Sudipa Chauhan, Shweta Upadhyaya, Payal Rana, Geetika Malik
Abstract An unprecedented and precise time-scheduled rollout for the vaccine is needed for an effective vaccination process. This study is based on the development of a novel mathematical model considering a delay in vaccination due to the inability to book a slot in one go for a system. Two models are proposed which involve a delay differential equation mathematical model whose dynamical analysis is done to show how the delay in vaccination can destabilize the system. Further, this delay led to the formulation of a queuing model that accounts for the need to retry for the vaccination at a certain rate as delay in vaccination can have negative repercussions. The transition rates from one stage to another follow an exponential distribution. The transient state probabilities of the model are acquired by applying the Runge-Kutta method and hence performance indices are also obtained. These performance measures include the expected number of people in various states. Finally, numerical analysis is also provided to validate both models. Our results would specifically focus on what happens if the delay time increases or if the retrial rate increases (delay time decreases). The results reveal that a delay in being vaccinated by the first dose (i.e., 80 days) leads to an unstable system whereas there exists a delay simultaneously in getting vaccinated by both doses that destabilize the system early (i.e., 80 and 120 days for dose one and two, respectively). The system destabilizes faster in the presence of a delay for slot booking for both doses as compared to one dose delay. Further, the numerical results of queuing models show that if the retrial rate increases in this delay time to book the slots, it not only increases in the vaccinated class but also increases the recovered population.
{"title":"Dynamic analysis of delayed vaccination process along with impact of retrial queues","authors":"Sudipa Chauhan, Shweta Upadhyaya, Payal Rana, Geetika Malik","doi":"10.1515/cmb-2022-0147","DOIUrl":"https://doi.org/10.1515/cmb-2022-0147","url":null,"abstract":"Abstract An unprecedented and precise time-scheduled rollout for the vaccine is needed for an effective vaccination process. This study is based on the development of a novel mathematical model considering a delay in vaccination due to the inability to book a slot in one go for a system. Two models are proposed which involve a delay differential equation mathematical model whose dynamical analysis is done to show how the delay in vaccination can destabilize the system. Further, this delay led to the formulation of a queuing model that accounts for the need to retry for the vaccination at a certain rate as delay in vaccination can have negative repercussions. The transition rates from one stage to another follow an exponential distribution. The transient state probabilities of the model are acquired by applying the Runge-Kutta method and hence performance indices are also obtained. These performance measures include the expected number of people in various states. Finally, numerical analysis is also provided to validate both models. Our results would specifically focus on what happens if the delay time increases or if the retrial rate increases (delay time decreases). The results reveal that a delay in being vaccinated by the first dose (i.e., 80 days) leads to an unstable system whereas there exists a delay simultaneously in getting vaccinated by both doses that destabilize the system early (i.e., 80 and 120 days for dose one and two, respectively). The system destabilizes faster in the presence of a delay for slot booking for both doses as compared to one dose delay. Further, the numerical results of queuing models show that if the retrial rate increases in this delay time to book the slots, it not only increases in the vaccinated class but also increases the recovered population.","PeriodicalId":34018,"journal":{"name":"Computational and Mathematical Biophysics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42816028","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
D. Nayak, Bishal Chhetri, Krishna Kiran Vamsi Dasu, Swapna Muthusamy, V. Bhagat
Abstract Leprosy (Hansen’s disease) is an infectious, neglected tropical disease caused by the Mycobacterium Leprae (M. Leprae). About 2,02,189 new cases are diagnosed worldwide each year. Lepra reactions are an off shoot of leprosy infection causing major nerve damage leading to disability. Early detection of lepra reactions through the study of biomarkers can prevent subsequent disabilities. Motivated by these observations, in this study, we have proposed and analyzed a three-dimensional mathematical model to capture the dynamics of susceptible schwann cells, infected schwann cells, and the bacterial load based on the pathogenesis of leprosy. We did the stability analysis, numerical simulations, and also performed the sensitivity analysis using Spearman’s rank correlation coefficient, partial rank correlation coefficient, and Sobol’s index methods. We later performed the optimal control studies with both multi-drug therapy and steroid interventions as control variables. Finally, we did the comparative and effectiveness study of these different control interventions.
{"title":"A comprehensive and detailed within-host modeling study involving crucial biomarkers and optimal drug regimen for type I Lepra reaction: A deterministic approach","authors":"D. Nayak, Bishal Chhetri, Krishna Kiran Vamsi Dasu, Swapna Muthusamy, V. Bhagat","doi":"10.2139/ssrn.4216314","DOIUrl":"https://doi.org/10.2139/ssrn.4216314","url":null,"abstract":"Abstract Leprosy (Hansen’s disease) is an infectious, neglected tropical disease caused by the Mycobacterium Leprae (M. Leprae). About 2,02,189 new cases are diagnosed worldwide each year. Lepra reactions are an off shoot of leprosy infection causing major nerve damage leading to disability. Early detection of lepra reactions through the study of biomarkers can prevent subsequent disabilities. Motivated by these observations, in this study, we have proposed and analyzed a three-dimensional mathematical model to capture the dynamics of susceptible schwann cells, infected schwann cells, and the bacterial load based on the pathogenesis of leprosy. We did the stability analysis, numerical simulations, and also performed the sensitivity analysis using Spearman’s rank correlation coefficient, partial rank correlation coefficient, and Sobol’s index methods. We later performed the optimal control studies with both multi-drug therapy and steroid interventions as control variables. Finally, we did the comparative and effectiveness study of these different control interventions.","PeriodicalId":34018,"journal":{"name":"Computational and Mathematical Biophysics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43190551","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract This article consists of a detailed and novel stochastic optimal control analysis of a coupled non-linear dynamical system. The state equations are modelled as an additional food-provided prey–predator system with Holling type III functional response for predator and intra-specific competition among predators. We first discuss the optimal control problem as a Lagrangian problem with a linear quadratic control. Second, we consider an optimal control problem in the time-optimal control setting. We initially establish the existence of optimal controls for both these problems and later characterize these optimal controls using the Stochastic maximum principle. Further numerical simulations are performed based on stochastic forward-backward sweep methods for realizing the theoretical findings. The results obtained in these optimal control problems are discussed in the context of biological conservation and pest management.
{"title":"Stochastic optimal and time-optimal control studies for additional food provided prey–predator systems involving Holling type III functional response","authors":"Daliparthi Bhanu Prakash, D. Vamsi","doi":"10.1515/cmb-2022-0144","DOIUrl":"https://doi.org/10.1515/cmb-2022-0144","url":null,"abstract":"Abstract This article consists of a detailed and novel stochastic optimal control analysis of a coupled non-linear dynamical system. The state equations are modelled as an additional food-provided prey–predator system with Holling type III functional response for predator and intra-specific competition among predators. We first discuss the optimal control problem as a Lagrangian problem with a linear quadratic control. Second, we consider an optimal control problem in the time-optimal control setting. We initially establish the existence of optimal controls for both these problems and later characterize these optimal controls using the Stochastic maximum principle. Further numerical simulations are performed based on stochastic forward-backward sweep methods for realizing the theoretical findings. The results obtained in these optimal control problems are discussed in the context of biological conservation and pest management.","PeriodicalId":34018,"journal":{"name":"Computational and Mathematical Biophysics","volume":"11 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42123428","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract 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.
{"title":"Derangement model of ligand-receptor binding","authors":"Mobolaji Williams","doi":"10.1515/cmb-2022-0137","DOIUrl":"https://doi.org/10.1515/cmb-2022-0137","url":null,"abstract":"Abstract 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.","PeriodicalId":34018,"journal":{"name":"Computational and Mathematical Biophysics","volume":"10 1","pages":"123 - 166"},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42739537","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Shraddha Ramdas Bandekar, Tanuja Das, Akhil Kumar Srivastav, Anuradha Yadav, Anuj Kumar, P. Srivastava, M. Ghosh
Abstract 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.
{"title":"Modeling and prediction of the third wave of COVID-19 spread in India","authors":"Shraddha Ramdas Bandekar, Tanuja Das, Akhil Kumar Srivastav, Anuradha Yadav, Anuj Kumar, P. Srivastava, M. Ghosh","doi":"10.1515/cmb-2022-0138","DOIUrl":"https://doi.org/10.1515/cmb-2022-0138","url":null,"abstract":"Abstract 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.","PeriodicalId":34018,"journal":{"name":"Computational and Mathematical Biophysics","volume":"10 1","pages":"231 - 248"},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47124730","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Bishal Chhetri, D. Vamsi, D. Prakash, S. Balasubramanian, C. Sanjeevi
Abstract 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.
{"title":"Age Structured Mathematical Modeling Studies on COVID-19 with respect to Combined Vaccination and Medical Treatment Strategies","authors":"Bishal Chhetri, D. Vamsi, D. Prakash, S. Balasubramanian, C. Sanjeevi","doi":"10.1515/cmb-2022-0143","DOIUrl":"https://doi.org/10.1515/cmb-2022-0143","url":null,"abstract":"Abstract 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.","PeriodicalId":34018,"journal":{"name":"Computational and Mathematical Biophysics","volume":"10 1","pages":"281 - 303"},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41439058","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract 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 C20. 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.
{"title":"Neighborhood hypergraph model for topological data analysis","authors":"Jian Liu, Dong Chen, Jingyan Li, Jie Wu","doi":"10.1515/cmb-2022-0142","DOIUrl":"https://doi.org/10.1515/cmb-2022-0142","url":null,"abstract":"Abstract 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 C20. 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.","PeriodicalId":34018,"journal":{"name":"Computational and Mathematical Biophysics","volume":"10 1","pages":"262 - 280"},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48095844","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract 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.
{"title":"Modeling, Analysis and Physics Informed Neural Network approaches for studying the dynamics of COVID-19 involving human-human and human-pathogen interaction","authors":"L. Nguyen, M. Raissi, P. Seshaiyer","doi":"10.1515/cmb-2022-0001","DOIUrl":"https://doi.org/10.1515/cmb-2022-0001","url":null,"abstract":"Abstract 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.","PeriodicalId":34018,"journal":{"name":"Computational and Mathematical Biophysics","volume":"10 1","pages":"1 - 17"},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41900512","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract 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.
{"title":"Evolutionary trend of SARS-CoV-2 inferred by the homopolymeric nucleotide repeats","authors":"Changchuan Yin","doi":"10.1515/cmb-2022-0135","DOIUrl":"https://doi.org/10.1515/cmb-2022-0135","url":null,"abstract":"Abstract 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.","PeriodicalId":34018,"journal":{"name":"Computational and Mathematical Biophysics","volume":"10 1","pages":"105 - 122"},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46338904","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract 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.
{"title":"A Mathematical Model for Blood Flow Accounting for the Hematological Disorders","authors":"A. Karthik, Panthagani Praveen Kumar, T. Radhika","doi":"10.1515/cmb-2022-0136","DOIUrl":"https://doi.org/10.1515/cmb-2022-0136","url":null,"abstract":"Abstract 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.","PeriodicalId":34018,"journal":{"name":"Computational and Mathematical Biophysics","volume":"10 1","pages":"184 - 198"},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47915921","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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