scholarly journals A nonlinear population dynamics model of patient diagnosis and treatment involving in two level medical institutions and its qualitative analysis of positive singularity

2022 ◽  
Vol 19 (3) ◽  
pp. 2575-2591
Author(s):  
Xiaoxia Zhao ◽  
◽  
Lihong Jiang ◽  
Kaihong Zhao ◽  
◽  
...  
Keyword(s):  
Sufficient Conditions ◽  
Practical Application ◽  
Dynamics Model ◽  
Qualitative Properties ◽  
Homotopy Invariance ◽  
Patient Diagnosis ◽  
Population Dynamics Model ◽  
Medical Institutions ◽  
And Function ◽  
Invariance Theorem

<abstract><p>In this article, we firstly establish a nonlinear population dynamical model to describe the changes and interaction of the density of patient population of China's primary medical institutions (PHCIs) and hospitals in China's medical system. Next we get some sufficient conditions of existence of positive singularity by utilising homotopy invariance theorem of topological degree. Meanwhile, we study the qualitative properties of positive singularity based on Perron's first theorem. Furthermore, we briefly analyze the significance and function of the mathematical results obtained in this paper in practical application. As verifications, some numerical examples are ultimately exploited the correctness of our main results. Combined with the numerical simulation results and practical application, we give some corresponding suggestions. Our research can provide a certain theoretical basis for government departments to formulate relevant policies.</p></abstract>

ON THE STABILITY OF A POPULATION DYNAMICS MODEL WITH DELAY

2018 ◽  
pp. 456-465
Author(s):  
Vera Vladimirovna Malygina
Keyword(s):  
Differential Equation ◽  
Sufficient Conditions ◽  
Distributed Delay ◽  
Isolated Population ◽  
Dynamics Model ◽  
Population Dynamics Model ◽  
Three Stages ◽  
Pass Through ◽  
The Stability ◽  
Concentrated And Distributed Delay

We consider a model of the dynamics of an isolated population whose individuals pass through the three stages of evolution. We use a nonlinear autonomous differential equation with concentrated and distributed delay for description of the model. Effective sufficient conditions for the asymptotic stability of the nontrivial equilibrium point are obtained.

scholarly journals A random effects population dynamics model based on proportions-at-age and removal data for estimating total mortality

2012 ◽  
Vol 69 (11) ◽  
pp. 1881-1893 ◽  
Author(s):  
Verena M. Trenkel ◽  
Mark V. Bravington ◽  
Pascal Lorance
Keyword(s):  
Population Dynamics ◽  
Random Effects ◽  
Fixed Effects ◽  
Random Effect ◽  
Total Mortality ◽  
Estimation Bias ◽  
Effective Sample Size ◽  
Dynamics Model ◽  
Population Dynamics Model ◽  
Study Parameter

Catch curves are widely used to estimate total mortality for exploited marine populations. The usual population dynamics model assumes constant recruitment across years and constant total mortality. We extend this to include annual recruitment and annual total mortality. Recruitment is treated as an uncorrelated random effect, while total mortality is modelled by a random walk. Data requirements are minimal as only proportions-at-age and total catches are needed. We obtain the effective sample size for aggregated proportion-at-age data based on fitting Dirichlet-multinomial distributions to the raw sampling data. Parameter estimation is carried out by approximate likelihood. We use simulations to study parameter estimability and estimation bias of four model versions, including models treating mortality as fixed effects and misspecified models. All model versions were, in general, estimable, though for certain parameter values or replicate runs they were not. Relative estimation bias of final year total mortalities and depletion rates were lower for the proposed random effects model compared with the fixed effects version for total mortality. The model is demonstrated for the case of blue ling (Molva dypterygia) to the west of the British Isles for the period 1988 to 2011.

A microbial treatment population dynamics optimization approach

2021 ◽  
pp. 1-15
Author(s):  
Jinding Gao
Keyword(s):  
Population Dynamics ◽  
Information Exchange ◽  
Information Diffusion ◽  
Optimization Problems ◽  
Microbial Control ◽  
Function Optimization ◽  
Optimization Approach ◽  
Dynamics Model ◽  
Population Dynamics Model ◽  
Number Of Individuals

In order to solve some function optimization problems, Population Dynamics Optimization Algorithm under Microbial Control in Contaminated Environment (PDO-MCCE) is proposed by adopting a population dynamics model with microbial treatment in a polluted environment. In this algorithm, individuals are automatically divided into normal populations and mutant populations. The number of individuals in each category is automatically calculated and adjusted according to the population dynamics model, it solves the problem of artificially determining the number of individuals. There are 7 operators in the algorithm, they realize the information exchange between individuals the information exchange within and between populations, the information diffusion of strong individuals and the transmission of environmental information are realized to individuals, the number of individuals are increased or decreased to ensure that the algorithm has global convergence. The periodic increase of the number of individuals in the mutant population can greatly increase the probability of the search jumping out of the local optimal solution trap. In the iterative calculation, the algorithm only deals with 3/500∼1/10 of the number of individual features at a time, the time complexity is reduced greatly. In order to assess the scalability, efficiency and robustness of the proposed algorithm, the experiments have been carried out on realistic, synthetic and random benchmarks with different dimensions. The test case shows that the PDO-MCCE algorithm has better performance and is suitable for solving some optimization problems with higher dimensions.

scholarly journals The strong Suslin reciprocity law

2021 ◽  
Vol 157 (4) ◽  
pp. 649-676
Author(s):  
Daniil Rudenko
Keyword(s):  
Rational Functions ◽  
Projective Curve ◽  
Main Ingredient ◽  
Homotopy Invariance ◽  
Reciprocity Law ◽  
Hyperbolic Volume ◽  
Scissors Congruence ◽  
Dehn Invariant ◽  
Contracting Homotopy ◽  
Invariance Theorem

We prove the strong Suslin reciprocity law conjectured by A. Goncharov. The Suslin reciprocity law is a generalization of the Weil reciprocity law to higher Milnor $K$ -theory. The Milnor $K$ -groups can be identified with the top cohomology groups of the polylogarithmic motivic complexes; Goncharov's conjecture predicts the existence of a contracting homotopy underlying Suslin reciprocity. The main ingredient of the proof is a homotopy invariance theorem for the cohomology of the polylogarithmic motivic complexes in the ‘next to Milnor’ degree. We apply these results to the theory of scissors congruences of hyperbolic polytopes. For every triple of rational functions on a compact projective curve over $\mathbb {C}$ we construct a hyperbolic polytope (defined up to scissors congruence). The hyperbolic volume and the Dehn invariant of this polytope can be computed directly from the triple of rational functions on the curve.

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