WITH the ever-widening scope of modern mathematical analysis and its many ramifications, it is quite impossible to include, in a single volume of reasonable size, an adequate and exhaustive discussion of the calculus in its more advanced stages. It therefore becomes necessary, in planning a thoroughly sound course in the subject, to consider several important aspects of the vast field confronting a modern writer. The limitation of space renders the selection of subject-matter fundamentally dependent upon the aim of the course, which may or may not be related to the content of specific examination syllabuses. Logical development, too, may lead to the inclusion of many topics which, at present, may only be of academic interest, while others, of greater practical value, may have to be omitted. The experience and training of the writer may also have, more or less, a bearing on both these considerations.Advanced CalculusBy Dr. C. A. Stewart. Pp. xviii + 523. (London: Methuen and Co., Ltd., 1940.) 25s.

Advanced Calculus I

Coronavirus disease 2019 (COVID-19) infection is currently a great cause of concern for the healthcare sector around the globe. SARS-CoV-2 is an RNA virus that causes a serious infection that is associated with numerous adverse effects and multiple complications associated with different organs and systems during its pathogenic cycle in humans. Individuals affected by COVID-19, especially elderly populations and immunocompromised people, are greatly vulnerable to opportunistic fungal pathogens. Aspergillosis, invasive candidiasis, and mucormycosis are widespread fungal coinfections in COVID-19 patients. Other fungal infections that are rare but are exhibiting increased incidence in the current scenario include infections caused by Pneumocystis jirovecii, Histoplasma sp., Cryptococcus sp., etc. By producing virulent spores, these pathogens increase the severity of the disease and increase the morbidity and fatality rates in COVID-19 patients globally. These infections generally occur in patients recovering from COVID-19 infection, resulting in rehospitalization. Older and immunocompromised individuals are at higher risk of developing opportunistic fungal infections. This review focuses on understanding the opportunistic fungal infections prevalent in COVID-19 patients, especially elderly people. We have also highlighted the important preventive methods, diagnostic approaches, and prophylactic measures for fungal infections.

/pdf/post-covid-19-fungal-infection-in-the-aged-population-2mz7xlbp.pdf

Post-COVID-19 Fungal Infection in the Aged Population

The main idea of this study is to examine the dynamics of the viral disease, hepatitis C. To this end, the steady states of the hepatitis C virus model are described to investigate the local as well as global stability. It is proved by the standard results that the virus-free equilibrium state is locally asymptotically stable if the value of $ R_0 $ is taken less than unity. Similarly, the virus existing state is locally asymptotically stable if $ R_0 $ is chosen greater than unity. The Routh-Hurwitz criterion is applied to prove the local stability of the system. Further, the disease-free equilibrium state is globally asymptotically stable if $ R_0 < 1 $. The viral disease model is studied after reshaping the integer-order hepatitis C model into the fractal-fractional epidemic illustration. The proposed numerical method attains the fixed points of the model. This fact is described by the simulated graphs. In the end, the conclusion of the manuscript is furnished.

New applications related to hepatitis C model

Among the co-infectious agents in COVID-19 patients, Aspergillus species cause invasive pulmonary aspergillosis (IPA). IPA is difficult to diagnose and is associated with high morbidity and mortality. This study is aimed at identifying Aspergillus spp. from sputum and tracheal aspirate (TA) samples of COVID-19 patients and at determining their antifungal susceptibility profiles. A total of 50 patients with COVID-19 hospitalized in their intensive care units (ICU) were included in the study. Identification of Aspergillus isolates was performed by phenotypic and molecular methods. ECMM/ISHAM consensus criteria were used for IPA case definitions. The antifungal susceptibility profiles of isolates were determined by the microdilution method. Aspergillus spp. was detected in 35 (70%) of the clinical samples. Among the Aspergillus spp., 20 (57.1%) A. fumigatus, six (17.1%) A. flavus, four (11.4%) A. niger, three (8.6%) A. terreus, and two (5.7%) A. welwitschiae were identified. In general, Aspergillus isolates were susceptible to the tested antifungal agents. In the study, nine patients were diagnosed with possible IPA, 11 patients were diagnosed with probable IPA, and 15 patients were diagnosed with Aspergillus colonization according to the used algorithms. Serum galactomannan antigen positivity was found in 11 of the patients diagnosed with IPA. Our results provide data on the incidence of IPA, identification of Aspergillus spp., and its susceptibility profiles in critically ill COVID-19 patients. Prospective studies are needed for a faster diagnosis or antifungal prophylaxis to manage the poor prognosis of IPA and reduce the risk of mortality. 

https://link.springer.com/content/pdf/10.1007/s12223-023-01069-5.pdf

COVID-19-associated pulmonary aspergillosis (CAPA): identification of Aspergillus species and determination of antifungal susceptibility profiles

Commercial titania photocatalyst—P25 was chosen for an antifungal property examination due to it exhibiting one of the highest photocatalytic activities among titania photocatalysts. Titania P25 was homogenized first (HomoP25) and then annealed at different temperatures. Additionally, HomoP25 was modified with 0.5 wt% or 2.0 wt% of platinum by a photodeposition method. The obtained samples were characterized by diffuse-reflectance spectroscopy (DRS), X-ray photoabsorption spectroscopy (XPS), X-ray diffraction (XRD) and Raman spectroscopy. Moreover, photocatalytic activity was tested for methanol dehydrogenation under UV/vis irradiation. The spore-destroying effect of photocatalysts was investigated against two mold fungal species, i.e., Aspergillus fumigatus and Aspergillus niger. Both the mycelium growth and API ZYM (estimation of enzymatic activity) tests were applied for the assessment of antifungal effect. It was found that annealing caused a change of surface properties of the titania samples, i.e., an increase in the noncrystalline part, a growth of particles and enhanced oxygen adsorption on its surface, which resulted in an increase in both the hydrogen evolution rate and the antifungal effect. Titania samples annealed at 300–500 °C were highly active during 60-min UV/vis irradiation, inhibiting the germination of both fungal spores, whereas titania modification with platinum (0.5 and 2.0 wt%) had negligible effect, despite being highly active for hydrogen evolution. The control experiments revealed the lack of titania activity in the dark, as well as high resistance of fungi for applied UV/vis irradiation in the absence of photocatalysts. Moreover, the complete inhibition of 19 hydrolases, secreted by both tested fungi, was noted under UV/vis irradiation on the annealed P25 sample. It is proposed that titania photocatalysts of large particle sizes (>150 nm) and enriched surface with oxygen might efficiently destroy fungal structures under mild irradiation conditions and, thus, be highly promising as covering materials for daily products.

https://www.mdpi.com/2072-666X/13/11/1851/pdf?version=1666958456

Evaluation of Antifungal Properties of Titania P25

Groundbreaking new drugs called direct acting antivirals have been introduced recently for
the treatment of chronic Hepatitis C virus infection.We introduce a mathematical model for
Hepatitis C dynamics treated with the direct acting antiviral drug, telaprevir, alongside
traditional interferon and ribavirin treatments to understand how this combination therapy
affects the viral load of patients exhibiting different types of response.We use sensitivity and
identifiability techniques to determine which model parameters can be best estimated from
viral load data. Parameter estimationwith these best estimable parameters is then performed
to give patient-specific fits of the model to partial virologic response, sustained virologic
response and breakthrough patients.

/pdf/hepatitis-c-viral-dynamics-using-a-combination-therapy-of-31l7jmd7eg.pdf

Hepatitis C Viral Dynamics Using a Combination Therapy of Interferon, Ribavirin, and Telaprevir: Mathematical Modeling and Model Validation

COVID-19-associated pulmonary aspergillosis (CAPA) refers to co-infection with Aspergillus spp. in patients with COVID-19. It has a higher mortality rate when compared with patients only infected with COVID-19, but we still know little about the epidemiology, diagnosis, and best treatment options for patients with CAPA. We report our findings from a year-long retrospective case series of patients with CAPA in two tertiary hospitals in the United Kingdom. We included all patients admitted to critical care with CAPA between March 2020–2021. We used the European Confederation for Medical Mycology and the International Society for Human and Animal Mycology consensus criteria to categorise CAPA. Demographic data, patients’ co-morbidities, time to and method of diagnosis, COVID-19 and aspergillosis treatment, and outcomes were analysed. Thirteen patients were diagnosed with probable CAPA between October/2020–March/2021, and 54.8% also had hypertension. Diagnosis was established after a median of 18 days post-COVID-19 infection, and a median of 7 days post-intubation. All patients had received corticosteroids, as well as tocilizumab (7; 53.8%) and remdesivir (3; 23%). Eleven patients received antifungal treatment. Nine (69%) patients died by 30 days post-ICU admission, one patient died on day 32, and three (23%) patients survived. CAPA has a very high mortality rate. We also identified three areas that merit further investigation: lack of positive tests between March–October 2020; COVID-19 treatments and possible relationship with increased CAPA rates; and the rationale behind antifungal treatment in our hospitals compared to recommended treatment in the literature.

/pdf/covid-19-associated-pulmonary-aspergillosis-a-year-long-ijbffclq.pdf

COVID-19-Associated Pulmonary Aspergillosis: A Year-Long Retrospective Case Series

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Hepatitis C Viral Dynamics Using a Combination Therapy of Interferon, Ribavirin, and Telaprevir: Mathematical Modeling and Model Validation

COVID-19-Associated Pulmonary Aspergillosis: A Year-Long Retrospective Case Series