Modeling Abrupt Changes in Population Dynamics with Two Threshold States*

J. Comput. Syst. Sci. Int.

2021

Self Cite

We consider a methodology for organizing hybrid computing structures to simulate abrupt changes in controlled natural processes and analyzing phases of extreme environmental phenomena. Systems of differential equations with the dynamically redefinable right-hand side at special moments (events) are used. The truth conditions for transitions are obtained from computing other equations for additional characteristics of the state of a generation. Threshold states in process modeling are the result of the inclusion of trigger functions. Their values on the right-hand side are specifically different from the neutral value only in narrow ranges of the space of changing characteristics of a hybrid system and depend on the initial conditions. The restricted limits of functions and their domain of values rest on the core of the threshold effects for the simulated biosystem, which are observed under special conditions. The method allows us to implement actual qualitative changes in management scenarios as bifurcations of the appearance (reduction) of equilibrium states or the boundary crisis of a complex attractor consisting of intervals scattered in a limited area. Computational scenarios for different population processes are investigated. The collapse of fish stocks is described in the model by the examples of cod in the North Atlantic and sturgeon in the Caspian Sea. The rapid outbreak of their abundance is modeled according to observations on the pulsation of the population size of pests of relict evergreen forests. The threshold scenario of the outbreak of insects in the scenario ends spontaneously due to the local exhaustion of forest resources with a sharp transition to fluctuations of the pest, which are ordinary for the environment. The methodology of organizing the structure for the population model is summarized to predict a wide range of extreme processes related to rapid changes in controlled biological systems and the spread of unwanted biological invasions.

Section: Methodology For Building Hybrid Structures In Ecodynamicsmentioning

confidence: 99%

Methodology of the Construction of Computational Scenarios for Modeling Extreme States in Living Systems

J. Comput. Syst. Sci. Int.

2021

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“…Points in time for events that lead to rearrangements in a system of continuous equations can be defined in different ways-explicitly or indirectly-since biological problems are specific and biosystem processes develop variably. Currently, "hybrid models" is a broad and interdisciplinary term [11]. A more precise and narrower definition needs to be given.…”

Section: Formalization Of Hierarchical Continuous Time With Eventsmentioning

confidence: 99%

Modeling of a Crisis in the Biophysical Process by the Method of Predicative Hybrid Structures

2022

Tech. Phys.

Crisis processes of biosystems often develop according to scenarios of rapid collapse, which cannot be predicted by statistical methods. This paper develops a method for constructing hybrid computational models using event-hierarchy representation for biophysical processes. System events calculated by the algorithm change the order of calculation of equations according to a given set of rules. The rules of physically conditioned redefinition of the right-hand sides of differential equations are used. The predicates employ the calculations of a group of accompanying characteristics, which are an integral part of the controlled biophysical dynamics. The model is investigated by presenting a computational scenario with a set of parameters, initial values, and an algorithm for making decisions about changing the impact for discrete time. Using computational experiments, a real outcome scenario for a situation that leads to the collapse of a biophysical system at a controlled level of exposure is described. The scenario sets the logic for making control decisions to change the level of external pressure on the natural environment. It is shown as a result of modeling that the transition of the process to an oscillatory mode leads to the choice of a risky control mode. It has been established that the dynamics of many real water populations has a point of threshold reduction in the efficiency of replenishment of stocks. The model scenario uses transformations of the phase portrait of iterations, which, in the presence of disconnected boundaries of the areas of attraction of alternative attractors and a strange chaotic repeller, lead to the uncertainty effects arising due to chaotic modes in a deterministic model. The properties of the described model scenario with a chaotic regime of dynamics are confirmed by the example of the catch of oceanic species of crustaceans.

“…Delay equations provide a common means to construct biological models with intricate dynamics [32] (a synonym of Volterra's hereditary phenomena). In this approach, the regulation of an ongoing process corresponds to a past state observed in the system a certain period of time previously [33].…”

Section: Formalization Of Delayed Regulation In Population Processesmentioning

confidence: 99%

A Continuous Model of Three Scenarios of the Infection Process with Delayed Immune Response Factors

2021

BIOPHYSICS

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The course of an infection was modeled as a controlled nonlinear process. Understanding the substantial differences observed in the trajectory of the disease caused by the new coronavirus SARS-CoV-2 is of critical importance at the moment. Numerous factors have been considered to explain the fact that symptoms vary highly among different people and the infection transmission rate varies among local populations. Virus replication within the host cell and the development of an immune response to virus antigens in the body are two interdependent processes, which have aftereffects and depend on the preexisting states of the cell and virus populations. Different scenarios with the same input parameters are necessary to consider for modeling the properties of the states. The efficiency of the immune response is the most important factor, including the time it takes to develop defense responses from three levels of the immune system, which is a complex system of the body. A computational description of infection scenarios was proposed on the basis of a delay differential equation with two values of the time lag. In the new model, transitions between phases of infectious disease depend on the initial virus dose and the delayed immune response to infection. A variation in the dose of the virus and response time can lead to a transition from an acute phase of the disease with overt symptoms to a chronic phase or fatal outcome. Asymptomatic transmission of viral infection was calculated and described in the model as a situation where the virus is rapidly and efficiently suppressed after a short replication phase, while still persisting in the body in minor amounts. An analysis of the model behavior is consistent with the theory that the initial number of virions can affect the quality of the immune response. The reasons that high individual differences are observed in the trajectory of COVID-19 disease and the formation of types of the immune response to coronavirus are still poorly understood. Known trajectories of hepatitis C virus (HCV) infection were used as a basis for model scenarios.