Pub Date : 2022-12-31DOI: 10.1142/s0218339023500031
A. Misra, A. Yadav
In this research work, a nonlinear mathematical model is proposed and analyzed to study the adverse effects of insects on agricultural productivity by controlling the insect population using insecticides. In the model formulation, it is assumed that agricultural crops grow logistically and the growth rate of insects wholly depends on agricultural crops with Holling type-II functional response. It is further assumed that insects uptake insecticides; thus, the amount of insecticides decreases at a rate proportional to its amount and the density of insect population, and the growth rate of insect population decrease in the same proportion. The feasibility of all non-negative equilibria and their stability properties are discussed. Stability analysis specifies that agricultural crop consumption rate destabilizes the system; however, the spraying rate of insecticides stabilizes the system. The conditions for the existence of pitchfork and Hopf-bifurcation are derived. Considering the spraying rate of insecticides as time-dependent, we have also discussed the optimal control strategy to minimize both insect density and the associated cost. The numerical simulation validates the analytical findings.
{"title":"MODELING THE EFFECTS OF INSECTICIDES ON CROP PRODUCTION IN THE PRESENCE OF INSECT POPULATION","authors":"A. Misra, A. Yadav","doi":"10.1142/s0218339023500031","DOIUrl":"https://doi.org/10.1142/s0218339023500031","url":null,"abstract":"In this research work, a nonlinear mathematical model is proposed and analyzed to study the adverse effects of insects on agricultural productivity by controlling the insect population using insecticides. In the model formulation, it is assumed that agricultural crops grow logistically and the growth rate of insects wholly depends on agricultural crops with Holling type-II functional response. It is further assumed that insects uptake insecticides; thus, the amount of insecticides decreases at a rate proportional to its amount and the density of insect population, and the growth rate of insect population decrease in the same proportion. The feasibility of all non-negative equilibria and their stability properties are discussed. Stability analysis specifies that agricultural crop consumption rate destabilizes the system; however, the spraying rate of insecticides stabilizes the system. The conditions for the existence of pitchfork and Hopf-bifurcation are derived. Considering the spraying rate of insecticides as time-dependent, we have also discussed the optimal control strategy to minimize both insect density and the associated cost. The numerical simulation validates the analytical findings.","PeriodicalId":54872,"journal":{"name":"Journal of Biological Systems","volume":" ","pages":""},"PeriodicalIF":1.6,"publicationDate":"2022-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42899326","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-12-31DOI: 10.1142/s0218339023500079
F. Al Basir, Sudip Samanta, P. Tiwari
Introduction of biopesticides and predators in the crop fields has a crucial impact on the pest management as the biopesticides induce infection among the pest population and the infected pests are easy to be captured by the predators. In this paper, we investigate a mathematical model for a pest management system with farming awareness-based inclusion of predators and biopesticides. The level of awareness among the farmers is assumed to grow at a constant rate besides its growth due to an increase in the pest population in the crop field. The proposed model is analyzed mathematically for the feasibility and stability of the equilibrium points; existence of Hopf bifurcation together with direction and stability of the bifurcating periodic solutions are discussed; sufficient conditions are derived for which the system does not exhibit any periodic solution. Our simulation results show that the activeness of farmers for employing biopesticides in the crop field potentially suppresses the oscillations and brings forth stability in the system. Further, we observe that the system showcases the appearances of Generalized Hopf bifurcation, Zero-Hopf bifurcation, transcritical bifurcation and bistability. Overall, our findings manifest that by imparting knowledge among the farmers regarding the use of biopesticides and predators in the crop fields, the pest population can be effectively controlled.
{"title":"BISTABILITY, GENERALIZED AND ZERO-HOPF BIFURCATIONS IN A PEST CONTROL MODEL WITH FARMING AWARENESS","authors":"F. Al Basir, Sudip Samanta, P. Tiwari","doi":"10.1142/s0218339023500079","DOIUrl":"https://doi.org/10.1142/s0218339023500079","url":null,"abstract":"Introduction of biopesticides and predators in the crop fields has a crucial impact on the pest management as the biopesticides induce infection among the pest population and the infected pests are easy to be captured by the predators. In this paper, we investigate a mathematical model for a pest management system with farming awareness-based inclusion of predators and biopesticides. The level of awareness among the farmers is assumed to grow at a constant rate besides its growth due to an increase in the pest population in the crop field. The proposed model is analyzed mathematically for the feasibility and stability of the equilibrium points; existence of Hopf bifurcation together with direction and stability of the bifurcating periodic solutions are discussed; sufficient conditions are derived for which the system does not exhibit any periodic solution. Our simulation results show that the activeness of farmers for employing biopesticides in the crop field potentially suppresses the oscillations and brings forth stability in the system. Further, we observe that the system showcases the appearances of Generalized Hopf bifurcation, Zero-Hopf bifurcation, transcritical bifurcation and bistability. Overall, our findings manifest that by imparting knowledge among the farmers regarding the use of biopesticides and predators in the crop fields, the pest population can be effectively controlled.","PeriodicalId":54872,"journal":{"name":"Journal of Biological Systems","volume":"1 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2022-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41329590","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-12-31DOI: 10.1142/s0218339023500055
Torikul Islam Palash, M. R. Kaysir, Md Jahirul Islam, Sabiha Aziz, Taskia Nadriba Mimma, N. Akther
In recent days, the number of cancer cases is escalating promptly around the world. In general, conventional ablation methods, encompassing comprehensive drawbacks, are employed to cure cancer. At present, photo thermal therapy (PTT) is showing great promise to the treatment of cancer. However, the effective implementation of this technology is utmost challenging as several parameters affect the tumor surroundings. In this work, the effects of different parameters on the performance of PTT have been thoroughly investigated by considering a realistic model of human tissue underneath the skin using a finite element solver, COMSOL Multiphysics. Two different conditions, with and without considering gold nanoparticles at tumor site, are investigated where a laser beam is used as a source of energy. Fluence rate, temperature distribution, and thermal damage are highlighted in this work. It is observed that by utilizing a miniature needle with integrated waveguide and gold nanoparticles, a tumor can be effectively eradicated along with assuaging the conventional drawbacks of PTT. This study would also be useful for designing operative PTT for different parts of human tissue.
{"title":"IN-SILICO PERFORMANCE INVESTIGATION OF NANOPARTICLE-ASSISTED PHOTO THERMAL ABLATION","authors":"Torikul Islam Palash, M. R. Kaysir, Md Jahirul Islam, Sabiha Aziz, Taskia Nadriba Mimma, N. Akther","doi":"10.1142/s0218339023500055","DOIUrl":"https://doi.org/10.1142/s0218339023500055","url":null,"abstract":"In recent days, the number of cancer cases is escalating promptly around the world. In general, conventional ablation methods, encompassing comprehensive drawbacks, are employed to cure cancer. At present, photo thermal therapy (PTT) is showing great promise to the treatment of cancer. However, the effective implementation of this technology is utmost challenging as several parameters affect the tumor surroundings. In this work, the effects of different parameters on the performance of PTT have been thoroughly investigated by considering a realistic model of human tissue underneath the skin using a finite element solver, COMSOL Multiphysics. Two different conditions, with and without considering gold nanoparticles at tumor site, are investigated where a laser beam is used as a source of energy. Fluence rate, temperature distribution, and thermal damage are highlighted in this work. It is observed that by utilizing a miniature needle with integrated waveguide and gold nanoparticles, a tumor can be effectively eradicated along with assuaging the conventional drawbacks of PTT. This study would also be useful for designing operative PTT for different parts of human tissue.","PeriodicalId":54872,"journal":{"name":"Journal of Biological Systems","volume":" ","pages":""},"PeriodicalIF":1.6,"publicationDate":"2022-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45971479","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-12-01DOI: 10.1142/s0218339022500322
K. D. Prasad, S. K. Sasmal
Predator–prey interactions are the ubiquitous and natural phenomenon in an ecological system. Predators reduce the prey population’s density by direct killing, which is an essential part of any ecological system. Based on the experimental works, for overcoming predation pressure, prey uses a variety of mechanisms. With Holling type-II functional response, we examined a prey–predator system incorporating anti-predator behavior and the cost of fear into prey. Prey anti-predator activity is a counterattacking strategy in which adult prey targets adolescent predators in order to counteract the potential predation pressure. Fear of predation may disrupt the physiological state of prey species and lead to long loss of prey species. In this study, we investigated this aspect to use a dynamical modeling approach. This research finds a plethora of fascinating phenomena. The studied system exhibits a wide range of dynamics and bifurcations, including saddle-node, Hopf, homoclinic, and a Bogdanov–Takens bifurcation in co-dimension two are among the dynamics and bifurcations observed in the analyzed system. We performed some numerical simulations to investigate the effects of anti-predator behavior and fear on prey and found both affect the prey–predator dynamics significantly. Our numerical examples clearly show that as prey carrying capacity increases, so does the prey’s ability to perceive the risk of predation.
{"title":"DYNAMICS OF ANTI-PREDATOR BEHAVIOR AND EFFECT OF FEAR ON PREY–PREDATOR MODEL","authors":"K. D. Prasad, S. K. Sasmal","doi":"10.1142/s0218339022500322","DOIUrl":"https://doi.org/10.1142/s0218339022500322","url":null,"abstract":"Predator–prey interactions are the ubiquitous and natural phenomenon in an ecological system. Predators reduce the prey population’s density by direct killing, which is an essential part of any ecological system. Based on the experimental works, for overcoming predation pressure, prey uses a variety of mechanisms. With Holling type-II functional response, we examined a prey–predator system incorporating anti-predator behavior and the cost of fear into prey. Prey anti-predator activity is a counterattacking strategy in which adult prey targets adolescent predators in order to counteract the potential predation pressure. Fear of predation may disrupt the physiological state of prey species and lead to long loss of prey species. In this study, we investigated this aspect to use a dynamical modeling approach. This research finds a plethora of fascinating phenomena. The studied system exhibits a wide range of dynamics and bifurcations, including saddle-node, Hopf, homoclinic, and a Bogdanov–Takens bifurcation in co-dimension two are among the dynamics and bifurcations observed in the analyzed system. We performed some numerical simulations to investigate the effects of anti-predator behavior and fear on prey and found both affect the prey–predator dynamics significantly. Our numerical examples clearly show that as prey carrying capacity increases, so does the prey’s ability to perceive the risk of predation.","PeriodicalId":54872,"journal":{"name":"Journal of Biological Systems","volume":" ","pages":""},"PeriodicalIF":1.6,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46658816","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-11-22DOI: 10.1142/s0218339022500334
Joydeb Bhattacharyya, Anal Chatterjee
There is a global decline in marine fish abundance due to unsustainable harvesting. An effective harvesting policy can protect the overfished population from possible extinction. In this study, we used a mathematical model characterized by density-dependent refuge protection for herbivorous fish, exhibiting an anti-predator response in presence of a generalist invasive fish. The anti-predator behavior entails predator density-dependent reduced fecundity of the herbivorous fish. The model assumes a continuous threshold harvesting policy (CTHP) for the herbivorous fish and uses the catch-per-unit-effort (CPUE) hypothesis for harvesting the invasive fish. The CTHP allows harvesting of the herbivorous fish only when the density of the herbivorous fish exceeds a specified threshold value, thus ensuring the long-term sustainability of the herbivorous fish stock. The existence and stability of steady-state solutions and the bifurcations of the model are investigated. Our study reveals that the level of apprehension of the herbivorous fish and fishing efforts will play a significant role in the stability of the system. We examine the existence of the bionomic equilibrium and then study the dynamic optimization of the harvesting policy by employing Pontryagin’s maximum principle. We discuss different subsidies and tax policies for the effective management of a sustainable fishery. We use numerical simulations to compare the revenues corresponding to the harvest policies based on maximum sustainable yield (MSY), maximum economic yield (MEY), and optimal sustainable yield (OSY) for inferring an ecologically sustainable and economically viable harvesting policy.
{"title":"DYNAMICS OF A FISHERY MODEL WITH CONTINUOUS THRESHOLD HARVESTING POLICY AND ITS LEVERAGE FOR CONSERVATION AND MANAGEMENT","authors":"Joydeb Bhattacharyya, Anal Chatterjee","doi":"10.1142/s0218339022500334","DOIUrl":"https://doi.org/10.1142/s0218339022500334","url":null,"abstract":"There is a global decline in marine fish abundance due to unsustainable harvesting. An effective harvesting policy can protect the overfished population from possible extinction. In this study, we used a mathematical model characterized by density-dependent refuge protection for herbivorous fish, exhibiting an anti-predator response in presence of a generalist invasive fish. The anti-predator behavior entails predator density-dependent reduced fecundity of the herbivorous fish. The model assumes a continuous threshold harvesting policy (CTHP) for the herbivorous fish and uses the catch-per-unit-effort (CPUE) hypothesis for harvesting the invasive fish. The CTHP allows harvesting of the herbivorous fish only when the density of the herbivorous fish exceeds a specified threshold value, thus ensuring the long-term sustainability of the herbivorous fish stock. The existence and stability of steady-state solutions and the bifurcations of the model are investigated. Our study reveals that the level of apprehension of the herbivorous fish and fishing efforts will play a significant role in the stability of the system. We examine the existence of the bionomic equilibrium and then study the dynamic optimization of the harvesting policy by employing Pontryagin’s maximum principle. We discuss different subsidies and tax policies for the effective management of a sustainable fishery. We use numerical simulations to compare the revenues corresponding to the harvest policies based on maximum sustainable yield (MSY), maximum economic yield (MEY), and optimal sustainable yield (OSY) for inferring an ecologically sustainable and economically viable harvesting policy.","PeriodicalId":54872,"journal":{"name":"Journal of Biological Systems","volume":" ","pages":""},"PeriodicalIF":1.6,"publicationDate":"2022-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45310684","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-11-10DOI: 10.1142/s0218339022500346
P. Tiwari, Subarna Roy, G. Douglas, A. Misra
In this study, we investigate the effects of excessive inputs of bioavailable phosphorus into a lake from agricultural fields and households on algal bloom formation, and its potential management by using the lanthanum-modified clay Phoslock as a bioavailable phosphorus adsorbent. We also investigate the impact of time delay involved in the process of applying Phoslock after measuring the density of algal biomass in the lake. Moreover, the seasonal effects in the input of bioavailable phosphorus from the agricultural lands and the application rate of Phoslock have been investigated. Our simulation results show that the algal growth accelerates if the bioavailable phosphorus is excessively loaded through agricultural runoff and domestic discharges. However, algal biomass can be effectively controlled by employing Phoslock in a sufficiently large quantity. Further, we find that a delay in the application of Phoslock induces limit cycle oscillations. Furthermore, our findings show that the combined actions of delay and periodicity in the application of Phoslock bring forth dynamical complexity in the lake system by giving rise to higher periodic solutions and bursting patterns. Lastly, we investigate an optimal control problem to estimate the optimum dosage of Phoslock for the mitigation of algal biomass from the lake system.
{"title":"AN OPTIMAL CONTROL MODEL FOR THE IMPACT OF PHOSLOCK ON THE MITIGATION OF ALGAL BIOMASS IN LAKES","authors":"P. Tiwari, Subarna Roy, G. Douglas, A. Misra","doi":"10.1142/s0218339022500346","DOIUrl":"https://doi.org/10.1142/s0218339022500346","url":null,"abstract":"In this study, we investigate the effects of excessive inputs of bioavailable phosphorus into a lake from agricultural fields and households on algal bloom formation, and its potential management by using the lanthanum-modified clay Phoslock as a bioavailable phosphorus adsorbent. We also investigate the impact of time delay involved in the process of applying Phoslock after measuring the density of algal biomass in the lake. Moreover, the seasonal effects in the input of bioavailable phosphorus from the agricultural lands and the application rate of Phoslock have been investigated. Our simulation results show that the algal growth accelerates if the bioavailable phosphorus is excessively loaded through agricultural runoff and domestic discharges. However, algal biomass can be effectively controlled by employing Phoslock in a sufficiently large quantity. Further, we find that a delay in the application of Phoslock induces limit cycle oscillations. Furthermore, our findings show that the combined actions of delay and periodicity in the application of Phoslock bring forth dynamical complexity in the lake system by giving rise to higher periodic solutions and bursting patterns. Lastly, we investigate an optimal control problem to estimate the optimum dosage of Phoslock for the mitigation of algal biomass from the lake system.","PeriodicalId":54872,"journal":{"name":"Journal of Biological Systems","volume":" ","pages":""},"PeriodicalIF":1.6,"publicationDate":"2022-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46220219","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-11-04DOI: 10.1142/s0218339022500255
Qing Guo, Chuanjun Dai, Lijun Wang, He Liu, Yi Wang, Jianbing Li, Min Zhao
In this paper, a stochastic nutrient–plankton model with seasonal fluctuation was developed to investigate how seasonality and environmental noise affect the dynamics of aquatic ecosystems. First, the survival analysis of plankton was proposed. Then, by using Lyapunov function and Khasminskii’s theory for periodic Markov processes, we derive the sufficient conditions for the existence of positive periodic solution. The numerical simulations were carried out to provide a better understanding of the model, and the results indicate that seasonal fluctuation is beneficial to the coexistence of plankton species.
{"title":"STOCHASTIC PERIODIC SOLUTION OF A NUTRIENT–PLANKTON MODEL WITH SEASONAL FLUCTUATION","authors":"Qing Guo, Chuanjun Dai, Lijun Wang, He Liu, Yi Wang, Jianbing Li, Min Zhao","doi":"10.1142/s0218339022500255","DOIUrl":"https://doi.org/10.1142/s0218339022500255","url":null,"abstract":"In this paper, a stochastic nutrient–plankton model with seasonal fluctuation was developed to investigate how seasonality and environmental noise affect the dynamics of aquatic ecosystems. First, the survival analysis of plankton was proposed. Then, by using Lyapunov function and Khasminskii’s theory for periodic Markov processes, we derive the sufficient conditions for the existence of positive periodic solution. The numerical simulations were carried out to provide a better understanding of the model, and the results indicate that seasonal fluctuation is beneficial to the coexistence of plankton species.","PeriodicalId":54872,"journal":{"name":"Journal of Biological Systems","volume":" ","pages":""},"PeriodicalIF":1.6,"publicationDate":"2022-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41483350","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-11-04DOI: 10.1142/s0218339022500279
I. Elbaz, H. EL-METWALLY, M. Sohaly
The extinction and the persistence of the population of the harmful sheep blowfly (Lucilia cuprina) are discussed in this paper through a stochastic mathematical model. Using appropriate Lyapunov functionals, the extinction of these flies depends on the time to oviposition and the time between generations. The oviposition period must be sufficiently short. Another species of blowfly, called Lucilia sericata, also attacks sheep in many areas. Both blowflies are ectoparasites of warm-blooded vertebrates, particularly domestic sheep. These two blowflies are related to sharing the same mitochondrial DNA sequences, although the two species are distinct. A sufficiently small egg-laying delay then leads to the rapid extinction of both blowfly populations.
{"title":"DYNAMICS OF DELAYED NICHOLSON’S BLOWFLIES MODELS","authors":"I. Elbaz, H. EL-METWALLY, M. Sohaly","doi":"10.1142/s0218339022500279","DOIUrl":"https://doi.org/10.1142/s0218339022500279","url":null,"abstract":"The extinction and the persistence of the population of the harmful sheep blowfly (Lucilia cuprina) are discussed in this paper through a stochastic mathematical model. Using appropriate Lyapunov functionals, the extinction of these flies depends on the time to oviposition and the time between generations. The oviposition period must be sufficiently short. Another species of blowfly, called Lucilia sericata, also attacks sheep in many areas. Both blowflies are ectoparasites of warm-blooded vertebrates, particularly domestic sheep. These two blowflies are related to sharing the same mitochondrial DNA sequences, although the two species are distinct. A sufficiently small egg-laying delay then leads to the rapid extinction of both blowfly populations.","PeriodicalId":54872,"journal":{"name":"Journal of Biological Systems","volume":" ","pages":""},"PeriodicalIF":1.6,"publicationDate":"2022-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44447188","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-11-04DOI: 10.1142/s0218339022500267
L. Bouzid, O. Belhamiti, F. Belgacem
In this paper, we propose a new dynamical system model pertaining to Dengue transmission, and investigate its consequent morphology. We present and study various ramifications of our mathematical model for Dengue spread, encapsulated in a spatio-temporal differential system made of reaction–diffusion equations. Diffusion terms are incorporated into the said model by using specific derivations for infected mosquitoes, and infected humans, as well. Moreover, mechanisms for the nearest neighbor(s) infections are integrated into the model. Furthermore, using adaptive multigrid finite difference with decoupling and quasi-linearization techniques, we investigate two main factors for Dengue spatial propagation. We determine the effects of temperature variations, and the mobility of infectious agents, be they mosquitoes or humans. Finally, the proposed model-based analytico-numerical results are obtained, and rendered in graphical profiles, which show the major role the climate temperature and the mobility of infected humans have on the spread and speed of the disease. The consequent proposed model outcomes and health-based ramifications are then raised, discussed, and then validated.
{"title":"EFFECT OF HUMAN MOBILITY ON PREDICTIVE SPATIO-TEMPORAL MODEL OF DENGUE EPIDEMIC TRANSMISSION","authors":"L. Bouzid, O. Belhamiti, F. Belgacem","doi":"10.1142/s0218339022500267","DOIUrl":"https://doi.org/10.1142/s0218339022500267","url":null,"abstract":"In this paper, we propose a new dynamical system model pertaining to Dengue transmission, and investigate its consequent morphology. We present and study various ramifications of our mathematical model for Dengue spread, encapsulated in a spatio-temporal differential system made of reaction–diffusion equations. Diffusion terms are incorporated into the said model by using specific derivations for infected mosquitoes, and infected humans, as well. Moreover, mechanisms for the nearest neighbor(s) infections are integrated into the model. Furthermore, using adaptive multigrid finite difference with decoupling and quasi-linearization techniques, we investigate two main factors for Dengue spatial propagation. We determine the effects of temperature variations, and the mobility of infectious agents, be they mosquitoes or humans. Finally, the proposed model-based analytico-numerical results are obtained, and rendered in graphical profiles, which show the major role the climate temperature and the mobility of infected humans have on the spread and speed of the disease. The consequent proposed model outcomes and health-based ramifications are then raised, discussed, and then validated.","PeriodicalId":54872,"journal":{"name":"Journal of Biological Systems","volume":" ","pages":""},"PeriodicalIF":1.6,"publicationDate":"2022-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42660629","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-10-29DOI: 10.1142/s0218339022500310
R. Viriyapong, N. Thammawong
In this study, we propose a deterministic model describing the dynamics of anthrax transmission in animals. It is assumed in the model that anthrax is contracted when susceptible animal comes into contact with infected animals, infected carcasses or the spores of Bacillus anthracis. Conditions for disease-free and endemic equilibria are derived and the basic reproduction number ([Formula: see text]) is computed. The disease-free equilibrium is stable when [Formula: see text] and the disease will be eliminated. If [Formula: see text], the disease persists, therefore, the endemic equilibrium is globally stable. Further, we extend our model by applying optimal control problem in which vaccination for susceptible animals and sanitation are control variables to minimize the anthrax transmission. We study three strategies to investigate the impact of the controls. Our numerical results demonstrate that both vaccination and sanitation help minimizing the transmission although vaccination alone gives more significant impact than sanitation alone. However, the combination of both controls gives the best result in wiping out the anthrax transmission overall. Further, cost-effectiveness analysis shows that the most effective strategy to control anthrax disease is a combination of vaccination and sanitation of the infected areas, therefore these two interventions should be encouraged.
{"title":"GLOBAL DYNAMICS, OPTIMAL CONTROL AND COST-EFFECTIVENESS ANALYSIS FOR ANTHRAX TRANSMISSION MODEL IN ANIMAL POPULATIONS WITH VACCINATION AND SANITATION","authors":"R. Viriyapong, N. Thammawong","doi":"10.1142/s0218339022500310","DOIUrl":"https://doi.org/10.1142/s0218339022500310","url":null,"abstract":"In this study, we propose a deterministic model describing the dynamics of anthrax transmission in animals. It is assumed in the model that anthrax is contracted when susceptible animal comes into contact with infected animals, infected carcasses or the spores of Bacillus anthracis. Conditions for disease-free and endemic equilibria are derived and the basic reproduction number ([Formula: see text]) is computed. The disease-free equilibrium is stable when [Formula: see text] and the disease will be eliminated. If [Formula: see text], the disease persists, therefore, the endemic equilibrium is globally stable. Further, we extend our model by applying optimal control problem in which vaccination for susceptible animals and sanitation are control variables to minimize the anthrax transmission. We study three strategies to investigate the impact of the controls. Our numerical results demonstrate that both vaccination and sanitation help minimizing the transmission although vaccination alone gives more significant impact than sanitation alone. However, the combination of both controls gives the best result in wiping out the anthrax transmission overall. Further, cost-effectiveness analysis shows that the most effective strategy to control anthrax disease is a combination of vaccination and sanitation of the infected areas, therefore these two interventions should be encouraged.","PeriodicalId":54872,"journal":{"name":"Journal of Biological Systems","volume":" ","pages":""},"PeriodicalIF":1.6,"publicationDate":"2022-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42528684","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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