scholarly journals Investigation of the Stochastic Modeling of COVID-19 with Environmental Noise from the Analytical and Numerical Point of View

Mathematics ◽  
2021 ◽  
Vol 9 (23) ◽  
pp. 3122
Author(s):  
Shah Hussain ◽  
Elissa Nadia Madi ◽  
Hasib Khan ◽  
Sina Etemad ◽  
Shahram Rezapour ◽  
...  

In this article, we propose a novel mathematical model for the spread of COVID-19 involving environmental white noise. The new stochastic model was studied for the existence and persistence of the disease, as well as the extinction of the disease. We noticed that the existence and extinction of the disease are dependent on R0 (the reproduction number). Then, a numerical scheme was developed for the computational analysis of the model; with the existing values of the parameters in the literature, we obtained the related simulations, which gave us more realistic numerical data for the future prediction. The mentioned stochastic model was analyzed for different values of σ1,σ2 and β1,β2, and both the stochastic and the deterministic models were compared for the future prediction of the spread of COVID-19.

2018 ◽  
Vol 2018 ◽  
pp. 1-13 ◽  
Author(s):  
Rachel Waema Mbogo ◽  
Livingstone S. Luboobi ◽  
John W. Odhiambo

Malaria is one of the three most dangerous infectious diseases worldwide (along with HIV/AIDS and tuberculosis). In this paper we compare the disease dynamics of the deterministic and stochastic models in order to determine the effect of randomness in malaria transmission dynamics. Relationships between the basic reproduction number for malaria transmission dynamics between humans and mosquitoes and the extinction thresholds of corresponding continuous-time Markov chain models are derived under certain assumptions. The stochastic model is formulated using the continuous-time discrete state Galton-Watson branching process (CTDSGWbp). The reproduction number of deterministic models is an essential quantity to predict whether an epidemic will spread or die out. Thresholds for disease extinction from stochastic models contribute crucial knowledge on disease control and elimination and mitigation of infectious diseases. Analytical and numerical results show some significant differences in model predictions between the stochastic and deterministic models. In particular, we find that malaria outbreak is more likely if the disease is introduced by infected mosquitoes as opposed to infected humans. These insights demonstrate the importance of a policy or intervention focusing on controlling the infected mosquito population if the control of malaria is to be realized.


1978 ◽  
Vol 20 (3) ◽  
pp. 143-148 ◽  
Author(s):  
L. A. Balzer

One of the significant disturbances to a tracked hovercraft or any other high-speed ground transport vehicle is the roughness of the guideway surface together with misalignment of the guideway structure itself. Existing methods of describing this roughness and misalignment are reviewed and their shortcomings noted. A description is proposed which is valid in both statistical and wavelength-amplitude domains. Numerical data from the Tracked Hovercraft Ltd test track at Earith are analysed and a mathematical model proposed for a typical commercial H.S.G.T. guideway. A method of computer generation of typical roughness profiles is discussed.


2018 ◽  
Vol 28 (09) ◽  
pp. 1850118
Author(s):  
Dorota Aniszewska

Chaos is a phenomenon which cannot be predicted if it manifests itself in a nonlinear system. Simple deterministic models, such as the logistic map [Formula: see text], are constructed to capture the essence of processes observed in nature. They are interesting also from a mathematical point of view: nonlinear models can behave in chaotic and complicated ways. The logistic map is the simplest mathematical model exhibiting chaotic behavior. Therefore, its dynamical properties, stable points and stable cycles are well known and widely described. In this paper, the properties of multiplicative calculus were employed to transform the classical logistic map into multiplicative ones. The multiplicative logistic maps were tested for chaotic behavior. The Lyapunov exponents together with the bifurcation diagrams are given.


2020 ◽  
Vol 21 (02) ◽  
pp. 2150011
Author(s):  
Tuan Anh Phan ◽  
Jianjun Paul Tian ◽  
Bixiang Wang

Based on our deterministic models for cholera epidemics, we propose a stochastic model for cholera epidemics to incorporate environmental fluctuations which is a nonlinear system of Itô stochastic differential equations. We conduct an asymptotical analysis of dynamical behaviors for the model. The basic stochastic reproduction value [Formula: see text] is defined in terms of the basic reproduction number [Formula: see text] for the corresponding deterministic model and noise intensities. The basic stochastic reproduction value determines the dynamical patterns of the stochastic model. When [Formula: see text], the cholera infection will extinct within finite periods of time almost surely. When [Formula: see text], the cholera infection will persist most of time, and there exists a unique stationary ergodic distribution to which all solutions of the stochastic model will approach almost surely as noise intensities are bounded. When the basic reproduction number [Formula: see text] for the corresponding deterministic model is greater than 1, and the noise intensities are large enough such that [Formula: see text], the cholera infection is suppressed by environmental noises. We carry out numerical simulations to illustrate our analysis, and to compare with the corresponding deterministic model. Biological implications are pointed out.


Chelovek RU ◽  
2020 ◽  
pp. 18-53
Author(s):  
Sergei Avanesov ◽  

Abstract. The article analyzes the autobiography of the famous Russian philosopher, theologian and scientist Pavel Florensky, as well as those of his texts that retain traces of memories. According to Florensky, the personal biography is based on family history and continues in children. He addresses his own biography to his children. Memories based on diary entries are designed as a memory diary, that is, as material for future memories. The past becomes actual in autobiography, turns into a kind of present. The past, from the point of view of its realization in the present, gains meaning and significance. The au-thor is active in relation to his own past, transforming it from a collection of disparate facts into a se-quence of events. A person can only see the true meaning of such events from a great distance. Therefore, the philosopher remembers not so much the circumstances of his life as the inner impressions of the en-counter with reality. The most powerful personality-forming experiences are associated with childhood. Even the moment of birth can decisively affect the character of a person and the range of his interests. The foundations of a person's worldview are laid precisely in childhood. Florensky not only writes mem-oirs about himself, but also tries to analyze the problems of time and memory. A person is immersed in time, but he is able to move into the past through memory and into the future through faith. An autobi-ography can never be written to the end because its author lives on. However, reaching the depths of life, he is able to build his path in such a way that at the end of this path he will unite with the fullness of time, with eternity.


2020 ◽  
Vol 10 (4) ◽  
pp. 38-43
Author(s):  
MARIETA EPREMYAN ◽  

The article examines the epistemological roots of conservative ideology, development trends and further prospects in political reform not only in modern Russia, but also in other countries. The author focuses on the “world” and Russian conservatism. In the course of the study, the author illustrates what opportunities and limitations a conservative ideology can have in political reform not only in modern Russia, but also in the world. In conclusion, it is concluded that the prospect of a conservative trend in the world is wide enough. To avoid immigration and to control the development of technology in society, it is necessary to adhere to a conservative policy. Conservatism is a consolidating ideology. It is no coincidence that the author cites as an example the understanding of conservative ideology by the French due to the fact that Russia has its own vision of the ideology of conservatism. If we say that conservatism seeks to preserve something and respects tradition, we must bear in mind that traditions in different societies, which form some kind of moral imperatives, cannot be a single phenomenon due to different historical destinies and differing religious views. Considered from the point of view of religion, Muslim and Christian conservatism will be somewhat confrontational on some issues. The purpose of the work was to consider issues related to the role, evolution and prospects of conservative ideology in the political reform of modern countries. The author focuses on Russia and France. To achieve this goal, the method of in-depth interviews with experts on how they understand conservatism was chosen. Already today, conservatism is quite diverse. It is quite possible that in the future it will transform even more and acquire new reflections.


Author(s):  
R. A. Orekhov ◽  

There is a common point of view in Egyptology that Memphis was a state capital since the earliest times and that its protecting gods were Ptah and his spouse Sekhmet. Arguing this concept, the author tries to find the reason why a pyramid city of Pepi I — Mennefer — became a core of the future capital. The main conclusion is following: Constructing his pyramid complex, Pepi I probably included into it a cult center of Habes where Bastet and Imhotep, a high priest of Ra, were worshiped. Imhotep, a companion of the king Djoser, was known as a priest and charmer who tamed the fiery forces of Sirius associated with Bastet, after which the great drought was over. To commemorate this, New Year celebration and the first sun calendar were established. Imhotep’s tomb became an important cult place, where ceremonies important for surviving of the Egyptian state were conducted. In the second half of the Old Kingdom period the Nile started to flood much less, which led to the decline of agriculture. Thus, the role of the cult center of Habes and Imhotep grew greatly. By including Habes, Pepi protected the dominion of his pyramid city from negative influence of Bastet and decreased flooding. The fact that Mennefer was a successor of the aforementioned cult center determined its capital functions in future.


2017 ◽  
Vol 992 (4) ◽  
pp. 32-38 ◽  
Author(s):  
E.G. Voronin

The article opens a cycle of three consecutive publications dedicated to the phenomenon of the displacement of the same points in overlapping scans obtained adjacent CCD matrices with opto-electronic imagery. This phenomenon was noticed by other authors, but the proposed explanation for the origin of displacements and the resulting estimates are insufficient, and developed their solutions seem controversial from the point of view of recovery of the measuring accuracy of opticalelectronic space images, determined by the physical laws of their formation. In the first article the mathematical modeling of the expected displacements based on the design features of a scanning opto-electronic imaging equipment. It is shown that actual bias cannot be forecast, because they include additional terms, which may be gross, systematic and random values. The proposed algorithm for computing the most probable values of the additional displacement and ways to address some of the systematic components of these displacements in a mathematical model of optical-electronic remote sensing.


2021 ◽  
Vol 14 (1) ◽  
Author(s):  
Dipo Aldila ◽  
Brenda M. Samiadji ◽  
Gracia M. Simorangkir ◽  
Sarbaz H. A. Khosnaw ◽  
Muhammad Shahzad

Abstract Objective Several essential factors have played a crucial role in the spreading mechanism of COVID-19 (Coronavirus disease 2019) in the human population. These factors include undetected cases, asymptomatic cases, and several non-pharmaceutical interventions. Because of the rapid spread of COVID-19 worldwide, understanding the significance of these factors is crucial in determining whether COVID-19 will be eradicated or persist in the population. Hence, in this study, we establish a new mathematical model to predict the spread of COVID-19 considering mentioned factors. Results Infection detection and vaccination have the potential to eradicate COVID-19 from Jakarta. From the sensitivity analysis, we find that rapid testing is crucial in reducing the basic reproduction number when COVID-19 is endemic in the population rather than contact trace. Furthermore, our results indicate that a vaccination strategy has the potential to relax social distancing rules, while maintaining the basic reproduction number at the minimum possible, and also eradicate COVID-19 from the population with a higher vaccination rate. In conclusion, our model proposed a mathematical model that can be used by Jakarta’s government to relax social distancing policy by relying on future COVID-19 vaccine potential.


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