In this paper,an improved Susceptible-Infected-Susceptible(SIS) epidemic spreading model is proposed in order to provide a theoretical method to analyze and predict the spreading of diseases.This model is based on the...In this paper,an improved Susceptible-Infected-Susceptible(SIS) epidemic spreading model is proposed in order to provide a theoretical method to analyze and predict the spreading of diseases.This model is based on the following ideas:in social networks,the contact probability between nodes is decided by their social distances and their active degrees.The contact probability of two indirectly connected nodes is decided by the shortest path between them.Theoretical analysis and simulation experiment were conducted to evaluate the performance of this improved model.Because the proposed model is independent of the network structure,simulation experiments were done in several kinds of networks,namely the ER network,the random regular network,the WS small world network,and the BA scale-free network,in order to study the influences of certain factors have on the epidemic spreading,such as the social contact active degree,the network structure,the average degree,etc.This improved model provides an idea for studying the spreading rule of computer virus,attitudes,fashion styles and public opinions in social networks.展开更多
Behavioral responses triggered by the perceived risk of experiencing the disease represent a key ingredient in the spread of epidemics across human population.In this paper,two forms of individual awareness(i.e.,the r...Behavioral responses triggered by the perceived risk of experiencing the disease represent a key ingredient in the spread of epidemics across human population.In this paper,two forms of individual awareness(i.e.,the risk perception of an emerging epidemic) are addressed:Contact awareness that increases with individual contact number,and local awareness that increases with the fraction of infected contacts.By extending the probability generating functionology,the author shows that it is possible to track the evolution of the degree distributions among susceptible and infected individuals when the underlying network of contacts is represented by a semi-random configuration model.It is hopefully to shed some light on the dynamic aspects of networked epidemiological models.展开更多
Disease in ecological systems plays an important role. In the present investigation we propose and analyze a predator-prey mathematical model in which both species are affected by infectious disease. The parasite is t...Disease in ecological systems plays an important role. In the present investigation we propose and analyze a predator-prey mathematical model in which both species are affected by infectious disease. The parasite is transmitted directly （by contact） within the prey population and indirectly （by consumption of infected prey） within the predator population. We derive biologically feasible and insightful quantities in terms of ecological as well as epidemiological reproduction numbers that allow us to describe the dynamics of the proposed system. Our observations indicate that predator-prey system is stable without disease but high infection rate drive the predator population toward extinction. We also observe that predation of vulnerable infected prey makes the disease to eradicate into the community composition of the model system. Local stability analysis of the interior equilibrium point near the disease-free equilibrium point is worked out. To study the global dynamics of the system, numerical simulations are performed. Our simulation results show that for higher values of the force of infection in the prey population the predator population goes to extinction. Our numerical analysis reveals that predation rates specially on susceptible prey population and recovery of infective predator play crucial role for preventing the extinction of the susceptible predator and disease propagation.展开更多
In this paper, we describe an SIS epidemic model where both the disease transmission rate and treatment function are considered in saturated forms. The dynamical behavior of the system is analyzed. The system is custo...In this paper, we describe an SIS epidemic model where both the disease transmission rate and treatment function are considered in saturated forms. The dynamical behavior of the system is analyzed. The system is customized by considering the disease trans- mission rate and treatment control as fuzzy numbers and then fuzzy expected value of the infected individuals is determined. The fuzzy basic reproduction number is investi- gated and a threshold condition of pathogen is derived at which the system undergoes a backward bifurcation.展开更多
In this paper, a mathematical model to study the impact of Twitter in controlling infectious disease is proposed. The model includes the dynamics of ＂tweets＂ which may enhance awareness of the disease and cause beha...In this paper, a mathematical model to study the impact of Twitter in controlling infectious disease is proposed. The model includes the dynamics of ＂tweets＂ which may enhance awareness of the disease and cause behavioral changes among the public, thus reducing the transmission of the disease. Furthermore, the model is improved by introducing a time delay between the outbreak of disease and the release of Twitter messages. The basic reproduction number and the conditions for the stability of the equilibria are derived. It is shown that the system undergoes Hopf bifurcation when time delay is increased. Finally, numerical simulations are given to verify the analytical results.展开更多
Predator prey model with harvesting is well studied. The role of disease in such system has a great importance and cannot be ignored. In this study we have considered a predator prey model with disease circulating in ...Predator prey model with harvesting is well studied. The role of disease in such system has a great importance and cannot be ignored. In this study we have considered a predator prey model with disease circulating in the predator population only and we have also considered harvesting in the prey and in the susceptible predator. We have studied the local stability, Hopf bifurcation of the model system around the equilibria. We have derived the ecological and the disease basic reproduction numbers and we have observed its importance in the community structure of the model system and in controlling disease propagation in the predator population. We have paid attention to chaotic dynamics for increasing the force of infection in the predator. Chaotic population dynamics can exhibit irregular fluctuations and violent oscillations with extremely small or large population abundances. In this study main objective is to show the role of harvesting in controlling chaotic dynamics. It is observed that reasonable harvesting on the prey and the susceptible predator prevents chaotic dynamics.展开更多
Two stochastic models are derived for a susceptible-infectious-susceptible epidemic spreading through a metapopulation： a continuous time Markov chain （CTMC） model and an It6 stochastic differential equation （SDE...Two stochastic models are derived for a susceptible-infectious-susceptible epidemic spreading through a metapopulation： a continuous time Markov chain （CTMC） model and an It6 stochastic differential equation （SDE） model. The stochastic models are numerically compared. Close agreement suggests that computationally intense CTMC simulations can be approximated by simpler SDE simulations. Differential equations for the moments of the SDE probability distribution are also derived, the steady states are solved numerically using a moment closure technique, and these results are compared to simulations. The moment closure technique only coarsely approximates simulation results. The effect of model parameters on stability of the disease-free equilibrium is also numerically investigated.展开更多
基金supported by National Natural Science Foundation of China 61301091Shaanxi Province Science and Technology Project 2015GY015
文摘In this paper,an improved Susceptible-Infected-Susceptible(SIS) epidemic spreading model is proposed in order to provide a theoretical method to analyze and predict the spreading of diseases.This model is based on the following ideas:in social networks,the contact probability between nodes is decided by their social distances and their active degrees.The contact probability of two indirectly connected nodes is decided by the shortest path between them.Theoretical analysis and simulation experiment were conducted to evaluate the performance of this improved model.Because the proposed model is independent of the network structure,simulation experiments were done in several kinds of networks,namely the ER network,the random regular network,the WS small world network,and the BA scale-free network,in order to study the influences of certain factors have on the epidemic spreading,such as the social contact active degree,the network structure,the average degree,etc.This improved model provides an idea for studying the spreading rule of computer virus,attitudes,fashion styles and public opinions in social networks.
基金supported by Air Force Office of Scientific Research under Grant No.FA9550-09-1-0165
文摘Behavioral responses triggered by the perceived risk of experiencing the disease represent a key ingredient in the spread of epidemics across human population.In this paper,two forms of individual awareness(i.e.,the risk perception of an emerging epidemic) are addressed:Contact awareness that increases with individual contact number,and local awareness that increases with the fraction of infected contacts.By extending the probability generating functionology,the author shows that it is possible to track the evolution of the degree distributions among susceptible and infected individuals when the underlying network of contacts is represented by a semi-random configuration model.It is hopefully to shed some light on the dynamic aspects of networked epidemiological models.
文摘Disease in ecological systems plays an important role. In the present investigation we propose and analyze a predator-prey mathematical model in which both species are affected by infectious disease. The parasite is transmitted directly （by contact） within the prey population and indirectly （by consumption of infected prey） within the predator population. We derive biologically feasible and insightful quantities in terms of ecological as well as epidemiological reproduction numbers that allow us to describe the dynamics of the proposed system. Our observations indicate that predator-prey system is stable without disease but high infection rate drive the predator population toward extinction. We also observe that predation of vulnerable infected prey makes the disease to eradicate into the community composition of the model system. Local stability analysis of the interior equilibrium point near the disease-free equilibrium point is worked out. To study the global dynamics of the system, numerical simulations are performed. Our simulation results show that for higher values of the force of infection in the prey population the predator population goes to extinction. Our numerical analysis reveals that predation rates specially on susceptible prey population and recovery of infective predator play crucial role for preventing the extinction of the susceptible predator and disease propagation.
文摘In this paper, we describe an SIS epidemic model where both the disease transmission rate and treatment function are considered in saturated forms. The dynamical behavior of the system is analyzed. The system is customized by considering the disease trans- mission rate and treatment control as fuzzy numbers and then fuzzy expected value of the infected individuals is determined. The fuzzy basic reproduction number is investi- gated and a threshold condition of pathogen is derived at which the system undergoes a backward bifurcation.
文摘In this paper, a mathematical model to study the impact of Twitter in controlling infectious disease is proposed. The model includes the dynamics of ＂tweets＂ which may enhance awareness of the disease and cause behavioral changes among the public, thus reducing the transmission of the disease. Furthermore, the model is improved by introducing a time delay between the outbreak of disease and the release of Twitter messages. The basic reproduction number and the conditions for the stability of the equilibria are derived. It is shown that the system undergoes Hopf bifurcation when time delay is increased. Finally, numerical simulations are given to verify the analytical results.
文摘Predator prey model with harvesting is well studied. The role of disease in such system has a great importance and cannot be ignored. In this study we have considered a predator prey model with disease circulating in the predator population only and we have also considered harvesting in the prey and in the susceptible predator. We have studied the local stability, Hopf bifurcation of the model system around the equilibria. We have derived the ecological and the disease basic reproduction numbers and we have observed its importance in the community structure of the model system and in controlling disease propagation in the predator population. We have paid attention to chaotic dynamics for increasing the force of infection in the predator. Chaotic population dynamics can exhibit irregular fluctuations and violent oscillations with extremely small or large population abundances. In this study main objective is to show the role of harvesting in controlling chaotic dynamics. It is observed that reasonable harvesting on the prey and the susceptible predator prevents chaotic dynamics.
文摘Two stochastic models are derived for a susceptible-infectious-susceptible epidemic spreading through a metapopulation： a continuous time Markov chain （CTMC） model and an It6 stochastic differential equation （SDE） model. The stochastic models are numerically compared. Close agreement suggests that computationally intense CTMC simulations can be approximated by simpler SDE simulations. Differential equations for the moments of the SDE probability distribution are also derived, the steady states are solved numerically using a moment closure technique, and these results are compared to simulations. The moment closure technique only coarsely approximates simulation results. The effect of model parameters on stability of the disease-free equilibrium is also numerically investigated.
