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Modeling of expansion of alien species in a new environment has become an important issue in view of the recent environmental conditions. Extensive effects of introduction of invasive species for the food chains of ecosystems are described quite regularly. Rapid changes in the form of a "population outbreak" are characteristic of certain insects, and their implications are important for agriculture. Monophagous insects are not only agricultural pests but also potential agents of biological weed control. This paper considers the development of a dynamic system for simulating the scenario of population outbreaks of Cardiaspina albitextura Taylor, 1962, described in the ecological literature. We propose a continuous-event driven computing structure of the new model which takes into account the mortality rate variation at different development stages and the factor of abrupt exhaustion of food resources at the peak of the outbreak.

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MATHEMATICAL AND COMPUTER MODELLING УДК 681.3.06 Переварюха А. Ю. Канд. техн. наук, старший научный сотрудник Санкт-Петербургского института информатики и автоматизации РАН,Санкт-Петербург, Россия КОМПЬЮТЕРНОЕ МОДЕЛИРОВАНИЕ ПОПУЛЯЦИЙ ОСЕТРОВЫХ КАСПИЯ С ДВУМЯ ВИДАМИ ВОЗНИКНОВЕНИЯ АПЕРИОДИЧЕСКИХ КОЛЕБАНИЙВ статье предложена оригинальная компьютерная модель жизненного цикла популяции осетровых рыб Каспийского моря, включенных в «Красную книгу» с 2010 г. В модели реализована событийно-стадийная вычислительная структура, которая включает непрерывные и дискретные составляющие времени. Особенности динамики модели рассмотрены на основе численного решения конечной последовательности задач Коши для системы дифференциальных уравнений убыли численности особей поколений. Получена интересующая ихтиологов функциональная зависимость, которая имеет два локальных экстремума. Установлены возможность притяжения траектории к двум аттракторам и появление переходного апериодического режима. После бифуркации исчезновения двух нетривиальных стационарных точек возникает интервальный аттрактор. Для данного типа аттрактора по классификации Гукенхеймера наблюдается явление граничного кризиса, что для популяций осетровых рыб интерпретируется как угрожающее их существованию событие.Ключевые слова: компьютерная модель биологических процессов, гибридная система, переходный хаос, бифуркация, вычислительный эксперимент. НОМЕНКЛАТУРА a -параметр репродуктивного потенциала; b -показатель действия лимитирующих факторов; g -параметр объема доступных кормовых ресурсов;

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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.