By using fixed point index theory of cone mapping and extension method, this paper discusses the existence of multiple positive solution of nonlinear neutral integral equatious modeling infectious disease.
Coxsackie A virus is one of the major pathogens associated with hand, foot and mouth disease (HFMD). The etiological characteristics of Coxsackie A virus type 16 (CA16) are thought to correlate with the pathological p...Coxsackie A virus is one of the major pathogens associated with hand, foot and mouth disease (HFMD). The etiological characteristics of Coxsackie A virus type 16 (CA16) are thought to correlate with the pathological process of its infection. Two CA16 strains that were isolated from a severe HFMD patient presented with different plaque forms. This observation, along with biological analysis, indicated that the differences in the strains' biological characteristics, such as proliferation kinetics and immunogenicity, correlate with differences in their pathogenicity toward neonatal mice. Furthermore, these differences are thought to be associated with the sequence of the 5′ non-coding region of the viral genome and the VP1 structural region sequence. The results suggest that the biological and genetic characteristics of the CA16 viral strains are relevant to their pathogenicity.展开更多
Ever since HIV was first diagnosed in human, a great number of scientific works have been undertaken to explore the biological mechanisms involved in the infection and progression of the disease. This paper deals with...Ever since HIV was first diagnosed in human, a great number of scientific works have been undertaken to explore the biological mechanisms involved in the infection and progression of the disease. This paper deals with stability and bifurcation analyses of mathematical model that represents the dynamics of HIV infection of thymus. The existence and stability of the equilibria are investigated. The model is described by a system of delay differential equations with logistic growth term, cure rate and discrete type of time delay. Choosing the time delay as a bifurcation parameter, the analysis is mainly focused on the Hopf bifurcation problem to predict the existence of a limit cycle bifurcating from the infected steady state.Further, using center manifold theory and normal form method we derive explicit formulae to determine the stability and direction of the limit cycles. Moreover the mitosis rate r also plays a vital role in the model, so we fix it as second bifurcation parameter in the incidence of viral infection. Our analysis shows that, while both the bifurcation parameters can destabilize the equilibrium E＊ and cause limit cycles. Numerical simulations are performed to investigate the qualitative behaviors of the inherent model.展开更多
Network and equation-based （EB） models are two prominent methods used in the study of epidemics. While EB models use a global approach to model aggregate population, net- work models focus on the behavior of individ...Network and equation-based （EB） models are two prominent methods used in the study of epidemics. While EB models use a global approach to model aggregate population, net- work models focus on the behavior of individuals in the population. The two approaches have been used in several areas of research, including finance, computer science, social science and epidemiology. In this study, epidemiology is used to contrast EB models with network models. The methods are based on the assumptions and properties of compartmental models. In EB models we solve a system of ordinary differential equations and in network models we simulate the spread of epidemics on contact networks using bond percolation. We examine the impact of network structures on the spread of infection by considering various networks, including Poisson, Erd3s R6nyi, Scale-free, and Watts- Strogatz small-world networks, and discuss how control measures can make use of the network structures. In addition, we simulate EB assumptions on Watts-Strogatz net- works to determine when the results are similar to that of EB models. As a case study, we use data from the 1918 Spanish flu pandemic and that from measles outbreak to validate our results.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
文摘By using fixed point index theory of cone mapping and extension method, this paper discusses the existence of multiple positive solution of nonlinear neutral integral equatious modeling infectious disease.
基金supported by the National Basic Research Program of China (Grant No. 2011CB504903)the National Natural Science Foundation of China (Grant No. 81171573)+1 种基金the Important National Science & Technology Specific Projects (Grant No. 2009ZX10004-308)the General Program of Applied Basic Research Programs Commission, Foundation of Yunnan Province (Grant No. 2011FB116)
文摘Coxsackie A virus is one of the major pathogens associated with hand, foot and mouth disease (HFMD). The etiological characteristics of Coxsackie A virus type 16 (CA16) are thought to correlate with the pathological process of its infection. Two CA16 strains that were isolated from a severe HFMD patient presented with different plaque forms. This observation, along with biological analysis, indicated that the differences in the strains' biological characteristics, such as proliferation kinetics and immunogenicity, correlate with differences in their pathogenicity toward neonatal mice. Furthermore, these differences are thought to be associated with the sequence of the 5′ non-coding region of the viral genome and the VP1 structural region sequence. The results suggest that the biological and genetic characteristics of the CA16 viral strains are relevant to their pathogenicity.
文摘Ever since HIV was first diagnosed in human, a great number of scientific works have been undertaken to explore the biological mechanisms involved in the infection and progression of the disease. This paper deals with stability and bifurcation analyses of mathematical model that represents the dynamics of HIV infection of thymus. The existence and stability of the equilibria are investigated. The model is described by a system of delay differential equations with logistic growth term, cure rate and discrete type of time delay. Choosing the time delay as a bifurcation parameter, the analysis is mainly focused on the Hopf bifurcation problem to predict the existence of a limit cycle bifurcating from the infected steady state.Further, using center manifold theory and normal form method we derive explicit formulae to determine the stability and direction of the limit cycles. Moreover the mitosis rate r also plays a vital role in the model, so we fix it as second bifurcation parameter in the incidence of viral infection. Our analysis shows that, while both the bifurcation parameters can destabilize the equilibrium E＊ and cause limit cycles. Numerical simulations are performed to investigate the qualitative behaviors of the inherent model.
文摘Network and equation-based （EB） models are two prominent methods used in the study of epidemics. While EB models use a global approach to model aggregate population, net- work models focus on the behavior of individuals in the population. The two approaches have been used in several areas of research, including finance, computer science, social science and epidemiology. In this study, epidemiology is used to contrast EB models with network models. The methods are based on the assumptions and properties of compartmental models. In EB models we solve a system of ordinary differential equations and in network models we simulate the spread of epidemics on contact networks using bond percolation. We examine the impact of network structures on the spread of infection by considering various networks, including Poisson, Erd3s R6nyi, Scale-free, and Watts- Strogatz small-world networks, and discuss how control measures can make use of the network structures. In addition, we simulate EB assumptions on Watts-Strogatz net- works to determine when the results are similar to that of EB models. As a case study, we use data from the 1918 Spanish flu pandemic and that from measles outbreak to validate our results.
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.
