its velocity drops down, and it forms a plug. At the last stage, the thickness of the mucus layer gradually increases because mucus is still produced but not removed by the flow. After some time, the thickness of the mucus layer in the small airways becomes comparable with their diameter leading to their complete obstruction.

A Coadunation of Biological and Mathematical Perspectives on the Pandemic COVID-19: A Review

Background: Coronavirus disease 2019 (COVID-19) outbreak has created an emergency globally, and social distancing and isolation are the only solution to prevent its spread. Several countries have announced a full lockdown to tackle this pandemic. The coronavirus family is inclu-sive of pathogens of both-animal species and humans, encapsulating the isolated severe acute respiratory syndrome coronavirus (SARS-CoV). Researchers around the globe have been dexterously working to decode this lethal virus. Many mathematical frameworks have also been depicted, which have helped to understand the dynamics of the COVID-19. Method(s): This systematic review highlights the virus genomic composition, preliminary phylogenetic analysis, pathogenesis, symptomatology, diagnosis, and prognosis along with mathematical models of disease transmission and dynamics. Result(s): Our preliminary phylogenetic analysis of the novel coronavirus sequence discerns that al-though shares its lineage with SARS, BAT-CoV, Beta-BAT-SARS, however, this protein is highly dissimilar to its ancestors. The widely prominent amino acid residues found in the protein are ala-nine (ALA), aspartic acid (ASP), phenylalanine (PHE), leucine (LEU), aspartic acid (ASP), threo-nine (THR), valine (VAL), tyrosine (TYR) and asparagine (ASN) that are responsible for its replication process. Conclusion(s): Research on coronaviruses continues towards developing a strong understanding of the rapidly evolving viral replication and its transmission between individuals.Copyright © 2021 Bentham Science Publishers.

STABILITY ANALYSIS OF A NONLINEAR MATHEMATICAL MODEL FOR COVID-19 TRANSMISSION DYNAMICS

The whole world had been plagued by the COVID-19 pandemic. It was first detected in the Wuhan city of China in December 2019, and has then spread worldwide. It has affected each one of us in the worst possible way. In the current study, a differential equation-based mathematical model is proposed. The present model highlights the infection dynamics of the COVID-19 spread taking hospitalization into account. The basic reproduction number is calculated. This is a crucial indicator of the outcome of the COVID-19 dynamics. Local stability of the equilibrium points has been studied. Global stability of the model is proven using the Lyapunov second method and the LaSalle invariance principle. Sensitivity analysis of the model is performed to distinguish the factor responsible for the faster spread of the infection. Finally, the theoretical aspects have been corroborated via numerical simulations performed for various initial conditions and different values of the parameters. © 2023 the author(s).