Abstract Additional food provided prey-predator systems have become a significant and important area of study for both theoretical and experimental ecologists. This is mainly because provision of additional food to the predator in the prey-predator systems has proven to facilitate wildlife conservation as well as reduction of pesticides in agriculture. Further, the mathematical modeling and analysis of these systems provide the eco-manager with various strategies that can be implemented on field to achieve the desired objectives. The outcomes of many theoretical and mathematical studies of such additional food systems have shown that the quality and quantity of additional food play a crucial role in driving the system to the desired state. However, one of the limitations of these studies is that they are asymptotic in nature, where the desired state is reached eventually with time. To overcome these limitations, we present a time optimal control study for an additional food provided prey-predator system involving inhibitory effect with quantity of additional food as the control parameter with the objective of reaching the desired state in finite (minimum) time. The results show that the optimal solution is a bang-bang control with a possibility of multiple switches. Numerical examples illustrate the theoretical findings. These results can be applied to both biological conservation and pest eradication.
{"title":"An Optimal Control Study with Quantity of Additional food as Control in Prey-Predator Systems involving Inhibitory Effect","authors":"V. Ananth, D. Vamsi","doi":"10.1515/cmb-2020-0121","DOIUrl":"https://doi.org/10.1515/cmb-2020-0121","url":null,"abstract":"Abstract Additional food provided prey-predator systems have become a significant and important area of study for both theoretical and experimental ecologists. This is mainly because provision of additional food to the predator in the prey-predator systems has proven to facilitate wildlife conservation as well as reduction of pesticides in agriculture. Further, the mathematical modeling and analysis of these systems provide the eco-manager with various strategies that can be implemented on field to achieve the desired objectives. The outcomes of many theoretical and mathematical studies of such additional food systems have shown that the quality and quantity of additional food play a crucial role in driving the system to the desired state. However, one of the limitations of these studies is that they are asymptotic in nature, where the desired state is reached eventually with time. To overcome these limitations, we present a time optimal control study for an additional food provided prey-predator system involving inhibitory effect with quantity of additional food as the control parameter with the objective of reaching the desired state in finite (minimum) time. The results show that the optimal solution is a bang-bang control with a possibility of multiple switches. Numerical examples illustrate the theoretical findings. These results can be applied to both biological conservation and pest eradication.","PeriodicalId":34018,"journal":{"name":"Computational and Mathematical Biophysics","volume":"9 1","pages":"114 - 145"},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42844015","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}
Pub Date : 2021-01-01DOI: 10.1101/2021.01.25.428122
C. Ramana
Abstract Type I interferons (IFN α/β) play a central role in innate immunity to respiratory viruses, including coronaviruses. In this study, transcription factor profiling in the transcriptome was used to gain novel insights into the role of inducible transcription factors in response to type I interferon signaling in immune cells and in lung epithelial cells after SARS-CoV-2 infection. Modeling the interferon-inducible transcription factor mRNA data in terms of distinct sub-networks based on biological functions such as antiviral response, immune modulation, and cell growth revealed enrichment of specific transcription factors in mouse and human immune cells. Interrogation of multiple microarray datasets revealed that SARS-CoV-2 induced high levels of IFN-beta and interferon-inducible transcription factor mRNA in human lung epithelial cells. Transcription factor mRNA of the three sub-networks were differentially regulated in human lung epithelial cell lines after SARS-CoV-2 infection and in COVID-19 patients. A subset of type I interferon-inducible transcription factors and inflammatory mediators were specifically enriched in the lungs and neutrophils of Covid-19 patients. The emerging complex picture of type I IFN transcriptional regulation consists of a rapid transcriptional switch mediated by the Jak-Stat cascade and a graded output of the inducible transcription factor activation that enables temporal regulation of gene expression.
{"title":"Profiling transcription factor sub-networks in type I interferon signaling and in response to SARS-CoV-2 infection","authors":"C. Ramana","doi":"10.1101/2021.01.25.428122","DOIUrl":"https://doi.org/10.1101/2021.01.25.428122","url":null,"abstract":"Abstract Type I interferons (IFN α/β) play a central role in innate immunity to respiratory viruses, including coronaviruses. In this study, transcription factor profiling in the transcriptome was used to gain novel insights into the role of inducible transcription factors in response to type I interferon signaling in immune cells and in lung epithelial cells after SARS-CoV-2 infection. Modeling the interferon-inducible transcription factor mRNA data in terms of distinct sub-networks based on biological functions such as antiviral response, immune modulation, and cell growth revealed enrichment of specific transcription factors in mouse and human immune cells. Interrogation of multiple microarray datasets revealed that SARS-CoV-2 induced high levels of IFN-beta and interferon-inducible transcription factor mRNA in human lung epithelial cells. Transcription factor mRNA of the three sub-networks were differentially regulated in human lung epithelial cell lines after SARS-CoV-2 infection and in COVID-19 patients. A subset of type I interferon-inducible transcription factors and inflammatory mediators were specifically enriched in the lungs and neutrophils of Covid-19 patients. The emerging complex picture of type I IFN transcriptional regulation consists of a rapid transcriptional switch mediated by the Jak-Stat cascade and a graded output of the inducible transcription factor activation that enables temporal regulation of gene expression.","PeriodicalId":34018,"journal":{"name":"Computational and Mathematical Biophysics","volume":"9 1","pages":"273 - 288"},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42360479","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}
Pub Date : 2021-01-01DOI: 10.1101/2021.02.25.432861
R. Penner
Abstract Tools developed by Moderna, BioNTech/Pfizer, and Oxford/Astrazeneca, among others, provide universal solutions to previously problematic aspects of drug or vaccine delivery, uptake and toxicity, portending new tools across the medical sciences. A novel method is presented based on estimating protein backbone free energy via geometry to predict effective antiviral targets, antigens and vaccine cargos that are resistant to viral mutation. This method is reviewed and reformulated in light of the recent proliferation of structural data on the SARS-CoV-2 spike glycoprotein and its mutations in multiple lineages. Key findings include: collections of mutagenic residues reoccur across strains, suggesting cooperative convergent evolution; most mutagenic residues do not participate in backbone hydrogen bonds; metastability of the glyco-protein limits the change of free energy through mutation thereby constraining selective pressure; and there are mRNA or virus-vector cargos targeting low free energy peptides proximal to conserved high free energy peptides providing specific recipes for vaccines with greater specificity than the full-spike approach. These results serve to limit peptides in the spike glycoprotein with high mutagenic potential and thereby provide a priori constraints on viral and attendant vaccine evolution. Scientific and regulatory challenges to nucleic acid therapeutic and vaccine development and deployment are finally discussed.
{"title":"Antiviral Resistance against Viral Mutation: Praxis and Policy for SARS-CoV-2","authors":"R. Penner","doi":"10.1101/2021.02.25.432861","DOIUrl":"https://doi.org/10.1101/2021.02.25.432861","url":null,"abstract":"Abstract Tools developed by Moderna, BioNTech/Pfizer, and Oxford/Astrazeneca, among others, provide universal solutions to previously problematic aspects of drug or vaccine delivery, uptake and toxicity, portending new tools across the medical sciences. A novel method is presented based on estimating protein backbone free energy via geometry to predict effective antiviral targets, antigens and vaccine cargos that are resistant to viral mutation. This method is reviewed and reformulated in light of the recent proliferation of structural data on the SARS-CoV-2 spike glycoprotein and its mutations in multiple lineages. Key findings include: collections of mutagenic residues reoccur across strains, suggesting cooperative convergent evolution; most mutagenic residues do not participate in backbone hydrogen bonds; metastability of the glyco-protein limits the change of free energy through mutation thereby constraining selective pressure; and there are mRNA or virus-vector cargos targeting low free energy peptides proximal to conserved high free energy peptides providing specific recipes for vaccines with greater specificity than the full-spike approach. These results serve to limit peptides in the spike glycoprotein with high mutagenic potential and thereby provide a priori constraints on viral and attendant vaccine evolution. Scientific and regulatory challenges to nucleic acid therapeutic and vaccine development and deployment are finally discussed.","PeriodicalId":34018,"journal":{"name":"Computational and Mathematical Biophysics","volume":"9 1","pages":"81 - 89"},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42125607","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, V. Bhagat, Swapna Muthusamy, V. Ananth, D. Vamsi, C. Sanjeevi
Abstract COVID -19 pandemic has resulted in more than 257 million infections and 5.15 million deaths worldwide. Several drug interventions targeting multiple stages of the pathogenesis of COVID -19 can significantly reduce induced infection and thus mortality. In this study, we first develop SIV model at within-host level by incorporating the intercellular time delay and analyzing the stability of equilibrium points. The model dynamics admits a disease-free equilibrium and an infected equilibrium with their stability based on the value of the basic reproduction number R0. We then formulate an optimal control problem with antiviral drugs and second-line drugs as control measures and study their roles in reducing the number of infected cells and viral load. The comparative study conducted in the optimal control problem suggests that if the first-line antiviral drugs show adverse effects, considering these drugs in reduced amounts along with the second-line drugs would be very effective in reducing the number of infected cells and viral load in a COVID-19 infected patient. Later, we formulate a time-optimal control problem with the goal of driving the system from any initial state to the desired infection-free equilibrium state in finite minimal time. Using Pontryagin’s Minimum Principle, it is shown that the optimal control strategy is of the bang-bang type, with the possibility of switching between two extreme values of the optimal controls. Numerically, it is shown that the desired infection-free state is achieved in a shorter time when the higher values of the optimal controls. The results of this study may be very helpful to researchers, epidemiologists, clinicians and physicians working in this field.
{"title":"Time Optimal Control Studies on COVID-19 Incorporating Adverse Events of the Antiviral Drugs","authors":"Bishal Chhetri, V. Bhagat, Swapna Muthusamy, V. Ananth, D. Vamsi, C. Sanjeevi","doi":"10.1515/cmb-2020-0125","DOIUrl":"https://doi.org/10.1515/cmb-2020-0125","url":null,"abstract":"Abstract COVID -19 pandemic has resulted in more than 257 million infections and 5.15 million deaths worldwide. Several drug interventions targeting multiple stages of the pathogenesis of COVID -19 can significantly reduce induced infection and thus mortality. In this study, we first develop SIV model at within-host level by incorporating the intercellular time delay and analyzing the stability of equilibrium points. The model dynamics admits a disease-free equilibrium and an infected equilibrium with their stability based on the value of the basic reproduction number R0. We then formulate an optimal control problem with antiviral drugs and second-line drugs as control measures and study their roles in reducing the number of infected cells and viral load. The comparative study conducted in the optimal control problem suggests that if the first-line antiviral drugs show adverse effects, considering these drugs in reduced amounts along with the second-line drugs would be very effective in reducing the number of infected cells and viral load in a COVID-19 infected patient. Later, we formulate a time-optimal control problem with the goal of driving the system from any initial state to the desired infection-free equilibrium state in finite minimal time. Using Pontryagin’s Minimum Principle, it is shown that the optimal control strategy is of the bang-bang type, with the possibility of switching between two extreme values of the optimal controls. Numerically, it is shown that the desired infection-free state is achieved in a shorter time when the higher values of the optimal controls. The results of this study may be very helpful to researchers, epidemiologists, clinicians and physicians working in this field.","PeriodicalId":34018,"journal":{"name":"Computational and Mathematical Biophysics","volume":"9 1","pages":"214 - 241"},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41648567","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 Background. Unfortunately, the COVID-19 pandemic is still far from stabilizing. Of particular concern is the sharp increase in the number of diseases in June-July, September-October 2020 and February-March 2021. The causes and consequences of this sharp increase in the number of cases are still waiting for their researchers, but there is already an urgent need to assess the possible duration of the pandemic, the expected number of patients and deaths. Correct simulation of the infectious disease dynamics needs complicated mathematical models and many efforts for unknown parameters identification. Constant changes in the pandemic conditions (in particular, the peculiarities of quarantine and its violation, situations with testing and isolation of patients) cause various epidemic waves, lead to changes in the parameter values of the mathematical models. Objective. In this article, pandemic waves in Ukraine will be detected, calculated and discussed. The estimations for durations and final sizes of the epidemic waves will be presented. Methods. We propose a simple method for the epidemic waves detection based on the differentiation of the smoothed number of cases. We use the generalized SIR (susceptible-infected-removed) model for the dynamics of the epidemic waves. The known exact solution of the SIR differential equations and statistical approach were used. We will use different data sets for accumulated number of cases in order to compare the results of simulations and predictions. Results. Nine pandemic waves were detected in Ukraine and corresponding optimal values of the SIR model parameters were identified. The number of cases and the number of patients spreading the infection versus time were calculated. In particular, the pandemic in Ukraine probably began in January 2020. If current trends continue, the end of the pandemic should be expected no earlier than in summer 2021. Conclusions. The differentiation of the smoothed number of cases, the SIR model and statistical approach to the parameter identification are helpful to select COVID-19 pandemic waves and make some reliable estimations and predictions. The obtained information will be useful to regulate the quarantine activities, to predict the medical and economic consequences of the pandemic.
{"title":"Detections and SIR simulations of the COVID-19 pandemic waves in Ukraine","authors":"I. Nesteruk","doi":"10.1515/cmb-2020-0117","DOIUrl":"https://doi.org/10.1515/cmb-2020-0117","url":null,"abstract":"Abstract Background. Unfortunately, the COVID-19 pandemic is still far from stabilizing. Of particular concern is the sharp increase in the number of diseases in June-July, September-October 2020 and February-March 2021. The causes and consequences of this sharp increase in the number of cases are still waiting for their researchers, but there is already an urgent need to assess the possible duration of the pandemic, the expected number of patients and deaths. Correct simulation of the infectious disease dynamics needs complicated mathematical models and many efforts for unknown parameters identification. Constant changes in the pandemic conditions (in particular, the peculiarities of quarantine and its violation, situations with testing and isolation of patients) cause various epidemic waves, lead to changes in the parameter values of the mathematical models. Objective. In this article, pandemic waves in Ukraine will be detected, calculated and discussed. The estimations for durations and final sizes of the epidemic waves will be presented. Methods. We propose a simple method for the epidemic waves detection based on the differentiation of the smoothed number of cases. We use the generalized SIR (susceptible-infected-removed) model for the dynamics of the epidemic waves. The known exact solution of the SIR differential equations and statistical approach were used. We will use different data sets for accumulated number of cases in order to compare the results of simulations and predictions. Results. Nine pandemic waves were detected in Ukraine and corresponding optimal values of the SIR model parameters were identified. The number of cases and the number of patients spreading the infection versus time were calculated. In particular, the pandemic in Ukraine probably began in January 2020. If current trends continue, the end of the pandemic should be expected no earlier than in summer 2021. Conclusions. The differentiation of the smoothed number of cases, the SIR model and statistical approach to the parameter identification are helpful to select COVID-19 pandemic waves and make some reliable estimations and predictions. The obtained information will be useful to regulate the quarantine activities, to predict the medical and economic consequences of the pandemic.","PeriodicalId":34018,"journal":{"name":"Computational and Mathematical Biophysics","volume":"9 1","pages":"46 - 65"},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/cmb-2020-0117","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43201691","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 Dengue is the most common mosquito-borne viral infection transmitted disease. It is due to the four types of viruses (DENV-1, DENV-2, DENV-3, DENV-4), which transmit through the bite of infected Aedes aegypti and Aedes albopictus female mosquitoes during the daytime. The first globally commercialized vaccine is Dengvaxia, also known as the CYD-TDV vaccine, manufactured by Sanofi Pasteur. This paper presents a Ross-type epidemic model to describe the vaccine interaction between humans and mosquitoes using an entomological mosquito growth population and constant human population. After establishing the basic reproduction number ℛ0, we present three control strategies: vaccination, vector control, and the combination of vaccination and vector control. We use Pontryagin’s minimum principle to characterize optimal control and apply numerical simulations to determine which strategies best suit each compartment. Results show that vector control requires shorter time applications in minimizing mosquito populations. Whereas vaccinating the primary susceptible human population requires a shorter time compared to the secondary susceptible human.
{"title":"Optimal Control of a Dengue-Dengvaxia Model: Comparison Between Vaccination and Vector Control","authors":"Cheryl Q. Mentuda","doi":"10.1515/cmb-2020-0124","DOIUrl":"https://doi.org/10.1515/cmb-2020-0124","url":null,"abstract":"Abstract Dengue is the most common mosquito-borne viral infection transmitted disease. It is due to the four types of viruses (DENV-1, DENV-2, DENV-3, DENV-4), which transmit through the bite of infected Aedes aegypti and Aedes albopictus female mosquitoes during the daytime. The first globally commercialized vaccine is Dengvaxia, also known as the CYD-TDV vaccine, manufactured by Sanofi Pasteur. This paper presents a Ross-type epidemic model to describe the vaccine interaction between humans and mosquitoes using an entomological mosquito growth population and constant human population. After establishing the basic reproduction number ℛ0, we present three control strategies: vaccination, vector control, and the combination of vaccination and vector control. We use Pontryagin’s minimum principle to characterize optimal control and apply numerical simulations to determine which strategies best suit each compartment. Results show that vector control requires shorter time applications in minimizing mosquito populations. Whereas vaccinating the primary susceptible human population requires a shorter time compared to the secondary susceptible human.","PeriodicalId":34018,"journal":{"name":"Computational and Mathematical Biophysics","volume":"9 1","pages":"198 - 213"},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47300940","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 The rapid and surprised emergence of COVID-19, having infected three million and killed two hundred thousand people worldwide in less than five months, has led many experts to focus on simulating its propagation dynamics in order to have an estimated outlook for the not too distante future and so supporting the local and national governments in making decisions. In this paper, we apply the SIR model to simulating the propagation dynamics of COVID-19 on the Cape Verde Islands. It will be done firstly for Santiago and Boavista Islands, and then for Cape Verde in general. The choice of Santiago rests on the fact that it is the largest island, with more than 50% of the Population of the country, whereas Boavista was chosen because it is the island where the first case of COVID-19 in Cape Verde was diagnosed. Observations made after the date of the simulations were carried out corroborate our projections.
{"title":"Modeling COVID-19 in Cape Verde Islands - An application of SIR model","authors":"A. da Silva","doi":"10.1515/cmb-2020-0114","DOIUrl":"https://doi.org/10.1515/cmb-2020-0114","url":null,"abstract":"Abstract The rapid and surprised emergence of COVID-19, having infected three million and killed two hundred thousand people worldwide in less than five months, has led many experts to focus on simulating its propagation dynamics in order to have an estimated outlook for the not too distante future and so supporting the local and national governments in making decisions. In this paper, we apply the SIR model to simulating the propagation dynamics of COVID-19 on the Cape Verde Islands. It will be done firstly for Santiago and Boavista Islands, and then for Cape Verde in general. The choice of Santiago rests on the fact that it is the largest island, with more than 50% of the Population of the country, whereas Boavista was chosen because it is the island where the first case of COVID-19 in Cape Verde was diagnosed. Observations made after the date of the simulations were carried out corroborate our projections.","PeriodicalId":34018,"journal":{"name":"Computational and Mathematical Biophysics","volume":"9 1","pages":"1 - 13"},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/cmb-2020-0114","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44004295","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}
Randy L. Caga-anan, M. Raza, Grace Shelda G. Labrador, E. Metillo, P. Castillo, Y. Mammeri
Abstract A mathematical model of COVID-19 with a delay-term for the vaccinated compartment is developed. It has parameters accounting for vaccine-induced immunity delay, vaccine effectiveness, vaccination rate, and vaccine-induced immunity duration. The model parameters before vaccination are calibrated with the Philippines’ confirmed cases. Simulations show that vaccination has a significant effect in reducing future infections, with the vaccination rate being the dominant determining factor of the level of reduction. Moreover, depending on the vaccination rate and the vaccine-induced immunity duration, the system could reach a disease-free state but could not attain herd immunity. Simulations are also done to compare the effects of the various available vaccines. Results show that Pfizer-BioNTech has the most promising effect while Sinovac has the worst result relative to the others.
{"title":"Effect of Vaccination to COVID-19 Disease Progression and Herd Immunity","authors":"Randy L. Caga-anan, M. Raza, Grace Shelda G. Labrador, E. Metillo, P. Castillo, Y. Mammeri","doi":"10.1515/cmb-2020-0127","DOIUrl":"https://doi.org/10.1515/cmb-2020-0127","url":null,"abstract":"Abstract A mathematical model of COVID-19 with a delay-term for the vaccinated compartment is developed. It has parameters accounting for vaccine-induced immunity delay, vaccine effectiveness, vaccination rate, and vaccine-induced immunity duration. The model parameters before vaccination are calibrated with the Philippines’ confirmed cases. Simulations show that vaccination has a significant effect in reducing future infections, with the vaccination rate being the dominant determining factor of the level of reduction. Moreover, depending on the vaccination rate and the vaccine-induced immunity duration, the system could reach a disease-free state but could not attain herd immunity. Simulations are also done to compare the effects of the various available vaccines. Results show that Pfizer-BioNTech has the most promising effect while Sinovac has the worst result relative to the others.","PeriodicalId":34018,"journal":{"name":"Computational and Mathematical Biophysics","volume":"9 1","pages":"262 - 272"},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42501026","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 Fear of predation plays an important role in the growth of a prey species in a prey-predator system. In this work, a two-species model is formulated where the prey species move in a herd to protect themselves and so it acts as a defense strategy. The birth rate of the prey here is affected due to fear of being attacked by predators and so, is considered as a decreasing function. Moreover, there is another fear term in the death rate of the prey population to emphasize the fact that the prey may die out of fear of predator too. But, in this model, the function characterizing the fear effect in the death of prey is assumed in such a way that it is increased only up to a certain level. The results show that the system performs oscillating behavior when the fear coefficient implemented in the birth of prey is considered in a small amount but it changes its dynamics through Hopf bifurcation and becomes stable for a higher value of the coefficient. Regulating the fear terms ultimately makes an impact on the growth of the predator population as the predator is taken as a specialist predator here. The increasing value of the fear terms (either implemented in birth or death of prey) decrease the count of the predator population with time. Also, the fear implemented in the birth rate of prey makes a higher impact on the growth of the predator population than in the case of the fear-induced death rate.
{"title":"Impact of fear in a prey-predator system with herd behaviour","authors":"Sangeeta Saha, G. Samanta","doi":"10.1515/cmb-2020-0123","DOIUrl":"https://doi.org/10.1515/cmb-2020-0123","url":null,"abstract":"Abstract Fear of predation plays an important role in the growth of a prey species in a prey-predator system. In this work, a two-species model is formulated where the prey species move in a herd to protect themselves and so it acts as a defense strategy. The birth rate of the prey here is affected due to fear of being attacked by predators and so, is considered as a decreasing function. Moreover, there is another fear term in the death rate of the prey population to emphasize the fact that the prey may die out of fear of predator too. But, in this model, the function characterizing the fear effect in the death of prey is assumed in such a way that it is increased only up to a certain level. The results show that the system performs oscillating behavior when the fear coefficient implemented in the birth of prey is considered in a small amount but it changes its dynamics through Hopf bifurcation and becomes stable for a higher value of the coefficient. Regulating the fear terms ultimately makes an impact on the growth of the predator population as the predator is taken as a specialist predator here. The increasing value of the fear terms (either implemented in birth or death of prey) decrease the count of the predator population with time. Also, the fear implemented in the birth rate of prey makes a higher impact on the growth of the predator population than in the case of the fear-induced death rate.","PeriodicalId":34018,"journal":{"name":"Computational and Mathematical Biophysics","volume":"9 1","pages":"175 - 197"},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42625687","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. Prakash, Bishal Chhetri, D. Vamsi, S. Balasubramanian, C. Sanjeevi
Abstract The dynamics of COVID-19 in India are captured using a set of delay differential equations by dividing a population into five compartments. The Positivity and Boundedness of the system is shown. The Existence and Uniqueness condition for the solution of system of equations is presented. The equilibrium points are calculated and stability analysis is performed. Sensitivity analysis is performed on the parameters of the model. Bifurcation analysis is performed and the critical delay is calculated. By formulating the spread parameter as a function of temperature, the impact of temperature on the population is studied. We concluded that with the decrease in temperature, the average infections in the population increases. In view of the coming winter season in India, there will be an increase in new infections. This model falls in line with the characteristics that increase in isolation delay increases average infections in the population.
{"title":"Low temperatures or high isolation delay increases the average COVID-19 infections in India : A Mathematical modeling approach","authors":"D. Prakash, Bishal Chhetri, D. Vamsi, S. Balasubramanian, C. Sanjeevi","doi":"10.1515/cmb-2020-0122","DOIUrl":"https://doi.org/10.1515/cmb-2020-0122","url":null,"abstract":"Abstract The dynamics of COVID-19 in India are captured using a set of delay differential equations by dividing a population into five compartments. The Positivity and Boundedness of the system is shown. The Existence and Uniqueness condition for the solution of system of equations is presented. The equilibrium points are calculated and stability analysis is performed. Sensitivity analysis is performed on the parameters of the model. Bifurcation analysis is performed and the critical delay is calculated. By formulating the spread parameter as a function of temperature, the impact of temperature on the population is studied. We concluded that with the decrease in temperature, the average infections in the population increases. In view of the coming winter season in India, there will be an increase in new infections. This model falls in line with the characteristics that increase in isolation delay increases average infections in the population.","PeriodicalId":34018,"journal":{"name":"Computational and Mathematical Biophysics","volume":"9 1","pages":"146 - 174"},"PeriodicalIF":0.0,"publicationDate":"2020-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42330475","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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