In this paper the transmission of leptospirosis, an infectious disease caused by bacteria, is studied. Leptospirosis is currently spreading in Thailand and worldwide. A Susceptible-Infected-Removed sir model is used t...In this paper the transmission of leptospirosis, an infectious disease caused by bacteria, is studied. Leptospirosis is currently spreading in Thailand and worldwide. A Susceptible-Infected-Removed sir model is used to study the stability analysis, analytical solution and global behavior of the spreading of the disease. The model was analysed using the techniques of non-linear dynamical systems. Two equilibrium points were found and the stability conditions for these equilibrium points were established. It will be shown that the linearised solutions of the sir equations are in good agreement with numerical solutions.展开更多
The determination of critical conditions for thermal ignition of combustible materials has been traditionally studied by the use of one overall reaction with bounded parameter values for the activation energy and othe...The determination of critical conditions for thermal ignition of combustible materials has been traditionally studied by the use of one overall reaction with bounded parameter values for the activation energy and other chemical constants, Significant errors can occur in the values of the threshold parameters for ignition when there are two (or more) simultaneous reactions present with distinct values of the chemical constants. Recent work with simultaneous parallel reactions showed the thresholds for ignition could be lowered in this case. In this paper, motivated by experimental results for forest litter and coal, it is shown that for sequential reactions (different values of parameters in different temperature ranges) that the threshold conditions are changed (safer for lower ambient temperatures and less safe for higher ambient temperatures). The mathematical analysis is summarised and a detailed analysis is given for the forest litter and crushed coal applications. The experimental results show that variable activation energy does occur and that this extension of the classical Frank-Kamenetskii theory is needed. Here the analysis is confined to the slab geometry only but the ideas developed can easily be extended to more general systems, including those involving mass transport, consumption, and phase changes.展开更多
文摘In this paper the transmission of leptospirosis, an infectious disease caused by bacteria, is studied. Leptospirosis is currently spreading in Thailand and worldwide. A Susceptible-Infected-Removed sir model is used to study the stability analysis, analytical solution and global behavior of the spreading of the disease. The model was analysed using the techniques of non-linear dynamical systems. Two equilibrium points were found and the stability conditions for these equilibrium points were established. It will be shown that the linearised solutions of the sir equations are in good agreement with numerical solutions.
文摘The determination of critical conditions for thermal ignition of combustible materials has been traditionally studied by the use of one overall reaction with bounded parameter values for the activation energy and other chemical constants, Significant errors can occur in the values of the threshold parameters for ignition when there are two (or more) simultaneous reactions present with distinct values of the chemical constants. Recent work with simultaneous parallel reactions showed the thresholds for ignition could be lowered in this case. In this paper, motivated by experimental results for forest litter and coal, it is shown that for sequential reactions (different values of parameters in different temperature ranges) that the threshold conditions are changed (safer for lower ambient temperatures and less safe for higher ambient temperatures). The mathematical analysis is summarised and a detailed analysis is given for the forest litter and crushed coal applications. The experimental results show that variable activation energy does occur and that this extension of the classical Frank-Kamenetskii theory is needed. Here the analysis is confined to the slab geometry only but the ideas developed can easily be extended to more general systems, including those involving mass transport, consumption, and phase changes.
