In this article, we develop and analyze a continuous-time Markov chain (CTMC) model to study the resurgence of dengue. We also explore the large population asymptotic behavior of probabilistic model of dengue using th...In this article, we develop and analyze a continuous-time Markov chain (CTMC) model to study the resurgence of dengue. We also explore the large population asymptotic behavior of probabilistic model of dengue using the law of large numbers (LLN). Initially, we calculate and estimate the probabilities of dengue extinction and major outbreak occurrence using multi-type Galton-Watson branching processes. Subsequently, we apply the LLN to examine the convergence of the stochastic model towards the deterministic model. Finally, theoretical numerical simulations are conducted exploration to validate our findings. Under identical conditions, our numerical results demonstrate that dengue could vanish in the stochastic model while persisting in the deterministic model. The highlighting of the law of large numbers through numerical simulations indicates from what population size a deterministic model should be considered preferable.展开更多
In this paper, we give a variational characterization for the growth rate of a multitype population modelled by a multitype Galton-Watson branching process. In particular, the so-called retrospective process plays an ...In this paper, we give a variational characterization for the growth rate of a multitype population modelled by a multitype Galton-Watson branching process. In particular, the so-called retrospective process plays an important role in the description of the equilibrium state used in the variational characterization. We define the retrospective process associated with a multitype Galton-Watson branching process and identify it with the mutation process describing the type evolution along typical lineages of the multitype Galton-Watson branching process.展开更多
In this paper,we form a method to calculate the probability generating function of the total progeny of multitype branching process.As examples,we calculate probability generating function of the total progeny of the ...In this paper,we form a method to calculate the probability generating function of the total progeny of multitype branching process.As examples,we calculate probability generating function of the total progeny of the multitype branching processes within random walk which could stay at its position and（2-1） random walk.Consequently,we could give the probability generating functions and the distributions of the first passage time of corresponding random walks.Especially,for recurrent random walk which could stay at its position with probability 0 〈 r 〈 1,we show that the tail probability of the first passage time decays as 2/√π（1-r）1/√n= when n →∞.展开更多
Taenia solium taeniasis and cysticercosis are neglected zoonotic diseases that affect human health and economies of developing countries.In this work,we formulate and analyze deterministic and continuous time Markov c...Taenia solium taeniasis and cysticercosis are neglected zoonotic diseases that affect human health and economies of developing countries.In this work,we formulate and analyze deterministic and continuous time Markov chain(CTMC)stochastic models to determine parameters that drive Taenia solium taeniasis and cysticercosis and the likelihood of their extinction.The basic reproduction number R0 is computed by the next generation matrix approach,sensitivity index of each parameter in R0 is derived by the normalized forward sensitivity index and the likelihood of diseases’extinction is computed by the multitype branching process.The analysis shows that humans with Taenia solium taeniasis,infectious pork and Taenia solium eggs in the environment play an important role in the transmission of Taenia solium taeniasis and cysticercosis,and the model exhibits forward bifurcation at R0=1.This implies that R0<1 is a sufficient condition to eliminate Taenia solium taeniasis and cysticercosis.For CTMC model,analysis shows that the probability of Taenia solium taeniasis and cysticercosis extinction is high if the diseases emerge from humans with Taenia solium cysticercosis and there is an outbreak if the diseases emerge from either humans with Taenia solium taeniasis or infectious pork or Taenia solium eggs in the environment.To control Taenia solium taeniasis and cysticercosis,the intervention strategies should focus on improving hygiene and sanitation for reducing shedding rate of Taenia solium eggs in the environment,inspection of pork for reducing the rate of acquiring Taenia solium taeniasis and spraying of insecticides for killing Taenia solium eggs in the environment.展开更多
文摘In this article, we develop and analyze a continuous-time Markov chain (CTMC) model to study the resurgence of dengue. We also explore the large population asymptotic behavior of probabilistic model of dengue using the law of large numbers (LLN). Initially, we calculate and estimate the probabilities of dengue extinction and major outbreak occurrence using multi-type Galton-Watson branching processes. Subsequently, we apply the LLN to examine the convergence of the stochastic model towards the deterministic model. Finally, theoretical numerical simulations are conducted exploration to validate our findings. Under identical conditions, our numerical results demonstrate that dengue could vanish in the stochastic model while persisting in the deterministic model. The highlighting of the law of large numbers through numerical simulations indicates from what population size a deterministic model should be considered preferable.
基金Supported by MPG and CAS joint doctoral promotion program and the Klaus Tschira Stiftung through the International Max-Planck Research School
文摘In this paper, we give a variational characterization for the growth rate of a multitype population modelled by a multitype Galton-Watson branching process. In particular, the so-called retrospective process plays an important role in the description of the equilibrium state used in the variational characterization. We define the retrospective process associated with a multitype Galton-Watson branching process and identify it with the mutation process describing the type evolution along typical lineages of the multitype Galton-Watson branching process.
基金Supported by National Nature Science Foundation of China(Grant No.11226199)
文摘In this paper,we form a method to calculate the probability generating function of the total progeny of multitype branching process.As examples,we calculate probability generating function of the total progeny of the multitype branching processes within random walk which could stay at its position and（2-1） random walk.Consequently,we could give the probability generating functions and the distributions of the first passage time of corresponding random walks.Especially,for recurrent random walk which could stay at its position with probability 0 〈 r 〈 1,we show that the tail probability of the first passage time decays as 2/√π（1-r）1/√n= when n →∞.
文摘Taenia solium taeniasis and cysticercosis are neglected zoonotic diseases that affect human health and economies of developing countries.In this work,we formulate and analyze deterministic and continuous time Markov chain(CTMC)stochastic models to determine parameters that drive Taenia solium taeniasis and cysticercosis and the likelihood of their extinction.The basic reproduction number R0 is computed by the next generation matrix approach,sensitivity index of each parameter in R0 is derived by the normalized forward sensitivity index and the likelihood of diseases’extinction is computed by the multitype branching process.The analysis shows that humans with Taenia solium taeniasis,infectious pork and Taenia solium eggs in the environment play an important role in the transmission of Taenia solium taeniasis and cysticercosis,and the model exhibits forward bifurcation at R0=1.This implies that R0<1 is a sufficient condition to eliminate Taenia solium taeniasis and cysticercosis.For CTMC model,analysis shows that the probability of Taenia solium taeniasis and cysticercosis extinction is high if the diseases emerge from humans with Taenia solium cysticercosis and there is an outbreak if the diseases emerge from either humans with Taenia solium taeniasis or infectious pork or Taenia solium eggs in the environment.To control Taenia solium taeniasis and cysticercosis,the intervention strategies should focus on improving hygiene and sanitation for reducing shedding rate of Taenia solium eggs in the environment,inspection of pork for reducing the rate of acquiring Taenia solium taeniasis and spraying of insecticides for killing Taenia solium eggs in the environment.
