Optimal control for co-infection with COVID-19-Associated Pulmonary Aspergillosis in ICU patients with environmental contamination.

In this paper, we propose a mathematical model for COVID-19-Associated Pulmonary Aspergillosis (CAPA) co-infection, that enables the study of relationship between prevention and treatment. The next generation matrix is employed to find the reproduction number. We enhanced the co-infection model by incorporating time-dependent controls as interventions based on Pontryagin's maximum principle in obtaining the necessary conditions for optimal control. Finally, we perform numerical experiments with different control groups to assess the elimination of infection. In numerical results, transmission prevention control, treatment controls, and environmental disinfection control provide the best chance of preventing the spread of diseases more rapidly than any other combination of controls.

Dynamics of Fractional Delayed Reaction-Diffusion Equations.

The long-term behavior of the weak solution of a fractional delayed reaction-diffusion equation with a generalized Caputo derivative is investigated. By using the classic Galerkin approximation method and comparison principal, the existence and uniqueness of the solution is proved in the sense of weak solution. In addition, the global attracting set of the considered system is obtained, with the help of the Sobolev embedding theorem and Halanay inequality.

Fractional Euler numbers and generalized proportional fractional logistic differential equation.

We solve a logistic differential equation for generalized proportional Caputo fractional derivative. The solution is found as a fractional power series. The coefficients of that power series are related to the Euler polynomials and Euler numbers as well as to the sequence of Euler's fractional numbers recently introduced. Some numerical approximations are presented to show the good approximations obtained by truncating the fractional power series. This generalizes previous cases including the Caputo fractional logistic differential equation and Euler's numbers.

Impact of optimal vaccination and social distancing on COVID-19 pandemic.

The first COVID-19 case was reported at Wuhan in China at the end of December 2019 but till today the virus has caused millions of deaths worldwide. Governments of each country, observing the severity, took non-pharmaceutical interventions from the very beginning to break the chain of higher transmission. Fortunately, vaccines are available now in most countries and people are asked to take recommended vaccines as precautionary measures. In this work, an epidemiological model on COVID-19 is proposed where people from the susceptible and asymptomatically infected phase move to the vaccinated class after a full two-dose vaccination. The overall analysis says that the disease transmission rate from symptomatically infected people is most sensitive on the disease prevalence. Moreover, better disease control can be achieved by vaccination of the susceptible class. In the later part of the work, a corresponding optimal control problem is considered where maintaining social distancing and vaccination procedure change with time. The result says that even in absence of social distancing, only the vaccination to people can significantly reduce the overall infected population. From the analysis, it is observed that maintaining physical distancing and taking vaccines at an early stage decreases the infection level significantly in the environment by reducing the probability of becoming infected.

Spatiotemporal dynamics of a glioma immune interaction model.

We report a mathematical model which depicts the spatiotemporal dynamics of glioma cells, macrophages, cytotoxic-T-lymphocytes, immuno-suppressive cytokine TGF-ß and immuno-stimulatory cytokine IFN-γ through a system of five coupled reaction-diffusion equations. We performed local stability analysis of the biologically based mathematical model for the growth of glioma cell population and their environment. The presented stability analysis of the model system demonstrates that the temporally stable positive interior steady state remains stable under the small inhomogeneous spatiotemporal perturbations. The irregular spatiotemporal dynamics of gliomas, macrophages and cytotoxic T-lymphocytes are discussed extensively and some numerical simulations are presented. Performed some numerical simulations in both one and two dimensional spaces. The occurrence of heterogeneous pattern formation of the system has both biological and mathematical implications and the concepts of glioma cell progression and invasion are considered. Simulation of the model shows that by increasing the value of time, the glioma cell population, macrophages and cytotoxic-T-lymphocytes spread throughout the domain.

COVID-19 Vaccine Boosters: The Good, the Bad, and the Ugly.

Pursuing vaccinations against COVID-19 brings hope to limit the spread of SARS-CoV-2 and remains the most rational decision under pandemic conditions. However, it does not come without challenges, including temporary shortages in vaccine doses, significant vaccine inequity, and questions regarding the durability of vaccine-induced immunity that remain unanswered. Moreover, SARS-CoV-2 has undergone evolution with the emergence of its novel variants, characterized by enhanced transmissibility and ability to at least partially evade neutralizing antibodies. At the same time, serum antibody levels start to wane within a few months after vaccination, ultimately increasing the risk of breakthrough infections. This article discusses whether the administration of booster doses of COVID-19 vaccines is urgently needed to control the pandemic. We conclude that, at present, optimizing the immunity level of wealthy populations cannot come at the expense of low-income regions that suffer from vaccine unavailability. Although the efficiency of vaccination in protecting from infection may decrease over time, current data show that efficacy against severe disease, hospitalization, and death remains at a high level. If vaccine coverage continues at extremely low levels in various regions, including African countries, SARS-CoV-2 may sooner or later evolve into variants better adapted to evade natural and vaccine-induced immunity, ultimately bringing a global threat that, of course, includes wealthy populations. We offer key recommendations to increase vaccination rates in low-income countries. The pandemic is, by definition, a major epidemiological event and requires looking beyond one's immediate self-interest; otherwise, efforts to contain it will be futile.

New insights on novel coronavirus 2019-nCoV/SARS-CoV-2 modelling in the aspect of fractional derivatives and fixed points.

Extended orthogonal spaces are introduced and proved pertinent fixed point results. Thereafter, we present an analysis of the existence and unique solutions of the novel coronavirus 2019-nCoV/SARS-CoV-2 model via fractional derivatives. To strengthen our paper, we apply an efficient numerical scheme to solve the coronavirus 2019-nCoV/SARS-CoV-2 model with different types of differential operators.

Application of non-parametric models for analyzing survival data of COVID-19 patients.

BACKGROUND: COVID-19 Coronavirus variants are emerging across the globe causing ongoing pandemics. It is important to estimate the case fatality ratio (CFR) during such an epidemic of a potentially fatal disease. METHODS: Firstly, we have performed a non-parametric approach for odds ratios with corresponding confidence intervals (CIs) and illustrated relative risks and cumulative mortality rates of COVID-19 data of Spain. We have demonstrated the modified non-parametric approach based on Kaplan-Meier (KM) technique using COVID-19 data of Italy. We have also performed the significance of characteristics of patients regarding outcome by age for both genders. Furthermore, we have applied a non-parametric cure model using Nadaraya-Watson weight to estimate cure-rate using Israel data. Simulations are based on R-software. RESULTS: The analytical illustrations of these approaches predict the effects of patients based on covariates in different scenarios. Sex differences are increased from ages less than 60 years to 60-69 years but decreased thereafter with the smallest sex difference at ages 80 years in a case for estimating both purposes RR (relative risk) and OR (odds ratio). The non-parametric approach investigates the range of cure-rate ranges from 5.3% to 9% and from 4% to 7% approximately for male and female respectively. The modified KM estimator performs for such censored data and detects the changes in CFR more rapidly for both genders and age-wise. CONCLUSION: Older-age, male-sex, number of comorbidities and access to timely health care are identified as some of the risk factors associated with COVID-19 mortality in Spain. The non-parametric approach has investigated the influence of covariates on models and it provides the effect in both genders and age. The health impact of public for inaccurate estimates, inconsistent intelligence, conflicting messages, or resulting in misinformation can increase awareness among people and also induce panic situations that accompany major outbreaks of COVID-19.

One Year of the COVID-19 Pandemic in Galicia: A Global View of Age-Group Statistics during Three Waves.

In this work we look at the past in order to analyze four key variables after one year of the COVID-19 pandemic in Galicia (NW Spain): new infected, hospital admissions, intensive care unit admissions and deceased. The analysis is presented by age group, comparing at each stage the percentage of the corresponding group with its representation in the society. The time period analyzed covers 1 March 2020 to 1 April 2021, and includes the influence of the B.1.1.7 lineage of COVID-19 which in April 2021 was behind 90% of new cases in Galicia. It is numerically shown how the pandemic affects the age groups 80+, 70+ and 60+, and therefore we give information about how the vaccination process could be scheduled and hints at why the pandemic had different effects in different territories.

Interdisciplinary Approaches to COVID-19.

The coronavirus disease 2019 (COVID-19) pandemic has been a significant concern worldwide. The pandemic has demonstrated that public health issues are not merely a health concern but also affect society as a whole. In this chapter, we address the importance of bringing together the world's scientists to find appropriate solutions for controlling and managing the COVID-19 pandemic. Interdisciplinary cooperation, through modern scientific methods, could help to handle the consequences of the pandemic and to avoid the recurrence of future pandemics.

Forecasting the Effects of the New SARS-CoV-2 Variant in Europe.

Due to the emergence of a new SARS-CoV-2 variant, we use a previous model to simulate the behaviour of this new SARS-CoV-2 variant. The analysis and simulations are performed for Europe, in order to provide a global analysis of the pandemic. In this context, numerical results are obtained in the first 100 days of the pandemic assuming an infectivity of 70%, 56%, and 35%, respectively, higher for the new SAR-CoV-2 variant, as compared with the real data.

Fractional model of COVID-19 applied to Galicia, Spain and Portugal.

A fractional compartmental mathematical model for the spread of the COVID-19 disease is proposed. Special focus has been done on the transmissibility of super-spreaders individuals. Numerical simulations are shown for data of Galicia, Spain, and Portugal. For each region, the order of the Caputo derivative takes a different value, that is not close to one, showing the relevance of considering fractional models.

Optimal control of the COVID-19 pandemic: controlled sanitary deconfinement in Portugal.

The COVID-19 pandemic has forced policy makers to decree urgent confinements to stop a rapid and massive contagion. However, after that stage, societies are being forced to find an equilibrium between the need to reduce contagion rates and the need to reopen their economies. The experience hitherto lived has provided data on the evolution of the pandemic, in particular the population dynamics as a result of the public health measures enacted. This allows the formulation of forecasting mathematical models to anticipate the consequences of political decisions. Here we propose a model to do so and apply it to the case of Portugal. With a mathematical deterministic model, described by a system of ordinary differential equations, we fit the real evolution of COVID-19 in this country. After identification of the population readiness to follow social restrictions, by analyzing the social media, we incorporate this effect in a version of the model that allow us to check different scenarios. This is realized by considering a Monte Carlo discrete version of the previous model coupled via a complex network. Then, we apply optimal control theory to maximize the number of people returning to "normal life" and minimizing the number of active infected individuals with minimal economical costs while warranting a low level of hospitalizations. This work allows testing various scenarios of pandemic management (closure of sectors of the economy, partial/total compliance with protection measures by citizens, number of beds in intensive care units, etc.), ensuring the responsiveness of the health system, thus being a public health decision support tool.

Epidemic model of COVID-19 outbreak by inducing behavioural response in population.

COVID-19 has spread around the world since December 2019, creating one of the greatest pandemics ever witnessed. According to the current reports, this is a situation when people need to be more careful and take the precaution measures more seriously, unless the condition may become even worse. Maintaining social distances and proper hygiene, staying at isolation or adopting the self-quarantine method are some of the common practices that people should use to avoid the infection. And the growing information regarding COVID-19 and its symptoms help the people to take proper precautions. In this present study, we consider an SEIRS epidemiological model on COVID-19 transmission which accounts for the effect of an individual's behavioural response due to the information regarding proper precautions. Our results indicate that if people respond to the growing information regarding awareness at a higher rate and start to take the protective measures, then the infected population decreases significantly. The disease fatality can be controlled only if a large proportion of individuals become immune, either by natural immunity or by a proper vaccine. In order to apply the latter option, we need to wait until a safe and proper vaccine is developed and it is a time-taking process. Hence, in the latter part of the work, an optimal control problem is considered by implementing control strategies to reduce the disease burden. Numerical figures show that the control denoting behavioural response works with higher intensity immediately after implementation and then gradually decreases with time. Further, the control policy denoting hospitalisation of infected individuals works with its maximum intensity for quite a long time period following a sudden decrease. As, the implementation of the control strategies reduce the infected population and increase the recovered population, so, it may help to reduce the disease transmission at this current epidemic situation.

Corrigendum to "Mathematical modeling of COVID-19 transmission dynamics with a case study of Wuhan" [Chaos Solitons Fractals 135 (2020), 109846].

We correct some numerical results of [Chaos Solitons Fractals 135 (2020), 109846], by providing the correct numbers and plots. The conclusions of the paper remain, however, the same. In particular, the numerical simulations show the suitability of the proposed COVID-19 model for the outbreak that occurred in Wuhan, China. This time all our computer codes are provided, in order to make all computations reproducible. The authors would like to apologize for any inconvenience caused.

Modeling and forecasting the COVID-19 pandemic in India.

In India, 100,340 confirmed cases and 3155 confirmed deaths due to COVID-19 were reported as of May 18, 2020. Due to absence of specific vaccine or therapy, non-pharmacological interventions including social distancing, contact tracing are essential to end the worldwide COVID-19. We propose a mathematical model that predicts the dynamics of COVID-19 in 17 provinces of India and the overall India. A complete scenario is given to demonstrate the estimated pandemic life cycle along with the real data or history to date, which in turn divulges the predicted inflection point and ending phase of SARS-CoV-2. The proposed model monitors the dynamics of six compartments, namely susceptible (S), asymptomatic (A), recovered (R), infected (I), isolated infected (Iq ) and quarantined susceptible (Sq ), collectively expressed SARIIqSq . A sensitivity analysis is conducted to determine the robustness of model predictions to parameter values and the sensitive parameters are estimated from the real data on the COVID-19 pandemic in India. Our results reveal that achieving a reduction in the contact rate between uninfected and infected individuals by quarantined the susceptible individuals, can effectively reduce the basic reproduction number. Our model simulations demonstrate that the elimination of ongoing SARS-CoV-2 pandemic is possible by combining the restrictive social distancing and contact tracing. Our predictions are based on real data with reasonable assumptions, whereas the accurate course of epidemic heavily depends on how and when quarantine, isolation and precautionary measures are enforced.

The urgent need for integrated science to fight COVID-19 pandemic and beyond.

The COVID-19 pandemic has become the leading societal concern. The pandemic has shown that the public health concern is not only a medical problem, but also affects society as a whole; so, it has also become the leading scientific concern. We discuss in this treatise the importance of bringing the world's scientists together to find effective solutions for controlling the pandemic. By applying novel research frameworks, interdisciplinary collaboration promises to manage the pandemic's consequences and prevent recurrences of similar pandemics.

Mathematical modeling of COVID-19 transmission dynamics with a case study of Wuhan.

We propose a compartmental mathematical model for the spread of the COVID-19 disease with special focus on the transmissibility of super-spreaders individuals. We compute the basic reproduction number threshold, we study the local stability of the disease free equilibrium in terms of the basic reproduction number, and we investigate the sensitivity of the model with respect to the variation of each one of its parameters. Numerical simulations show the suitability of the proposed COVID-19 model for the outbreak that occurred in Wuhan, China.

Reproductive behaviour and concurrent sound production of Gulf grouper Mycteroperca jordani (Epinephelidae) at a spawning aggregation site.

The reproductive and acoustic behaviours of Gulf grouper Mycteroperca jordani were studied at a spawning aggregation site in the southern Gulf of California, México. In May 2015-2017, divers located and surveyed a spawning aggregation site within Cabo Pulmo National Park. Adult M. jordani conformed to a lek mating system in which large males formed territories over sand adjacent to a rocky reef that were spatially segregated from smaller females outside of courtship and spawning periods. Females moved into male territories during evening hours to spawn. Male courtship behaviours targeted a single female, included head shakes and burst rises and preceded pair spawning prior to sunset. Males and females displayed three shared colour phases, but four phases were sex-specific. During evening hours, courtship and spawning, both sexes exhibited sexual dichromatism concurrent with reproductive behaviours. The pair-spawning mating system and observations of bimodal size distributions by sex support previous claims of protogyny in the species. Males produced sounds during territorial patrols, courtship and spawning rushes, which corroborated the importance of acoustic communication within the behavioural repertoire associated with spawning. Long-term acoustic monitoring revealed increases in total sounds detected day-1 from March through June with diel increases (e.g., evenings) that may be indicative of the spawning season. Observations of spawning on 12 consecutive evenings in May 2017 coupled with extended periods of sound production suggest that spawning does not follow a lunar rhythm. This first description of the mating system and sounds of the endangered M. jordani facilitates future development of seasonal and areal protections to restore and manage the species.