Abstract This article presents a cost-effective optimal control analysis of interventions applied to a S2EI2RS type deterministic compartmental model of COVID-19, considering community awareness and immunity loss. We introduce two time-dependent controls, namely, home quarantine and treatment, to the model for defining an optimal control problem (OCP). In addition to some basic qualitative properties, we obtain the reproductive threshold R 0 {R}_{0} by using the next-generation method and see the impact of controls on it. We also investigate the effect of community awareness and waning immunity, when no controls are applied. The existence and characterization of optimal controls is proved to establish the optimality system, and the OCP is solved using the forward–backward sweep method. The results are simulated using MATLAB. Our comparative cost-effective analysis indicates that implementing both control strategies simultaneously, along with community awareness, is the most optimal and sustainable way to flatten COVID-19 curves in a short period of time than that of implementing single controls. This article offers valuable insights that can assist policymakers and public health experts in designing targeted and effective control measures for COVID-19 and future epidemics in the post-COVID era. Therefore, this piece of work could be a valuable contribution to the existing literature.
{"title":"Cost-effective optimal control analysis of a COVID-19 transmission model incorporating community awareness and waning immunity","authors":"Sonu Lamba, P. Srivastava","doi":"10.1515/cmb-2023-0154","DOIUrl":"https://doi.org/10.1515/cmb-2023-0154","url":null,"abstract":"Abstract This article presents a cost-effective optimal control analysis of interventions applied to a S2EI2RS type deterministic compartmental model of COVID-19, considering community awareness and immunity loss. We introduce two time-dependent controls, namely, home quarantine and treatment, to the model for defining an optimal control problem (OCP). In addition to some basic qualitative properties, we obtain the reproductive threshold R 0 {R}_{0} by using the next-generation method and see the impact of controls on it. We also investigate the effect of community awareness and waning immunity, when no controls are applied. The existence and characterization of optimal controls is proved to establish the optimality system, and the OCP is solved using the forward–backward sweep method. The results are simulated using MATLAB. Our comparative cost-effective analysis indicates that implementing both control strategies simultaneously, along with community awareness, is the most optimal and sustainable way to flatten COVID-19 curves in a short period of time than that of implementing single controls. This article offers valuable insights that can assist policymakers and public health experts in designing targeted and effective control measures for COVID-19 and future epidemics in the post-COVID era. Therefore, this piece of work could be a valuable contribution to the existing literature.","PeriodicalId":34018,"journal":{"name":"Computational and Mathematical Biophysics","volume":"11 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42493366","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 article, the behavior of an susceptible exposed infected recovered (SEIR) epidemic model with nonlinear incidence rate and Holling type II treatment function is presented and analyzed. Reproduction number of the model is calculated. Equilibrium points are determined. Disease-free equilibrium exists when R0 is below 1. Behavior of disease-free equilibrium is examined at R0 = 1. Endemic equilibrium exists when R0 crosses 1. Stability of both equilibrium points is investigated locally and globally. Simulation is provided to support the result.
{"title":"An SEIR model with modified saturated incidence rate and Holling type II treatment function","authors":"Shilpa Umdekar, P. Sharma, Shivram Sharma","doi":"10.1515/cmb-2022-0146","DOIUrl":"https://doi.org/10.1515/cmb-2022-0146","url":null,"abstract":"Abstract In this article, the behavior of an susceptible exposed infected recovered (SEIR) epidemic model with nonlinear incidence rate and Holling type II treatment function is presented and analyzed. Reproduction number of the model is calculated. Equilibrium points are determined. Disease-free equilibrium exists when R0 is below 1. Behavior of disease-free equilibrium is examined at R0 = 1. Endemic equilibrium exists when R0 crosses 1. Stability of both equilibrium points is investigated locally and globally. Simulation is provided to support the result.","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":"43845578","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 Switching mechanism is adopted by predator populations when they are provided with two types of prey: susceptible and infected. In this study, we propose a modification of an eco-epidemiological model with the predator switching mechanism. In the presence of switching behavior, the existence of steady states and their stability have been discussed. The qualitative changes in the proposed model have been observed by the existence of transcritical and Hopf bifurcation. Numerical simulations are performed to support our numerical findings. In the context of species’ survival when disease is present in the system, it gives some theoretical views for eco-managers to understand the dynamics.
{"title":"An eco-epidemiological model with predator switching behavior","authors":"Deepak Tripathi, Anuraj Singh","doi":"10.1515/cmb-2023-0101","DOIUrl":"https://doi.org/10.1515/cmb-2023-0101","url":null,"abstract":"Abstract Switching mechanism is adopted by predator populations when they are provided with two types of prey: susceptible and infected. In this study, we propose a modification of an eco-epidemiological model with the predator switching mechanism. In the presence of switching behavior, the existence of steady states and their stability have been discussed. The qualitative changes in the proposed model have been observed by the existence of transcritical and Hopf bifurcation. Numerical simulations are performed to support our numerical findings. In the context of species’ survival when disease is present in the system, it gives some theoretical views for eco-managers to understand the dynamics.","PeriodicalId":34018,"journal":{"name":"Computational and Mathematical Biophysics","volume":"293 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135445361","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 discusses a novel idea from cell therapy in which nanoparticles (NPs) are adsorbed on red blood cells (RBCs). RBCs serve as a drug carrier for NPs or nanodrugs adsorbed on the cell membrane of RBC. For the purpose of examination, Fe3O4 {{rm{Fe}}}_{3}{{rm{O}}}_{4} NPs are adsorbed on RBCs, collectively called NP-RBC complex. RBCs being a natural vascular carrier, have high transfusion rates and biocompatibility. This mathematical study provides a basis to attempt nanodrug delivery via RBCs, as carriers for nanodrugs, to the stenosed sites in an artery. The mathematical model is developed for an artery with stenosis and a catheter that regards the temperature and velocity of the NP-RBC complex. Catheter coated with the NP-RBC complex is inserted into the lumen of the stenosed artery. The mathematical problem is solved numerically using Bernstein polynomials. The physical features were discussed through graphs plotted using MATLAB. The influence of parameters such as volume fraction, radius of the NP-RBC complex in blood, and the thickness of the nanolayer on RBCs was studied. A noticeable outcome states that the nanolayer of optimum thickness about 50–40 nm is suitable for this purpose. Thus, this is an attempt to study the delivery of NPs adsorbed on the surface of RBCs to develop newfangled strategies in nanomedicine bearing high precision and efficiency.
摘要:本文讨论了纳米颗粒(NPs)吸附在红细胞(rbc)上的细胞治疗新思路。红细胞作为一种药物载体，吸附在红细胞细胞膜上的NPs或纳米药物。为了便于检测，Fe 3 O 4 {{rm{Fe}}}_{3}{{rm{O}}}_{4} NPs被吸附在红细胞上，统称为NP-RBC复合物。红细胞是一种天然的血管载体，具有较高的输血率和生物相容性。这项数学研究为尝试通过红细胞作为纳米药物的载体将纳米药物递送到动脉狭窄部位提供了基础。建立了考虑NP-RBC复合物的温度和速度的狭窄动脉和导管的数学模型。将涂有NP-RBC复合物的导管插入狭窄动脉的管腔。用伯恩斯坦多项式对数学问题进行了数值求解。利用MATLAB绘制图形，讨论了其物理特征。研究了血液中NP-RBC复合物的体积分数、半径、纳米层厚度等参数对红细胞的影响。一个值得注意的结果表明，最佳厚度约为50-40纳米的纳米层适合于此目的。因此，本研究旨在研究吸附在红细胞表面的NPs的递送，以开发高精度和高效率的纳米医学新策略。
{"title":"Study of nanolayer on red blood cells as drug carrier in an artery with stenosis","authors":"Bhawini Prasad","doi":"10.1515/cmb-2023-0103","DOIUrl":"https://doi.org/10.1515/cmb-2023-0103","url":null,"abstract":"Abstract This article discusses a novel idea from cell therapy in which nanoparticles (NPs) are adsorbed on red blood cells (RBCs). RBCs serve as a drug carrier for NPs or nanodrugs adsorbed on the cell membrane of RBC. For the purpose of examination, <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msub> <m:mrow> <m:mi mathvariant=\"normal\">Fe</m:mi> </m:mrow> <m:mrow> <m:mn>3</m:mn> </m:mrow> </m:msub> <m:msub> <m:mrow> <m:mi mathvariant=\"normal\">O</m:mi> </m:mrow> <m:mrow> <m:mn>4</m:mn> </m:mrow> </m:msub> </m:math> {{rm{Fe}}}_{3}{{rm{O}}}_{4} NPs are adsorbed on RBCs, collectively called NP-RBC complex. RBCs being a natural vascular carrier, have high transfusion rates and biocompatibility. This mathematical study provides a basis to attempt nanodrug delivery via RBCs, as carriers for nanodrugs, to the stenosed sites in an artery. The mathematical model is developed for an artery with stenosis and a catheter that regards the temperature and velocity of the NP-RBC complex. Catheter coated with the NP-RBC complex is inserted into the lumen of the stenosed artery. The mathematical problem is solved numerically using Bernstein polynomials. The physical features were discussed through graphs plotted using MATLAB. The influence of parameters such as volume fraction, radius of the NP-RBC complex in blood, and the thickness of the nanolayer on RBCs was studied. A noticeable outcome states that the nanolayer of optimum thickness about 50–40 nm is suitable for this purpose. Thus, this is an attempt to study the delivery of NPs adsorbed on the surface of RBCs to develop newfangled strategies in nanomedicine bearing high precision and efficiency.","PeriodicalId":34018,"journal":{"name":"Computational and Mathematical Biophysics","volume":"258 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135448941","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 fever is an infectious viral fever. The complex behavior of the virus within the body can be explained through mathematical models to understand the virus’s dynamics. We propose two different with-in host models of dengue virus transmission with humoral immune response. The proposed models differ from one another because one of the models assumes that newly formed viruses infect healthy cells again. To understand the dynamics of the proposed models, we perform a comparative study of stability analysis, numerical simulation, and sensitivity analysis. The basic reproduction number (BRN) of the two models is computed using next-generation matrix method. The local stability (l.s) analysis is discussed using the linearization method. The Lyapunov’s direct method is used to check the global stability (g.s) of the models. It has been found that both the equilibrium states for both the models, namely, virus-free equilibrium state and endemic equilibrium state, are globally stable, based on the value of BRN. Results show the influence of immune response on the cell dynamics and virus particles. The virus neutralization rate by antibodies and rate that affects the antibody growth are highly sensitive for the two models. Optimal control is applied to explore the possible control strategies to prevent virus spread in the host system. It is evident from the results that the strategy to administrate antibiotic drugs and home remedies slow down the virus spread in the host.
{"title":"Within-host models of dengue virus transmission with immune response","authors":"P. Muthu, Bikash Modak","doi":"10.1515/cmb-2022-0150","DOIUrl":"https://doi.org/10.1515/cmb-2022-0150","url":null,"abstract":"Abstract Dengue fever is an infectious viral fever. The complex behavior of the virus within the body can be explained through mathematical models to understand the virus’s dynamics. We propose two different with-in host models of dengue virus transmission with humoral immune response. The proposed models differ from one another because one of the models assumes that newly formed viruses infect healthy cells again. To understand the dynamics of the proposed models, we perform a comparative study of stability analysis, numerical simulation, and sensitivity analysis. The basic reproduction number (BRN) of the two models is computed using next-generation matrix method. The local stability (l.s) analysis is discussed using the linearization method. The Lyapunov’s direct method is used to check the global stability (g.s) of the models. It has been found that both the equilibrium states for both the models, namely, virus-free equilibrium state and endemic equilibrium state, are globally stable, based on the value of BRN. Results show the influence of immune response on the cell dynamics and virus particles. The virus neutralization rate by antibodies and rate that affects the antibody growth are highly sensitive for the two models. Optimal control is applied to explore the possible control strategies to prevent virus spread in the host system. It is evident from the results that the strategy to administrate antibiotic drugs and home remedies slow down the virus spread in the host.","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":"45059290","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 article, a nonlinear mathematical model is proposed and analyzed to study the spread of coronavirus disease (COVID-19) and its control. Due to sudden emergence of a peculiar kind of infection, no vaccines were available, and therefore, the nonpharmaceutical interventions such as lockdown, isolation, and hospitalization were imposed to stop spreading of the infectious disease. The proposed model consists of six dependent variables, namely, susceptible population, infective population, isolated susceptible population who are aware of the undesirable consequences of the COVID-19, quarantined population of known infectives (symptomatic), recovered class, and the coronavirus population. The model exhibits two equilibria namely, the COVID-19-free equilibrium and the COVID-19-endemic equilibrium. It is observed that if basic reproduction number R 0 < 1 {R}_{0}lt 1 , then the COVID-19-free equilibrium is locally asymptotically stable. However, the endemic equilibrium is locally as well as nonlinearly asymptotically stable under certain conditions if R 0 > 1 {R}_{0}gt 1 . Model analysis shows that if safety measures are adopted by way of isolation of susceptibles and quarantine of infectives, the spread of COVID-19 disease can be kept under control.
{"title":"A mathematical model to study the spread of COVID-19 and its control in India","authors":"R. Naresh, S. Sundar, S. Verma, J. B. Shukla","doi":"10.1515/cmb-2022-0149","DOIUrl":"https://doi.org/10.1515/cmb-2022-0149","url":null,"abstract":"Abstract In this article, a nonlinear mathematical model is proposed and analyzed to study the spread of coronavirus disease (COVID-19) and its control. Due to sudden emergence of a peculiar kind of infection, no vaccines were available, and therefore, the nonpharmaceutical interventions such as lockdown, isolation, and hospitalization were imposed to stop spreading of the infectious disease. The proposed model consists of six dependent variables, namely, susceptible population, infective population, isolated susceptible population who are aware of the undesirable consequences of the COVID-19, quarantined population of known infectives (symptomatic), recovered class, and the coronavirus population. The model exhibits two equilibria namely, the COVID-19-free equilibrium and the COVID-19-endemic equilibrium. It is observed that if basic reproduction number R 0 < 1 {R}_{0}lt 1 , then the COVID-19-free equilibrium is locally asymptotically stable. However, the endemic equilibrium is locally as well as nonlinearly asymptotically stable under certain conditions if R 0 > 1 {R}_{0}gt 1 . Model analysis shows that if safety measures are adopted by way of isolation of susceptibles and quarantine of infectives, the spread of COVID-19 disease can be kept under control.","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":"45979551","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 COVID-19 pandemic recently caused a huge impact on India, not only in terms of health but also in terms of economy. Understanding the spatio-temporal patterns of the disease spread is crucial for controlling the outbreak. In this study, we apply the compatible window-wise dynamic mode decomposition (CwDMD) and dynamic mode decomposition (DMD) techniques to the COVID-19 data of India to model the spatial-temporal patterns of the epidemic. We preprocess the COVID-19 data into weekly time-series at the state-level and apply both the CwDMD and DMD methods to decompose the data into a set of spatial-temporal modes. We identify the key modes that capture the dominant features of the COVID-19 spread in India and analyze their phase, magnitude, and frequency relationships to extract the temporal and spatial patterns. By incorporating rank truncation in each window, we have achieved greater control over the system’s output, leading to better results. Our results reveal that the COVID-19 outbreak in India is driven by a complex interplay of regional, demographic, and environmental factors. We identify several key modes that capture the patterns of disease spread in different regions and over time, including seasonal fluctuations, demographic trends, and localized outbreaks. Overall, our study provides valuable insights into the patterns of the COVID-19 outbreak in India using both CwDMD and DMD methods. These findings can help public health organizations to develop more effective strategies for controlling the spread of the pandemic. The CwDMD and DMD methods can be applied to other countries to identify the unique drivers of the outbreak and develop effective control strategies.
{"title":"Application of dynamic mode decomposition and compatible window-wise dynamic mode decomposition in deciphering COVID-19 dynamics of India","authors":"Kanav Singh Rana, Nitu Kumari","doi":"10.1515/cmb-2022-0152","DOIUrl":"https://doi.org/10.1515/cmb-2022-0152","url":null,"abstract":"Abstract The COVID-19 pandemic recently caused a huge impact on India, not only in terms of health but also in terms of economy. Understanding the spatio-temporal patterns of the disease spread is crucial for controlling the outbreak. In this study, we apply the compatible window-wise dynamic mode decomposition (CwDMD) and dynamic mode decomposition (DMD) techniques to the COVID-19 data of India to model the spatial-temporal patterns of the epidemic. We preprocess the COVID-19 data into weekly time-series at the state-level and apply both the CwDMD and DMD methods to decompose the data into a set of spatial-temporal modes. We identify the key modes that capture the dominant features of the COVID-19 spread in India and analyze their phase, magnitude, and frequency relationships to extract the temporal and spatial patterns. By incorporating rank truncation in each window, we have achieved greater control over the system’s output, leading to better results. Our results reveal that the COVID-19 outbreak in India is driven by a complex interplay of regional, demographic, and environmental factors. We identify several key modes that capture the patterns of disease spread in different regions and over time, including seasonal fluctuations, demographic trends, and localized outbreaks. Overall, our study provides valuable insights into the patterns of the COVID-19 outbreak in India using both CwDMD and DMD methods. These findings can help public health organizations to develop more effective strategies for controlling the spread of the pandemic. The CwDMD and DMD methods can be applied to other countries to identify the unique drivers of the outbreak and develop effective control strategies.","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":"43841175","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 It is now known that early government interventions in pandemic management helps in slowing down the pandemic in the initial phase, during which a conservative basic reproduction number can be maintained. There have been several ways to evaluate these early response strategies for COVID-19 during its outbreak globally in 2020. As a novelty, we evaluate them through the lens of patient recovery logistics. Here, we use a data-driven approach of recovery analysis in a case study of Singapore during January 22–April 01, 2020, which is effectively the analysis of length-of-stay in the government healthcare facility, National Center for Infectious Diseases. We propose the use of a data-driven method involving periodization, statistical analysis, regression models, and epidemiological models. We demonstrate that the estimates of reproduction number in Singapore shows variation in different age groups and periods, indicating the success of early intervention strategy in the initial transmission stages of the pandemic.
{"title":"Evaluating early pandemic response through length-of-stay analysis of case logs and epidemiological modeling: A case study of Singapore in early 2020","authors":"Jaya Sreevalsan-Nair, Anuj Mubayi, Janvi Chhabra, Reddy Rani Vangimalla, Pritesh Rajesh Ghogale","doi":"10.1515/cmb-2023-0104","DOIUrl":"https://doi.org/10.1515/cmb-2023-0104","url":null,"abstract":"Abstract It is now known that early government interventions in pandemic management helps in slowing down the pandemic in the initial phase, during which a conservative basic reproduction number can be maintained. There have been several ways to evaluate these early response strategies for COVID-19 during its outbreak globally in 2020. As a novelty, we evaluate them through the lens of patient recovery logistics. Here, we use a data-driven approach of recovery analysis in a case study of Singapore during January 22–April 01, 2020, which is effectively the analysis of length-of-stay in the government healthcare facility, National Center for Infectious Diseases. We propose the use of a data-driven method involving periodization, statistical analysis, regression models, and epidemiological models. We demonstrate that the estimates of reproduction number in Singapore shows variation in different age groups and periods, indicating the success of early intervention strategy in the initial transmission stages of the pandemic.","PeriodicalId":34018,"journal":{"name":"Computational and Mathematical Biophysics","volume":"39 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135705153","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}
Rachana Pathak, A. S. Bhadauria, M. Chaudhary, Harendra Verma, P. Mathur, Manju R. Agrawal, Ram Singh
Abstract Ecotourism is a form of tourism involving responsible travel to natural areas, conserving the environment, and improving the well-being of the local people. Its purpose may be to educate the traveler, to provide funds for ecological censervation, to directly benifit the economic development, and political empowerment of local communities. Ecotourism has come up as an important conservation strategy in the tropical areas where diversity of species and habitats are threatened because of the traditional forms of development. This study deals with a non-linear mathematical model with a novel idea for sustainable development of biomass with ecotourism which is imperative in the present scenario. Stability and bifurcation analysis of the model is done and it is observed from our study that the system predicts unstability and exhibits bifurcation if ecotourism goes beyond a threshold value.
{"title":"Role of ecotourism in conserving forest biomass: A mathematical model","authors":"Rachana Pathak, A. S. Bhadauria, M. Chaudhary, Harendra Verma, P. Mathur, Manju R. Agrawal, Ram Singh","doi":"10.1515/cmb-2022-0153","DOIUrl":"https://doi.org/10.1515/cmb-2022-0153","url":null,"abstract":"Abstract Ecotourism is a form of tourism involving responsible travel to natural areas, conserving the environment, and improving the well-being of the local people. Its purpose may be to educate the traveler, to provide funds for ecological censervation, to directly benifit the economic development, and political empowerment of local communities. Ecotourism has come up as an important conservation strategy in the tropical areas where diversity of species and habitats are threatened because of the traditional forms of development. This study deals with a non-linear mathematical model with a novel idea for sustainable development of biomass with ecotourism which is imperative in the present scenario. Stability and bifurcation analysis of the model is done and it is observed from our study that the system predicts unstability and exhibits bifurcation if ecotourism goes beyond a threshold value.","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":"43503613","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 declaration of a nationwide lockdown in India led to millions of migrant workers, particularly from Uttar Pradesh (UP) and Bihar, returning to their home states without proper transportation and social distancing from cities such as Delhi, Mumbai, and Hyderabad. This unforeseen migration and social mixing accelerated the transmission of diseases across the country. To analyze the impact of reverse migration on disease progression, we have developed a disease transmission model for the neighboring Indian states of Delhi and UP. The model’s essential mathematical properties, including positivity, boundedness, equilibrium points (EPs), and their linear stability, as well as computation of the basic reproduction number ( R 0 ) left({R}_{0}) , are studied. The mathematical analysis reveals that the model with active reverse migration cannot reach a disease-free equilibrium, indicating that the failure of restrictive mobility intervention caused by reverse migration kept the disease propagation alive. Further, PRCC analysis highlights the need for effective home isolation, better disease detection techniques, and medical interventions to curb the spread. The study estimates a significantly shorter doubling time for exponential growth of the disease in both regions. In addition, the occurrence of synchronous patterns between epidemic trajectories of the Delhi and UP regions accentuates the severe implications of migrant plight on UP’s already fragile rural health infrastructure. By using COVID-19 incidence data, we quantify key epidemiological parameters, and our scenario analyses demonstrate how different lockdown plans might have impacted disease prevalence. Based on our observations, the transmission rate has the most significant impact on COVID-19 cases. This case study exemplifies the importance of carefully considering these issues before implementing lockdowns and social isolation throughout the country to combat future outbreaks.
{"title":"Impact of cross border reverse migration in Delhi–UP region of India during COVID-19 lockdown","authors":"Shubhangi Dwivedi, Saravana Perumal, Sumit Kumar, Samit Bhattacharyya, Nitu Kumari","doi":"10.1515/cmb-2022-0151","DOIUrl":"https://doi.org/10.1515/cmb-2022-0151","url":null,"abstract":"Abstract The declaration of a nationwide lockdown in India led to millions of migrant workers, particularly from Uttar Pradesh (UP) and Bihar, returning to their home states without proper transportation and social distancing from cities such as Delhi, Mumbai, and Hyderabad. This unforeseen migration and social mixing accelerated the transmission of diseases across the country. To analyze the impact of reverse migration on disease progression, we have developed a disease transmission model for the neighboring Indian states of Delhi and UP. The model’s essential mathematical properties, including positivity, boundedness, equilibrium points (EPs), and their linear stability, as well as computation of the basic reproduction number ( R 0 ) left({R}_{0}) , are studied. The mathematical analysis reveals that the model with active reverse migration cannot reach a disease-free equilibrium, indicating that the failure of restrictive mobility intervention caused by reverse migration kept the disease propagation alive. Further, PRCC analysis highlights the need for effective home isolation, better disease detection techniques, and medical interventions to curb the spread. The study estimates a significantly shorter doubling time for exponential growth of the disease in both regions. In addition, the occurrence of synchronous patterns between epidemic trajectories of the Delhi and UP regions accentuates the severe implications of migrant plight on UP’s already fragile rural health infrastructure. By using COVID-19 incidence data, we quantify key epidemiological parameters, and our scenario analyses demonstrate how different lockdown plans might have impacted disease prevalence. Based on our observations, the transmission rate has the most significant impact on COVID-19 cases. This case study exemplifies the importance of carefully considering these issues before implementing lockdowns and social isolation throughout the country to combat future outbreaks.","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":"47509907","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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