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In this work, the dynamics of the spread of COVID-19 is considered in the presence of both human-to-human transmission as well as environment-to-human transmission. Specifically, we expand and modify traditional epidemiological model for COVID-19 by incorporating a compartment to study the dynamics of pathogen concentration in the environmental reservoir, for instance concentration of droplets in closed spaces. We perform a mathematical analysis for the model proposed including an endemic equilibrium analysis as well as a next-generation approach both of which help to derive the basic reproduction number. We also study the e˚cacy of wearing a facemask through this model. Another important contribution of this work is the introduction to physics informed deep learning methods (PINNs) to study the dynamics. We propose this as an alternative to traditional numerical methods for solving system of differential equations used to describe dynamics of infectious diseases. Our results show that the proposed PINNs approach is a reliable candidate for both solving such systems and for helping identify important parameters that control the disease dynamics.

Dynamic compartmentalized data (DCD) and compartmentalized differential equations (CDEs) are key instruments for modeling transmission of pathogens such as the SARS-CoV-2 virus. We describe an effi-cient nowcasting algorithm for modeling transmission of SARS-CoV-2 with uncertainty quantification for the COVID-19 impact. A key concern for transmission of SARS-CoV-2 is under-reporting of cases, and this is addressed in our data-driven model by providing an estimate for the detection rate. Our novel top-down model is based on CDEs with stochastic constitutive parameters obtained from the DCD using Bayesian inference. We demonstrate the robustness of our algorithm for simulation studies using synthetic DCD, and nowcasting COVID-19 using real DCD from several regions across five continents.

In this paper, we study the dynamical effects of timely and delayed diagnosis on the spread of COVID-19 in Ghana during its initial phase by using reported data from March 12 to June 19, 2020. The estimated basic reproduction number, ℛ 0 , for the proposed model is 1.04. One of the main focus of this study is global stability results. Theoretically and numerically, we show that the disease persistence depends on ℛ 0 . We carry out a local and global sensitivity analysis. The local sensitivity analysis shows that the most positive sensitive parameter is the recruitment rate, followed by the relative transmissibility rate from the infectious with delayed diagnosis to the susceptible individuals. And that the most negative sensitive parameters are: self-quarantined, waiting time of the infectious for delayed diagnosis and the proportion of the infectious with timely diagnosis. The global sensitivity analysis using the partial rank correlation coefficient confirms the directional flow of the local sensitivity analysis. For public health benefit, our analysis suggests that, a reduction in the inflow of new individuals into the country or a reduction in the inter community inflow of individuals will reduce the basic reproduction number and thereby reduce the number of secondary infections (multiple peaks of the infection). Other recommendations for controlling the disease from the proposed model are provided in Section 7.

The review mainly focuses on the goals to evaluate the clinical and cost effectiveness of neonatal CPAP in a decrease of Mortality, Length of Stay, Respiratory support, Extubation and Intubation. Introduction: Inclusion criteria: This review is conducted in neonates with respiratory failure, Pneumonia sepsis, necrotizing infections, Pneumothorax, Broncho pulmonary distress, respiratory distress syndrome (RDS), COVID-19, and other comorbidities also included. Methods: The databases like PubMed, Google Scholar, and Cochrane were used in this review. Depending on inclusion criteria the full-text articles were assessed and chosen studies were recovered by methodological quality. Results: one twenty-six studies are retrieved which met the inclusion criteria and the extracted studies were pooled statistically and their outcomes were measured. All the studies explain the efficacy of CPAP by reducing Mortality, Length of Stay, Respiratory support, Extubation and Intubation. Conclusion: Currently the evidence states that CPAP reduces Mortality, Length of Stay, Respiratory support, Extubation and Intubation

This paper considers a mathematical model that accounts for the hematological disorders of blood in its flow in human arteries. Blood is described as a Newtonian fluid but with its viscosity as a function of the hematocrit, plasma viscosity, and shape factor of the red blood cells. The artery is modeled as a flexible circular pipe with the blood flow as oscillatory. This model is solved using HAM (Homotopy Analysis Method), an approximate analytical method, and we computed expressions for wall shear stress (WSS) and volumetric flow rate. With the help of publicly available data, blood flow in the human femoral artery for male and female populations aged 19 to 60 and above years is simulated for healthy, anemia, and polycythemia cases. The model projected a significant difference in the mean volumetric flow rates in the conditions mentioned above. Results also indicated that the mean WSS of healthy and anemic populations are not significantly different. However, a significant difference in the mean has been observed in healthy and polycythemic conditions. Furthermore, a 33.3% decrease in hematocrit value from that in the normal range (taken as 0.45) of a healthy population has increased the flow rate by 33.5%. For a value 33.3% above 0.45, there is a decrease of 42.7% in the flow rate.

In this work, we proposed a simple SEIHR compartmental model to study and analyse the third wave of COVID-19 in India. In addition to the other features of the disease, we also consider the reinfection of recovered individuals in the model. For the purpose of parameter estimation we separate the infective and deaths classes and plot them against the cumulative counts of infective and deaths from data, respectively. The estimated parameters from these two are used for prediction and further numerical simulations.We note that the infective will keep on growing and only slow down after around three months. We have studied impact of various parameters on our model and observe that the parameters associated with mask usage, screening and the care giving toCOVID-19 patients have significant impact on the prevalence and time taken to slow down the infection.We conclude that better use of mask, effective screening and timely care to infective will reduce infective and can help in disease control. Our numerical simulations can explicitly provide a short term prediction for such time line. Also we note that providing better care facilities will help reducing peak as well as the disease burden of predicted infected cases.

In this study, we develop a mathematical model incorporating age-specific transmission dynamics of COVID-19 to evaluate the role of vaccination and treatment strategies in reducing the size of COVID-19 burden. Initially, we establish the positivity and boundedness of the solutions of the non controlled model and calculate the basic reproduction number and do the stability analysis. We then formulate an optimal control problem with vaccination and treatment as control variables and study the same. Pontryagin’s Minimum Principle is used to obtain the optimal vaccination and treatment rates. Optimal vaccination and treatment policies are analysed for different values of the weight constant associated with the cost of vaccination and different efficacy levels of vaccine. Findings from these suggested that the combined strategies (vaccination and treatment) worked best in minimizing the infection and disease induced mortality. In order to reduce COVID-19 infection and COVID-19 induced deaths to maximum, it was observed that optimal control strategy should be prioritized to the population with age greater than 40 years. Varying the cost of vaccination it was found that sufficient implementation of vaccines (more than 77 %) reduces the size of COVID-19 infections and number of deaths. The infection curves varying the efficacies of the vaccines against infection were also analysed and it was found that higher efficacy of the vaccine resulted in lesser number of infections and COVID induced deaths. The findings would help policymakers to plan effective strategies to contain the size of the COVID-19 pandemic.

The venerable process of cellular respiration is essential for cells to produce energy from glucose molecules, in order to carry out cellular work. The process is responsible for producing molecules of ATP, a molecule which is thermodynamically coupled with other biochemical and biophysical processes in order to provide energy for such processes to occur. While the process of cellular respiration is essential to biology, one cycle of the process occurs only in a matter of milliseconds, and so, it would be impractical to measure the time it takes for the process to occur through conventional means. Therefore, using concepts from reaction rate theory, particularly Marcus Theory of electron transfer, Michaelis-Menten kinetics for enzymatic catalysis, and the hard-sphere model of collision theory, I formulate and propose a mathematical approximation for the amount of time it takes for cellular respiration to occur. Through this heuristic approach, quantitatively knowing the amount of time it takes for one cycle of cellular respiration to occur could potentially have future applications in biological research.

Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is the causative agent of the current global COVID-19 pandemic, in which millions of lives have been lost. Understanding the zoonotic evolution of the coronavirus may provide insights for developing effective vaccines, monitoring the transmission trends, and preventing new zoonotic infections. Homopolymeric nucleotide repeats (HP), the most simple tandem repeats, are a ubiquitous feature of eukaryotic genomes. Yet the HP distributions and roles in coronavirus genome evolution are poorly investigated. In this study, we characterize the HP distributions and trends in the genomes of bat and human coronaviruses and SARS-CoV-2 variants. The results show that the SARS-CoV-2 genome is abundant in HPs, and has augmented HP contents during evolution. Especially, the disparity of HP poly-(A/T) and ploy-(C/G) of coronaviruses increases during the evolution in human hosts. The disparity of HP poly-(A/T) and ploy-(C/G) is correlated to host adaptation and the virulence level of the coronaviruses. Therefore, we propose that the HP disparity can be a quantitative measure for the zoonotic evolution levels of coronaviruses. Peculiarly, the HP disparity measure infers that SARS-CoV-2 Omicron variants have a high disparity of HP poly-(A/T) and ploy-(C/G), suggesting a high adaption to the human hosts.

We introduce a derangement model of ligand-receptor binding that allows us to quantitatively frame the question “How can ligands seek out and bind to their optimal receptor sites in a sea of other competing ligands and suboptimal receptor sites?” To answer the question, we first derive a formula to count the number of partial generalized derangements in a list, thus extending the derangement result of Gillis and Even. We then compute the general partition function for the ligand-receptor system and derive the equilibrium expressions for the average number of bound ligands and the average number of optimally bound ligands. A visual model of squares assembling onto a grid allows us to easily identify fully optimal bound states. Equilibrium simulations of the system reveal its extremes to be one of two types, qualitatively distinguished by whether optimal ligand-receptor binding is the dominant form of binding at all temperatures and quantitatively distinguished by the relative values of two critical temperatures. One of those system types (termed “search-limited,” as it was in previous work) does not exhibit kinetic traps and we thus infer that biomolecular systems where optimal ligand-receptor binding is functionally important are likely to be search-limited.

The present model is dealt with prey-predator interactions in two different patches where only prey species are allowed to disperse among the patches. Each of these two patches has different predator population but the predator in Patch-2 only is affected with a disease. The proposed model is biologically welldefined. Also, the feasibility of the equilibrium points and corresponding stability conditions are analysed. It is found that the disease among predator, even in one patch, makes an important role to control the whole system dynamics as it starts to oscillates by regulating the disease transmission rate. Moreover, the disease transmission rate has a stabilizing as well as destabilizing effect on the system dynamics. From the results, it is observed that a high dispersal rate decreases the count of infected predator in a patch in presence of prey dispersal. There is another interesting result: it is observed that the prey dispersal cannot destabilize the coexistence state, i.e., the system which is stable in absence of dispersal remains stable when the prey species disperse between two patches.

Often described as the world’s most deadly infectious disease, Tuberculosis remains a serious health threat in many parts of the world, especially in the developing countries. One of the social barriers hindering TB patients to seek and complete medical attention is stigmatization. In this study, we incorporated stigmatization on a model published by Feng et al. last 2000. We obtained the basic reproduction number and showed conditions where multiple endemic equilibrium will exist depending on a reinfection threshold. The model predicted a significant increase in the basic reproduction number as the level of stigmatization increases. We used optimal control theory to investigate the effect of controls to combat stigmatization and compare these controls with the usual controls such as improving treatment and minimizing reinfection. Simulations show that although stigmatization controls are helpful, they are not enough to successfully control the disease. A combination of all the controls will be ideal and some optimal rates of doing it over time are given, depending on the perceived cost of implementation.

Hypergraph, as a generalization of the notions of graph and simplicial complex, has gained a lot of attention in many fields. It is a relatively new mathematical model to describe the high-dimensional structure and geometric shapes of data sets. In this paper,we introduce the neighborhood hypergraph model for graphs and combine the neighborhood hypergraph model with the persistent (embedded) homology of hypergraphs. Given a graph,we can obtain a neighborhood complex introduced by L. Lovász and a filtration of hypergraphs parameterized by aweight function on the power set of the vertex set of the graph. Theweight function can be obtained by the construction fromthe geometric structure of graphs or theweights on the vertices of the graph. We show the persistent theory of such filtrations of hypergraphs. One typical application of the persistent neighborhood hypergraph is to distinguish the planar square structure of cisplatin and transplatin. Another application of persistent neighborhood hypergraph is to describe the structure of small fullerenes such as C 20 . The bond length and the number of adjacent carbon atoms of a carbon atom can be derived from the persistence diagram. Moreover, our method gives a highly matched stability prediction (with a correlation coefficient 0.9976) of small fullerene molecules.

Severe Acute Respiratory Syndrome CoronaVirus-2 (SARS-CoV-2) infection is a major risk factor for mortality and morbidity in critical care hospitals around the world. Lung epithelial type II cells play a major role in the recognition and clearance of respiratory viruses as well as repair of lung injury in response to environmental toxicants. Gene expression profiling studies revealed that mouse lung epithelial type II cells express several cell-specific markers including surfactant proteins and Lysosomal associated membrane protein 3 (LAMP3) located in lysosomes, endosomes and lamellar bodies. These intracellular organelles are involved in vesicular transport and facilitate viral entry and release of the viral genome into the host cell cytoplasm. In this study, regulation of LAMP3 expression in human lung epithelial cells by several respiratory viruses and type I interferon signaling was investigated. Respiratory viruses including SARS-CoV-1 and SARS-CoV-2 significantly induced LAMP3 expression in lung epithelial cells within 24 hours after infection that required the presence of ACE2 viral entry receptors. Time course experiments revealed that the induced expression of LAMP3 was correlated with the induced expression of Interferon–beta (IFNB1) and STAT1 at mRNA levels. LAMP3 was also induced by direct IFN-beta treatment in multiple lung epithelial cell lines or by infection with influenza virus lacking the non-structural protein1(NS1) in NHBE bronchial epithelial cells. LAMP3 expression was also induced by several respiratory viruses in human lung epithelial cells including RSV and HPIV3. Location in lysosomes and endosomes aswell as induction by respiratory viruses and type I Interferon suggests that LAMP3 may have an important role in inter-organellar regulation of innate immunity and a potential target for therapeutic modulation in health and disease. Furthermore, bioinformatics revealed that a subset of lung type II genes were differentially regulated in the lungs of COVID-19 patients.