Preliminary assessment for sub-seasonal to seasonal precipitation model on four specific conditions over western Indonesia

Preliminary assessment of sub-seasonal to seasonal reforecast precipitation model (S2S) was conducted to analyze the model's performance over western Indonesia on four conditions. The ECMWF S2S model was compared to quality controlled daily precipitation data from 645 observation points over the region. The control and perturbed model for the first three time steps and the last three were utilized to obtain the best performance comparison. The analysis was conducted in monthly period, MJO events, NCS events, and when both of them were active during period of November-December-January-February (NDJF) from 1998 to 2017. The results show that the first three time steps perform much better than the last one with a slightly higher correlation coefficient from the control model with relatively similar RMSE in Natuna Islands. Spatial analysis indicates that both of the control and perturbed models can catch the variation brought by the wet season in the NDJF period, by the MJO, show a hint of NCS effect, and the combination when MJO and NCS were active at the same time. The models can depict the precipitation pattern pretty well with the tendency to overestimate low rainfall intensity and underestimate the high one. The models relatively overestimate the intensity in Sumatra for the whole period. Meanwhile, consistently good spatial performance is shown by the models over Java, both in NDJF periods or MJO events.

Relationship between Unstable Point Symmetries and Higher-Order Approximate Symmetries of Differential Equations with a Small Parameter

The framework of Baikov–Gazizov–Ibragimov approximate symmetries has proven useful for many examples where a small perturbation of an ordinary or partial differential equation (ODE, PDE) destroys its local exact symmetry group. For the perturbed model, some of the local symmetries of the unperturbed equation may (or may not) re-appear as approximate symmetries. Approximate symmetries are useful as a tool for systematic construction of approximate solutions. For algebraic and first-order differential equations, to every point symmetry of the unperturbed equation, there corresponds an approximate point symmetry of the perturbed equation. For second and higher-order ODEs, this is not the case: a point symmetry of the original ODE may be unstable, that is, not have an analogue in the approximate point symmetry classification of the perturbed ODE. We show that such unstable point symmetries correspond to higher-order approximate symmetries of the perturbed ODE and can be systematically computed. Multiple examples of computations of exact and approximate point and local symmetries are presented, with two detailed examples that include a fourth-order nonlinear Boussinesq equation reduction. Examples of the use of higher-order approximate symmetries and approximate integrating factors to obtain approximate solutions of higher-order ODEs are provided.

Modeling the dynamics of epidemics of infectious diseases under conditions of diffusion perturbations

The paper proposes a modification of the SIRS epidemic model to take into account the influence of diffusion perturbations on the dynamics of the spread of an infectious disease. A singularly perturbed model problem with delay is reduced to a sequence of problems without delay. The sought functions are represented in asymptotic series as perturbations of solutions of the corresponding degenerate problems. The results of numerical experiments illustrating the influence of spatially distributed diffusion redistributions on the spread of an infectious disease are presented.

DECISION MAKING IN MODELING THE DYNAMICS OF INFECTIOUS DISEASE TAKING INTO ACCOUNT DIFFUSION DISTURBANCES AND CONCENTRATED ACTIONS

To study the patterns of response of the immune system to viruses detected in the body, a very diverse range of models has been developed. The simplest infectious disease model, which describes the most general mechanisms of immune protection, built on the assumption that the environment of the «organism» is homogeneous, in which all components of the process are instantly mixed by Marchuk is known. The infectious disease mathematical model by Marchuk for generalization of diffusion perturbations and various concentrated influences is generalized. The corresponding singularly perturbed model problem with delay is reduced to a sequence of problems without delay, for which the corresponding asymptotic developments of solutions are obtained. The results of numerical experiments, which illustrate the influence of spatially distributed diffusion «redistributions» on the nature of the viral disease in the presence of concentrated sources of antigens and donor antibodies are presented. A model decrease in the maximum level of antigens in the infection epicenter due to their diffusion «erosion» in the process of infectious disease development has been demonstrated. It is emphasized that even if the initial concentration or intensity of the pulsed viral source in a certain part of the infection will exceed some critical value (immunological barrier) due to diffusion «redistribution» for a short period of time, the supercritical concentration of viral agents may decrease to lower than the critical level and further neutralization of antigens can be provided by the available level of antibodies and a more economical procedure of injection solution with donor antibodies. That is, within this model, the «severity» of the viral disease in such cases can be reduced more rationally, at lower cost.

A singularly perturbed vector-bias malaria model incorporating bed-net control

A malaria transmission disease model with host selectivity and Insecticide treated bed nets (ITNs), as an intervention for controlling the disease, is formulated. Since the vector is an insect, the vector time scale is much more expeditious than the host time scale. This leads to a singularly perturbed model with two distinctive intrinsic time scales, two-slow for the host and one-fast for the vector. The basic reproduction number R0 is calculated and the local stability analysis is performed at equilibria of the model when the perturbation parameter ɛ > 0. The model is analyzed when ɛ → 0 using asymptotic expansions technique. Merging bed-net control, vector-bias, and singular perturbation have a notable effect on the model dynamics. It is shown that if over %30 of humans use ITNs, malaria disease burden can be reduced. The dynamics on the slow surface indicate that the infected vectors decays very fast when ɛ = 0.001 according to the numerical simulations.

Dynamic characterization of a stochastic SIR infectious disease model with dual perturbation

Environmental perturbations are unavoidable in the propagation of infectious diseases. In this paper, we introduce the stochasticity into the susceptible–infected–recovered (SIR) model via the parameter perturbation method. The stochastic disturbances associated with the disease transmission coefficient and the mortality rate are presented with two perturbations: Gaussian white noise and Lévy jumps, respectively. This idea provides an overview of disease dynamics under different random perturbation scenarios. By using new techniques and methods, we study certain interesting asymptotic properties of our perturbed model, namely: persistence in the mean, ergodicity and extinction of the disease. For illustrative purposes, numerical examples are presented for checking the theoretical study.

Modeling the Influence of Small-Scale Diffusion Perturbations on the Development of Infectious Diseases under Immunotherapy

The article proposes a modification of the mathematical model of the immunotherapy influence on the immune response dynamics taking into account small-scale diffusion perturbations. The solution of the corresponding singularly perturbed model problem with time-delay is reduced to a sequence of solutions without time-delay, for that representations of the required functions in the form of asymptotic series as disturbances of solutions of the corresponding degenerate problems are constructed. We present the results of numerical modeling that illustrate the influence of diffusion redistribution of active factors on the infectious disease dynamics in the conditions of immunotherapy. The decrease in the level of the maximum concentration of antigens in the locus of infection as a result of their diffusion redistribution is illustrated.

On Singular Perturbation of Neutron Point Kinetics in the Dynamic Model of a PWR Nuclear Power Plant

This short communication makes use of the principle of singular perturbation to approximate the ordinary differential equation (ODE) of prompt neutron (in the point kinetics model) as an algebraic equation. This approximation is shown to yield a large gain in computational efficiency without compromising any significant accuracy in the numerical simulation of primary coolant system dynamics in a PWR nuclear power plant. The approximate (i.e., singularly perturbed) model has been validated with a numerical solution of the original set of neutron point-kinetic and thermal–hydraulic equations. Both models use variable-step Runge–Kutta numerical integration.

On Singular Perturbation of Neutron Point Kinetics in the Dynamic Model of a PWR Nuclear Power Plant

This short communication makes use of the principle of singular perturbation to approximate the ordinary differential equation (ODE) of prompt neutron (in the point kinetics model) as an algebraic equation. This approximation is shown to yield a large gain in computational efficiency without compromising any significant accuracy in the numerical simulation of primary coolant system dynamics in a PWR nuclear power plant. The approximate (i.e., singularly perturbed) model has been validated with a numerical solution of the original set of neutron point-kinetic and thermal–hydraulic equations. Both models use variable-step Runge–Kutta numerical integration.