Diffusion with stochastic resetting of interacting particles emerging in a model of population genetics

2021 ◽  
Author(s):  
Telles Timóteo Timóteo Da Silva ◽  
Marcelo Dutra Fragoso
Keyword(s):  
Population Genetics ◽  
Evolution Equations ◽  
Interacting Particles ◽  
Mathematical Technique ◽  
Individual Type ◽  
Multiple Interaction ◽  
Forward Equations ◽  
Fokker Planck Equations ◽  
Kolmogorov Forward Equations ◽  
And Diffusion

Abstract In this paper we put forward a Generalized Ohta-Kimura ladder model (GOKM) which bears a strong liaison with the so-called jump-type Fleming-Viot process (JFVP). The novelty here, when we compare with the classical Ohta-Kimura model, is that we now have an operator which allows multiple interaction among the individuals. It has to do with a generalized branching mechanism: m individual types extinguish and one individual type splits into m copies. The system of evolution equations arising from GOKM can be seen as a system of n-dimensional Kolmogorov forward equations (or Fokker-Planck equations). Besides the interest in its own right a favorable feature of GOKM, vis-`a-vis JFVP, is that its analysis requires a more amenable armory of concepts and mathematical technique to analyze some relevant issues such as correlation, indistinguishability of individuals and stationarity. In addition, as a by product, we show that the connection between Ohta-Kimura Model and diffusion with resetting, as previously structured in [6], can be extended to our setting.

A perfect probe: Resonance of underdamped scaled Brownian motion

2021 ◽  
Author(s):  
Yuhui Luo ◽  
Chunhua Zeng ◽  
Baowen Li
Keyword(s):  
Brownian Motion ◽  
Single Particle ◽  
Brownian Particle ◽  
Bistable System ◽  
Velocity Autocorrelation Function ◽  
Interacting Particles ◽  
Velocity Autocorrelation ◽  
Spectrum Density ◽  
Coupling Strengths ◽  
And Diffusion

Abstract We numerically investigate the resonance of the underdamped scaled Brownian motion in a bistable system for both cases of a single particle and interacting particles. Through the velocity autocorrelation function (VACF) and mean squared displacement (MSD) of a single particle, we find that for the steady state, diffusions are ballistic at short times and then become normal for most of parameter regimes. However, for certain parameter regimes, both VACF and MSD suggest that the transition between superdiffusion and subdiffusion takes place at intermediate times, and diffusion becomes normal at long times. Via the power spectrum density corresponding to the transitions, we find that there exists a nontrivial resonance. For interacting particles, we find that the interaction between the probe particle and other particles can lead to the resonance, too. Thus we theoretically propose the system with the Brownian particle as a probe, which can detect the temperature of the system and identify the number of the particles or the types of different coupling strengths in the system. The probe is potentially useful for detecting microscopic and nanometer-scale particles and for identifying cancer cells or healthy ones.

scholarly journals Modelling gambiense human African trypanosomiasis infection in villages of the Democratic Republic of Congo using Kolmogorov forward equations

2021 ◽  
Author(s):  
Christopher N Davis ◽  
Matt J Keeling ◽  
Kat S Rock
Keyword(s):  
Human African Trypanosomiasis ◽  
Democratic Republic ◽  
Democratic Republic Of Congo ◽  
Mechanistic Model ◽  
Stochastic Methods ◽  
African Trypanosomiasis ◽  
Exact Methods ◽  
Republic Of Congo ◽  
Forward Equations ◽  
Kolmogorov Forward Equations

Stochastic methods for modelling disease dynamics enables the direct computation of the probability of elimination of transmission (EOT). For the low-prevalence disease of human African trypanosomiasis (gHAT), we develop a new mechanistic model for gHAT infection that determines the full probability distribution of the gHAT infection using Kolmogorov forward equations. The methodology allows the analytical investigation of the probabilities of gHAT elimination in the spatially-connected villages of the Kwamouth and Mosango health zones of the Democratic Republic of Congo, and captures the uncertainty using exact methods. We predict that, if current active and passive screening continue at current levels, local elimination of infection will occur in 2029 for Mosango and after 2040 in Kwamouth, respectively. Our method provides a more realistic approach to scaling the probability of elimination of infection between single villages and much larger regions, and provides results comparable to established models without the requirement of detailed infection structure. The novel flexibility allows the interventions in the model to be implemented specific to each village, and this introduces the framework to consider the possible future strategies of test-and-treat or direct treatment of individuals living in villages where cases have been found, using a new drug.

scholarly journals On the Kolmogorov forward equations within Caputo and Riemann-Liouville fractions derivatives

2016 ◽  
Vol 24 (3) ◽  
pp. 5-19
Author(s):  
Mohsen Alipour ◽  
Dumitru Baleanu
Keyword(s):  
Exact Solutions ◽  
Fractional Derivatives ◽  
Laplace Transforms ◽  
Caputo Fractional Derivatives ◽  
The Right ◽  
Forward Equations ◽  
Kolmogorov Forward Equations

AbstractIn this work, we focus on the fractional versions of the well-known Kolmogorov forward equations. We consider the problem in two cases. In case 1, we apply the left Caputo fractional derivatives for α ∈ (0, 1] and in case 2, we use the right Riemann-Liouville fractional derivatives on R+, for α ∈ (1, +∞). The exact solutions are obtained for the both cases by Laplace transforms and stable subordinators.

The transition probabilities of the extended simple stochastic epidemic model and the Haskey model

1972 ◽  
Vol 9 (3) ◽  
pp. 471-485 ◽  
Author(s):  
Richard J. Kryscio
Keyword(s):  
Epidemic Model ◽  
Transition Probabilities ◽  
Cross Infection ◽  
Special System ◽  
Stochastic Epidemic ◽  
Stochastic Epidemic Model ◽  
Forward Equations ◽  
Kolmogorov Forward Equations

We present a solution to a special system of Kolmogorov forward equations. We use this result to present a useful expression for the transition probabilities of the extended simple stochastic epidemic model and an epidemic model involving cross-infection between two otherwise isolated groups.

scholarly journals Generalized Lemaítre–Tolman–Bondi spacetime under the influence of electric charge and Palatini f(R) gravity

2021 ◽  
Vol 81 (9) ◽  
Author(s):  
M. Z. Bhatti ◽  
Z. Yousaf ◽  
F. Hussain
Keyword(s):  
Electromagnetic Field ◽  
Evolution Equations ◽  
Mass Function ◽  
Diffusion Approximations ◽  
Riemann Curvature ◽  
Field Equations ◽  
Riemann Curvature Tensor ◽  
Inhomogeneous Universe ◽  
Dust Fluid ◽  
And Diffusion

AbstractThe objective of this article is to investigate the effects of electromagnetic field on the generalization of Lemaître–Tolman–Bondi (LTB) spacetime by keeping in view the Palatini f(R) gravity and dissipative dust fluid. For performing this analysis, we followed the strategy deployed by Herrera et al. (Phys Rev D 82(2):024021, 2010). We have explored the modified field equations along with kinematical quantities and mass function and constructed the evolution equations to study the dynamics of inhomogeneous universe along with Raychauduary and Ellis equations. We have developed the relation for Palatini f(R) scalar functions by splitting the Riemann curvature tensor orthogonally and associated them with metric coefficients using modified field equations. We have formulated these scalar functions for LTB and its generalized version, i.e., GLTB under the influence of charge. The properties of GLTB spacetime are consistent with those of the LTB geometry and the scalar functions found in both cases are comparable in the presence of charge and Palatini f(R) curvature terms. The symmetric properties of generalized LTB spacetime are also studied using streaming out and diffusion approximations.

scholarly journals On Jumps Stochastic Evolution Equations With Application of Homogenization and Large Deviations

2019 ◽  
Vol 11 (2) ◽  
pp. 125
Author(s):  
Cl´ement Manga ◽  
Alioune Coulibaly ◽  
Alassane Diedhiou
Keyword(s):  
Evolution Equation ◽  
Large Deviations ◽  
Evolution Equations ◽  
Stochastic Evolution Equation ◽  
Stochastic Evolution ◽  
Stochastic Evolution Equations ◽  
Large Deviations Principle ◽  
Viscosity Parameter ◽  
Two Parameters ◽  
And Diffusion

We consider a class of jumps and diffusion stochastic differential equations which are perturbed by to two parameters:  ε (viscosity parameter) and δ (homogenization parameter) both tending to zero. We analyse the problem taking into account the combinatorial effects of the two parameters  ε and δ . We prove a Large Deviations Principle estimate for jumps stochastic evolution equation in case that homogenization dominates.

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