Pub Date : 2019-03-21DOI: 10.1142/S1793048019500024
P. Panja
In this paper, a cholera disease transmission mathematical model has been developed. According to the transmission mechanism of cholera disease, total human population has been classified into four subpopulations such as (i) Susceptible human, (ii) Exposed human, (iii) Infected human and (iv) Recovered human. Also, the total bacterial population has been classified into two subpopulations such as (i) Vibrio Cholerae that grows in the infected human intestine and (ii) Vibrio Cholerae in the environment. It is assumed that the cholera disease can be transmitted in a human population through the consumption of contaminated food and water by Vibrio Cholerae bacterium present in the environment. Also, it is assumed that Vibrio Cholerae bacterium is spread in the environment through the vomiting and feces of infected humans. Positivity and boundedness of solutions of our proposed system have been investigated. Equilibrium points and the basic reproduction number [Formula: see text] are evaluated. Local stability conditions of disease-free and endemic equilibrium points have been discussed. A sensitivity analysis has been carried out on the basic reproduction number [Formula: see text]. To eradicate cholera disease from the human population, an optimal control problem has been formulated and solved with the help of Pontryagin’s maximum principle. Here treatment, vaccination and awareness programs have been considered as control parameters to reduce the number of infected humans from cholera disease. Finally, the optimal control and the cost-effectiveness analysis of our proposed model have been performed numerically.
{"title":"Optimal Control Analysis of a Cholera Epidemic Model","authors":"P. Panja","doi":"10.1142/S1793048019500024","DOIUrl":"https://doi.org/10.1142/S1793048019500024","url":null,"abstract":"In this paper, a cholera disease transmission mathematical model has been developed. According to the transmission mechanism of cholera disease, total human population has been classified into four subpopulations such as (i) Susceptible human, (ii) Exposed human, (iii) Infected human and (iv) Recovered human. Also, the total bacterial population has been classified into two subpopulations such as (i) Vibrio Cholerae that grows in the infected human intestine and (ii) Vibrio Cholerae in the environment. It is assumed that the cholera disease can be transmitted in a human population through the consumption of contaminated food and water by Vibrio Cholerae bacterium present in the environment. Also, it is assumed that Vibrio Cholerae bacterium is spread in the environment through the vomiting and feces of infected humans. Positivity and boundedness of solutions of our proposed system have been investigated. Equilibrium points and the basic reproduction number [Formula: see text] are evaluated. Local stability conditions of disease-free and endemic equilibrium points have been discussed. A sensitivity analysis has been carried out on the basic reproduction number [Formula: see text]. To eradicate cholera disease from the human population, an optimal control problem has been formulated and solved with the help of Pontryagin’s maximum principle. Here treatment, vaccination and awareness programs have been considered as control parameters to reduce the number of infected humans from cholera disease. Finally, the optimal control and the cost-effectiveness analysis of our proposed model have been performed numerically.","PeriodicalId":88835,"journal":{"name":"Biophysical reviews and letters","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1142/S1793048019500024","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43588887","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 : 2018-12-19DOI: 10.1142/S1793048019200029
K. Zioutas, Edward Valachovic, M. Maroudas
In arXiv:1812.02482 Socas-Navarro (SN) provided multiple confirmation of the claimed ~88 days melanoma periodicity [4] (which remarkably coincides with the orbital period of Mercury). This greatly strengthens the observation by Zioutas & Valachovic (ZV). Here we comment on the work by SN, because it objects the interpretation of the observation by ZV. Notice that SN objection is based on serious assumptions, which were explicitly excluded by ZV. Further, the conclusion made with a sub-set of data (4%) is statistically not significant to dispute ZV. On the contrary, since the same periodicity appears also in other 8 major cancer types, we consider it as a global oscillatory behaviour of cancer. At this stage, such a rather ubiquitous cancer periodicity makes any discussion of a small subset of data at least secondarily. Further, we show here that the ~88 days Melanoma periodicity is not related to solar activity. Planetary lensing of streaming low speed invisible massive particles remains the only viable explanation, as it has been introduced previously with a number of physics observations [4]. We also show that planetary lensing of low speed particles cannot be considered in isolation, because of the dominating Sun’s gravity, at least for the inner planets. Interestingly, gravitational lensing / deflection favours low speed particles. In a recent paper [1], H. Socas-Navarro (SN) has re-evaluated part of the work “Planetary Dependence of Melanoma” by K. Zioutas and E. Valachovic (ZV) [2], using even 8 more datasets. Here we comment on the work by SN, starting with two, in our opinion, positive aspects: 1) a) SN derives a periodicity of 87.6 days (4.17/year), confirming the value of (87.4±0.76) days as it was observed for the first time by ZV in ref. [2]. Interestingly, this periodicity appears also in all 8 major cancer categories, which have been Fourier analysed by SN. Obviously, this is a diversified confirmation, which strengthens greatly the initial observation by ZV. b) Figure 2 of the work by SN [1] confirms previous observation of the 11 years oscillation of melanoma [3]. 2) SN makes an extensive introduction to dark matter and WIMPs, arriving to conclusions objecting the work by ZV, since “it is incompatible with the current WIMP paradigm” [1]. We wish to stress here that the physics part of the work by ZV is based on ref.[4]; SN has apparently overlooked this important reference, since it is clarified there already in the introduction [4]: “...we refer to generic dark candidate constituents as “invisible massive matter”, in order to distinguish them from ordinary dark matter.” In addition, the words ‘dark matter’ and ‘WIMPs’ are not mentioned at all by ZV, (see ref.[2]). In other words, the conclusions made by SN are based just on dark matter and WIMPs, which are excluded by ZV (and in ref. [4] too); i.e., the objections by SN are thus based on assumptions considered as inapplicable [2,4]. 3) Melanoma and race: SN uses throughout his wo
{"title":"Comment On the Connection Between Planets, Dark Matter and Cancer, by Hector Socas-Navarro (arXiv:1812.02482 [physics.med-ph])","authors":"K. Zioutas, Edward Valachovic, M. Maroudas","doi":"10.1142/S1793048019200029","DOIUrl":"https://doi.org/10.1142/S1793048019200029","url":null,"abstract":"In arXiv:1812.02482 Socas-Navarro (SN) provided multiple confirmation of the claimed ~88 days melanoma periodicity [4] (which remarkably coincides with the orbital period of Mercury). This greatly strengthens the observation by Zioutas & Valachovic (ZV). Here we comment on the work by SN, because it objects the interpretation of the observation by ZV. Notice that SN objection is based on serious assumptions, which were explicitly excluded by ZV. Further, the conclusion made with a sub-set of data (4%) is statistically not significant to dispute ZV. On the contrary, since the same periodicity appears also in other 8 major cancer types, we consider it as a global oscillatory behaviour of cancer. At this stage, such a rather ubiquitous cancer periodicity makes any discussion of a small subset of data at least secondarily. Further, we show here that the ~88 days Melanoma periodicity is not related to solar activity. Planetary lensing of streaming low speed invisible massive particles remains the only viable explanation, as it has been introduced previously with a number of physics observations [4]. We also show that planetary lensing of low speed particles cannot be considered in isolation, because of the dominating Sun’s gravity, at least for the inner planets. Interestingly, gravitational lensing / deflection favours low speed particles. In a recent paper [1], H. Socas-Navarro (SN) has re-evaluated part of the work “Planetary Dependence of Melanoma” by K. Zioutas and E. Valachovic (ZV) [2], using even 8 more datasets. Here we comment on the work by SN, starting with two, in our opinion, positive aspects: 1) a) SN derives a periodicity of 87.6 days (4.17/year), confirming the value of (87.4±0.76) days as it was observed for the first time by ZV in ref. [2]. Interestingly, this periodicity appears also in all 8 major cancer categories, which have been Fourier analysed by SN. Obviously, this is a diversified confirmation, which strengthens greatly the initial observation by ZV. b) Figure 2 of the work by SN [1] confirms previous observation of the 11 years oscillation of melanoma [3]. 2) SN makes an extensive introduction to dark matter and WIMPs, arriving to conclusions objecting the work by ZV, since “it is incompatible with the current WIMP paradigm” [1]. We wish to stress here that the physics part of the work by ZV is based on ref.[4]; SN has apparently overlooked this important reference, since it is clarified there already in the introduction [4]: “...we refer to generic dark candidate constituents as “invisible massive matter”, in order to distinguish them from ordinary dark matter.” In addition, the words ‘dark matter’ and ‘WIMPs’ are not mentioned at all by ZV, (see ref.[2]). In other words, the conclusions made by SN are based just on dark matter and WIMPs, which are excluded by ZV (and in ref. [4] too); i.e., the objections by SN are thus based on assumptions considered as inapplicable [2,4]. 3) Melanoma and race: SN uses throughout his wo","PeriodicalId":88835,"journal":{"name":"Biophysical reviews and letters","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1142/S1793048019200029","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64047295","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 : 2018-12-06DOI: 10.1142/S1793048019200017
H. Socas-Navarro
In a recent paper, Zioutas and Valachovic (2018) claim that dark matter is responsible for a significant fraction of the melanoma skin cancer. This conclusion is drawn from their observation of a significant correlation between skin melanoma incidence in the US and the inner planets positions (especially those of Mercury and Earth). Here, I present a number of objections to their interpretation. Some (but not all) of the counterarguments are based on the analysis of a larger dataset from the same source, considering more cancer types and separating by patient attributes, such as race. One of the counterarguments is that if the melanoma fluctuations with periods similar to planetary orbits were produced by dark matter density enhancements on Earth, then we would have to conclude that the black population is somehow immune to dark matter, a conclusion that seems incompatible with the current Weakly-Interacting Massive Particles (WIMP) paradigm. Interestingly, some periodicities are present in the data, including the ones reported by Zioutas and Valachovic, but I argue that they must have a societal rather than astronomical origin.
{"title":"On the Connection between Planets, Dark Matter and Cancer: Comment on “Planetary Dependence of Melanoma”","authors":"H. Socas-Navarro","doi":"10.1142/S1793048019200017","DOIUrl":"https://doi.org/10.1142/S1793048019200017","url":null,"abstract":"In a recent paper, Zioutas and Valachovic (2018) claim that dark matter is responsible for a significant fraction of the melanoma skin cancer. This conclusion is drawn from their observation of a significant correlation between skin melanoma incidence in the US and the inner planets positions (especially those of Mercury and Earth). Here, I present a number of objections to their interpretation. Some (but not all) of the counterarguments are based on the analysis of a larger dataset from the same source, considering more cancer types and separating by patient attributes, such as race. One of the counterarguments is that if the melanoma fluctuations with periods similar to planetary orbits were produced by dark matter density enhancements on Earth, then we would have to conclude that the black population is somehow immune to dark matter, a conclusion that seems incompatible with the current Weakly-Interacting Massive Particles (WIMP) paradigm. Interestingly, some periodicities are present in the data, including the ones reported by Zioutas and Valachovic, but I argue that they must have a societal rather than astronomical origin.","PeriodicalId":88835,"journal":{"name":"Biophysical reviews and letters","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1142/S1793048019200017","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44614790","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 : 2018-12-01DOI: 10.1142/s1793048018990011
{"title":"Author Index Volume 13 (2018)","authors":"","doi":"10.1142/s1793048018990011","DOIUrl":"https://doi.org/10.1142/s1793048018990011","url":null,"abstract":"","PeriodicalId":88835,"journal":{"name":"Biophysical reviews and letters","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1142/s1793048018990011","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41631057","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 : 2018-12-01DOI: 10.1142/S1793048018500108
P. Panja
In this paper, a fuzzy mathematical model has been developed by considering forest biomass, human population and technological effort for the conservation of forest biomass as separate compartments. We have assumed that the forest biomass and human population grows logistically. We have considered that forest biomass decreases due to industrialization, food, shelter, etc., for humans. For the conservation of forest biomass, some modern technological efforts have been used in this model. Also, time delay of use of modern technological effort for the conservation of forest biomass has been considered on forest biomass. According to the assumptions, a fuzzy mathematical model on forest biomass is formulated. Next we have determined different possible equilibrium points. Also, the stability of our proposed system around these equilibrium points has been discussed. Finally, some numerical simulation results have been presented for better understanding of our proposed mathematical model.
{"title":"Fuzzy Parameter Based Mathematical Model on Forest Biomass","authors":"P. Panja","doi":"10.1142/S1793048018500108","DOIUrl":"https://doi.org/10.1142/S1793048018500108","url":null,"abstract":"In this paper, a fuzzy mathematical model has been developed by considering forest biomass, human population and technological effort for the conservation of forest biomass as separate compartments. We have assumed that the forest biomass and human population grows logistically. We have considered that forest biomass decreases due to industrialization, food, shelter, etc., for humans. For the conservation of forest biomass, some modern technological efforts have been used in this model. Also, time delay of use of modern technological effort for the conservation of forest biomass has been considered on forest biomass. According to the assumptions, a fuzzy mathematical model on forest biomass is formulated. Next we have determined different possible equilibrium points. Also, the stability of our proposed system around these equilibrium points has been discussed. Finally, some numerical simulation results have been presented for better understanding of our proposed mathematical model.","PeriodicalId":88835,"journal":{"name":"Biophysical reviews and letters","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1142/S1793048018500108","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43667028","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 : 2018-12-01DOI: 10.1142/S1793048018300013
P. Biswas
Protein–ligand interactions act as a pivot to the understanding of most of the biological interactions. The study of interactions between proteins and cellular molecules has led to the establishment and identification of various important pathways that control biological systems. Investigators working in different fields of biological sciences have an intrinsic interest in this field and complement their findings by the application of different biophysical approaches and tools to quantify protein–ligand interactions that include protein–small molecules, protein–DNA, protein–RNA, protein–protein both in vitro and in vivo. In this paper, the various biophysical techniques that can be employed to study such interactions will be discussed. In addition to native gel electrophoresis and fluorescence-based methods, more details will be discussed, on the broad range of modern day biophysical tools such as Circular Dichroism, Fourier Transform Infrared (FTIR) Spectroscopy, Isothermal Titration Calorimetry, Analytical Ultracentrifugation, Surface Plasmon Resonance, Fluorescence Correlation Spectroscopy, Differential Scanning Fluorimetry, Nuclear Magnetic Resonance, Mass Spectroscopy, Single Molecule Spectroscopy, Dual Polarization Interferometry, Micro Scale Thermophoresis and Electro–switchable Biosensors that can be used to study the different aspects of protein–ligand interactions.
{"title":"Modern Biophysical Approaches to Study Protein–Ligand Interactions","authors":"P. Biswas","doi":"10.1142/S1793048018300013","DOIUrl":"https://doi.org/10.1142/S1793048018300013","url":null,"abstract":"Protein–ligand interactions act as a pivot to the understanding of most of the biological interactions. The study of interactions between proteins and cellular molecules has led to the establishment and identification of various important pathways that control biological systems. Investigators working in different fields of biological sciences have an intrinsic interest in this field and complement their findings by the application of different biophysical approaches and tools to quantify protein–ligand interactions that include protein–small molecules, protein–DNA, protein–RNA, protein–protein both in vitro and in vivo. In this paper, the various biophysical techniques that can be employed to study such interactions will be discussed. In addition to native gel electrophoresis and fluorescence-based methods, more details will be discussed, on the broad range of modern day biophysical tools such as Circular Dichroism, Fourier Transform Infrared (FTIR) Spectroscopy, Isothermal Titration Calorimetry, Analytical Ultracentrifugation, Surface Plasmon Resonance, Fluorescence Correlation Spectroscopy, Differential Scanning Fluorimetry, Nuclear Magnetic Resonance, Mass Spectroscopy, Single Molecule Spectroscopy, Dual Polarization Interferometry, Micro Scale Thermophoresis and Electro–switchable Biosensors that can be used to study the different aspects of protein–ligand interactions.","PeriodicalId":88835,"journal":{"name":"Biophysical reviews and letters","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1142/S1793048018300013","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47367924","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 : 2018-12-01DOI: 10.1142/S1793048018500091
Sudeshna Mondal, A. Maiti, G. Samanta
A field observation on a terrestrial vertebrate has shown that the fear of predators can affect the behavior of prey populations and it can greatly reduce their reproduction. On the other hand, it has been observed that providing additional food to the predator decreases the predatory attack rate and increases the growth rate of the predator. In this paper, we have investigated the dynamical behavior of a predator–prey model incorporating both the effects of fear and additional food. Positivity, uniform boundedness and extinction criteria of the system are studied. Equilibrium points and their stability behaviors are also discussed here. Existence of a Hopf-bifurcation is established by considering the level of fear as bifurcation parameter. The effect of time-delay is discussed, where the delay may be considered as gestation time of the predator. Numerical simulations are performed using MATLAB to verify our analytical findings.
{"title":"Effects of Fear and Additional Food in a Delayed Predator–Prey Model","authors":"Sudeshna Mondal, A. Maiti, G. Samanta","doi":"10.1142/S1793048018500091","DOIUrl":"https://doi.org/10.1142/S1793048018500091","url":null,"abstract":"A field observation on a terrestrial vertebrate has shown that the fear of predators can affect the behavior of prey populations and it can greatly reduce their reproduction. On the other hand, it has been observed that providing additional food to the predator decreases the predatory attack rate and increases the growth rate of the predator. In this paper, we have investigated the dynamical behavior of a predator–prey model incorporating both the effects of fear and additional food. Positivity, uniform boundedness and extinction criteria of the system are studied. Equilibrium points and their stability behaviors are also discussed here. Existence of a Hopf-bifurcation is established by considering the level of fear as bifurcation parameter. The effect of time-delay is discussed, where the delay may be considered as gestation time of the predator. Numerical simulations are performed using MATLAB to verify our analytical findings.","PeriodicalId":88835,"journal":{"name":"Biophysical reviews and letters","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1142/S1793048018500091","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48658955","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 : 2018-12-01DOI: 10.1142/S1793048018500121
Yusuke Shibasaki, C. Yoshida-Noro, Minoru Saito
We proposed a new mathematical model for biological segment formation based on the clock and wavefront mechanism suggested in 1970s. Here, we chose an invertebrate, Enchytraeus japonensis, as a model animal and adopted multiple-loop negative feedback system based on its physiological features. We numerically showed the segment number of the model animal is autopoietically controlled by a size-dependent function. Additionally, we discussed two cases of the irregular oscillations by applying the biological conditions for abnormal development. The present model showed robustness under local noise perturbations like many other biological oscillators and qualitatively described unique development of the model animal. As a result, we suggested that a global interaction of chemical signals in the body can also drive “segmentation clock”.
{"title":"A Size-Dependent Multiple-Loop Negative Feedback System Describes Biological Segment Formation Based on the Clock and Wavefront Mechanism","authors":"Yusuke Shibasaki, C. Yoshida-Noro, Minoru Saito","doi":"10.1142/S1793048018500121","DOIUrl":"https://doi.org/10.1142/S1793048018500121","url":null,"abstract":"We proposed a new mathematical model for biological segment formation based on the clock and wavefront mechanism suggested in 1970s. Here, we chose an invertebrate, Enchytraeus japonensis, as a model animal and adopted multiple-loop negative feedback system based on its physiological features. We numerically showed the segment number of the model animal is autopoietically controlled by a size-dependent function. Additionally, we discussed two cases of the irregular oscillations by applying the biological conditions for abnormal development. The present model showed robustness under local noise perturbations like many other biological oscillators and qualitatively described unique development of the model animal. As a result, we suggested that a global interaction of chemical signals in the body can also drive “segmentation clock”.","PeriodicalId":88835,"journal":{"name":"Biophysical reviews and letters","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1142/S1793048018500121","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48836139","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 : 2018-12-01DOI: 10.1142/S179304801850011X
Soovoojeet Jana, Samadyuti Haldar, D. Das, S. Nandi, T. K. Kar
This paper describes a prey–predator type ecological model with infection in the prey populations. We also consider here a nonlinear functional response for disease transmission and a constant amount of refuge for the sound prey populations. The dynamical behavior of the mathematical model is described from the point of view of stability and bifurcation. A geometric method is also applied to establish the global asymptotic stability at the co-existence equilibrium point. Some computer simulation works have been presented to illustrate the theoretical results.
{"title":"Modeling and Analysis of an Ecological System Incorporating Infection and Prey Refuge","authors":"Soovoojeet Jana, Samadyuti Haldar, D. Das, S. Nandi, T. K. Kar","doi":"10.1142/S179304801850011X","DOIUrl":"https://doi.org/10.1142/S179304801850011X","url":null,"abstract":"This paper describes a prey–predator type ecological model with infection in the prey populations. We also consider here a nonlinear functional response for disease transmission and a constant amount of refuge for the sound prey populations. The dynamical behavior of the mathematical model is described from the point of view of stability and bifurcation. A geometric method is also applied to establish the global asymptotic stability at the co-existence equilibrium point. Some computer simulation works have been presented to illustrate the theoretical results.","PeriodicalId":88835,"journal":{"name":"Biophysical reviews and letters","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1142/S179304801850011X","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45627425","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 : 2018-09-01DOI: 10.1142/S1793048018500066
Anjana P. Das, M. Pal
In this paper, we have proposed and analyzed an agricultural pest control system. For this purpose, an eco-epidemiological type predator–prey model has been proposed with the consideration of a sound predator population and two classes of pest populations namely susceptible pest and infected pest. Further to consider uncertainty, we modify our model and transform it into a fuzzy system with incorporation of imprecise parameters. The dynamical behavior of the proposed model has been investigated by examining the existence and stability criteria of all feasible equilibria. An optimal control problem is formed by considering the pesticide control as the control parameter and then the problem is solved both theoretically and numerically with the help of some computer simulation works.
{"title":"An Imprecise Eco-Epidemic Model with Pesticide in Relevance to Agricultural Pest Control","authors":"Anjana P. Das, M. Pal","doi":"10.1142/S1793048018500066","DOIUrl":"https://doi.org/10.1142/S1793048018500066","url":null,"abstract":"In this paper, we have proposed and analyzed an agricultural pest control system. For this purpose, an eco-epidemiological type predator–prey model has been proposed with the consideration of a sound predator population and two classes of pest populations namely susceptible pest and infected pest. Further to consider uncertainty, we modify our model and transform it into a fuzzy system with incorporation of imprecise parameters. The dynamical behavior of the proposed model has been investigated by examining the existence and stability criteria of all feasible equilibria. An optimal control problem is formed by considering the pesticide control as the control parameter and then the problem is solved both theoretically and numerically with the help of some computer simulation works.","PeriodicalId":88835,"journal":{"name":"Biophysical reviews and letters","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1142/S1793048018500066","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41999339","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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