scholarly journals Analytical Solutions of the Transmissibility of the SARS-CoV-2 in Three Interactive Populations

2021 ◽  
Vol 2 (4) ◽  
pp. 1-8
Author(s):  
Raúl Isea
Keyword(s):  
Mathematical Model ◽  
Differential Equations ◽  
Analytical Solutions ◽  
Critical Points ◽  
Human Population ◽  
Equilibrium Conditions ◽  
Initial Source ◽  
Second Wave

This paper resolves analytically a mathematical model that reproduces the transmission of Covid-19 in three interactive populations, i.e. from the initial source of contagion associated with the bat population, subsequently transmitted to unknown host (usually associate with pangolins). The host were sent and distributed to Seafood Market in Wuhan (defined reservoir), and finally infected to the human population. The model is based on a system of ten differential equations reproducing all the possible infection scenarios among all of them, that is: (1) there is no infection in any of the three populations, (2) only the population of bats is infected, (3) only the pangolins, (4) only the human people. Later, combinations between them, this is: (5) both the bat and pangolin populations, (6) bats and humans, (7) pangolins and humans, and finally, (8) all the previous populations. In each scenario, I deduced the critical points as well as the eigenvalues ​​that indicate the equilibrium conditions. Finally, it is demonstrated the validity of the model with the data corresponding to the second wave of infections in Australia.

scholarly journals Analytical solutions of the transmissibility of the SARS-CoV-2 in three interactive populations

2021 ◽  
Author(s):  
Raúl Isea
Keyword(s):  
Mathematical Model ◽  
Differential Equations ◽  
Analytical Solutions ◽  
Critical Points ◽  
Human Population ◽  
Equilibrium Conditions ◽  
Initial Source ◽  
Second Wave

Abstract This paper resolves analytically a mathematical model that reproduces the transmission of Covid-19 in three interactive populations, i.e. from the initial source of contagion associated with the bat population, subsequently transmitted to unknown host (usually associate with pangolins). The host were sent and distributed to Seafood Market in Wuhan (defined reservoir), and finally infected to the human population. The model is based on a system of ten differential equations reproducing all the possible infection scenarios among all of them, that is: (1) there is no infection in any of the three populations, (2) only the population of bats is infected, (3) only the pangolins, (4) only the human people. Later, combinations between them, this is: (5) both the bat and pangolin populations, (6) bats and humans, (7) pangolins and humans, and finally, (8) all the previous populations. In each scenario, I deduced the critical points as well as the eigenvalues that indicate the equilibrium conditions. Finally, it is demonstrated the validity of the model with the data corresponding to the second wave of infections in Australia

scholarly journals Mathematical model for acquiring immunity to malaria: a PDE approach

BIOMATH ◽  
2021 ◽  
Vol 10 (2) ◽  
pp. 2107227
Author(s):  
S Y Tchoumi ◽  
Y T Kouakep ◽  
D J M Fotsa ◽  
F G T Kamba ◽  
J C Kamgang ◽  
...  
Keyword(s):  
Differential Equation ◽  
Mathematical Model ◽  
Partial Differential Equation ◽  
Differential Equations ◽  
Numerical Simulations ◽  
Spectral Radius ◽  
Human Population ◽  
Reproduction Rate ◽  
Basic Reproduction Rate ◽  
Disease Free

We develop a new model of integro-differential equations coupled with a partial differential equation that focuses on the study of the? naturally acquiring immunity to malaria induced by exposure to infection. We analyze a continuous acquisition of immunity after infected individuals are treated. It exhibits complex and realistic mechanisms precised mathematically in both disease free or endemic context and in several numerical simulations showing the interplay between infection through the bite of mosquitoes. The model confirms the (partial) premunition of the human population in the regions where malaria is endemic. As common in literature, we indicate an equivalence of the basic reproduction rate as the spectral radius of a next generation operator.

Glycemia monitoring

1998 ◽  
Vol 2 ◽  
pp. 23-30
Author(s):  
Igor Basov ◽  
Donatas Švitra
Keyword(s):  
Diabetes Mellitus ◽  
Mathematical Model ◽  
Numerical Methods ◽  
Differential Equations ◽  
Blood Sugar ◽  
Self Regulation ◽  
Physiological System ◽  
Non Linear ◽  
The Mathematical Model

Here a system of two non-linear difference-differential equations, which is mathematical model of self-regulation of the sugar level in blood, is investigated. The analysis carried out by qualitative and numerical methods allows us to conclude that the mathematical model explains the functioning of the physiological system "insulin-blood sugar" in both normal and pathological cases, i.e. diabetes mellitus and hyperinsulinism.

Application of the exp(-φ)-expansion method to the Pochhammer-Chree equation

Filomat ◽  
2018 ◽  
Vol 32 (9) ◽  
pp. 3347-3354 ◽  
Author(s):  
Nematollah Kadkhoda ◽  
Michal Feckan ◽  
Yasser Khalili
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Exact Solutions ◽  
Present Article ◽  
Analytical Solutions ◽  
Nonlinear Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Rational Functions ◽  
Expansion Method ◽  
Exponential Functions

In the present article, a direct approach, namely exp(-?)-expansion method, is used for obtaining analytical solutions of the Pochhammer-Chree equations which have a many of models. These solutions are expressed in exponential functions expressed by hyperbolic, trigonometric and rational functions with some parameters. Recently, many methods were attempted to find exact solutions of nonlinear partial differential equations, but it seems that the exp(-?)-expansion method appears to be efficient for finding exact solutions of many nonlinear differential equations.

Vibration of Beams with a Single Delamination under Axial Loading

2011 ◽  
Vol 675-677 ◽  
pp. 477-480
Author(s):  
Dong Wei Shu
Keyword(s):  
Free Vibration ◽  
Natural Frequency ◽  
Analytical Solutions ◽  
Axial Load ◽  
Natural Frequencies ◽  
Axial Loading ◽  
Composite Beams ◽  
Mode Shapes ◽  
Equilibrium Conditions ◽  
Monotonic Relation

In this work analytical solutions are developed to study the free vibration of composite beams under axial loading. The beam with a single delamination is modeled as four interconnected Euler-Bernoulli beams using the delamination as their boundary. The continuity and the equilibrium conditions are satisfied between the adjoining beams. The studies show that the sizes and the locations of the delaminations significantly influence the natural frequencies and mode shapes of the beam. A monotonic relation between the natural frequency and the axial load is predicted.

scholarly journals Ultrasonic Waves in Bubbly Liquids: An Analytic Approach

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1309
Author(s):  
P. R. Gordoa ◽  
A. Pickering
Keyword(s):  
Mathematical Model ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Acoustic Waves ◽  
Elliptic Functions ◽  
Coupled System ◽  
Ultrasonic Waves ◽  
Partial Differential ◽  
Special Cases ◽  
Spherical Bubbles

We consider the problem of the propagation of high-intensity acoustic waves in a bubble layer consisting of spherical bubbles of identical size with a uniform distribution. The mathematical model is a coupled system of partial differential equations for the acoustic pressure and the instantaneous radius of the bubbles consisting of the wave equation coupled with the Rayleigh–Plesset equation. We perform an analytic analysis based on the study of Lie symmetries for this system of equations, concentrating our attention on the traveling wave case. We then consider mappings of the resulting reductions onto equations defining elliptic functions, and special cases thereof, for example, solvable in terms of hyperbolic functions. In this way, we construct exact solutions of the system of partial differential equations under consideration. We believe this to be the first analytic study of this particular mathematical model.

Mathematical model implementation in conditions of uncertainty and possible risks

2021 ◽  
pp. 137-145
Author(s):  
A. Kravtsov ◽  
◽  
D. Levkin ◽  
O. Makarov ◽  
◽  
...  
Keyword(s):  
Thermal Conductivity ◽  
Mathematical Model ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Layer Structure ◽  
Boundary Value ◽  
Goal Function ◽  
Cauchy Problems ◽  
System Of Differential Equations

The article presents the theoretical and methodological principles for forecasting and mathematical modeling of possible risks in technological and biotechnological systems. The authors investigated in details the possible approach to the calculation of the goal function and its parameters. Considerable attention is paid to substantiating the correctness of boundary value problems and Cauchy problems. In mechanics, engineering, and biology, Cauchy problems and boundary value problems of differential equations are used to model physical processes. It is important that differential equations have a single physically sound solution. The authors of this article investigate the specific features of boundary value problems and Cauchy problems with boundary conditions in a two-point medium, and determine the conditions for the correctness of such problems in the spaces of power growth functions. The theory of pseudo-differential operators in the space of generalized functions was used to prove the correctness of boundary value problems. The application of the obtained results will make it possible to guarantee the correctness of mathematical models built in conditions of uncertainty and possible risks. As an example of a computational mathematical model that describes the state of the studied object of non-standard shape, the authors considered the boundary value problem of the system of differential equations of thermal conductivity for the embryo under the action of a laser beam. For such a boundary value problem, it is impossible to guarantee the existence and uniqueness of the solution of the system of differential equations. To be sure of the existence of a single solution, it is necessary either not to take into account the three-layer structure of the microbiological object, or to determine the conditions for the correctness of the boundary value problem. Applying the results obtained by the authors, the correctness of the boundary value problem of systems of differential equations of thermal conductivity for the embryo is proved taking into account the three-layer structure of the microbiological object. This makes it possible to increase the accuracy and speed of its implementation on the computer. Key words: forecasting, risk, correctness, boundary value problems, conditions of uncertainty

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