arXiv subjects

Shigui Ruan

Publications and source records attributed to Shigui Ruan.

14 recordsLinked to original sources

arXiv2026

Propagation dynamics for nonlocal dispersal predator-prey systems in shifting habitats: A Hamilton-Jacobi approach

This paper is concerned with the spreading speeds of nonlocal dispersal predator-prey systems in shifting habitats under general initial conditions. By employing geometric optics techniques and theory of viscosity solutions, we reformulate the problem into the study of Hamilton-Jacobi equations. Through a detailed analysis of the structure of viscosity solutions, we provide a complete classification of explicit formulas for the spreading speed of the prey population, especially in cases where it invades the habitat more rapidly than predators, yielding two fundamentally distinct ``nonlocal determinacy'' results derived by different mechanisms. We also obtain an upper bound for spreading speed of the predators, incorporating the decay rate of the initial data and the speed of shifting habitats. These findings demonstrate that there are complex connections among spreading speeds, habitat shifting speed and initial conditions, and emphasize the significance of nonlocal dispersal in determining the propagation dynamics of predator-prey systems.

math.AP↗

arXiv2025

Impact of Resistance Development Mechanisms on Antibiotic Treatment Outcomes

Bacteria develop resistance to antibiotics through various mechanisms, with the specific mechanism depending on the drug-bacteria pair. It remains unclear, however, which resistance mechanism best supports favorable treatment outcomes, specifically in clearing infections and inhibiting further resistance. In this study, we use periodic ordinary differential equation models to simulate different antibiotic treatment protocols for bacterial infections. Using stability analysis and numerical simulations, we investigate how different resistance mechanisms, including plasmid-induced and mutation-induced resistance, affect treatment outcomes. Our findings suggest that antibiotic treatments with fixed dosing schedules are more likely to be effective when resistance arises exclusively through plasmid-mediated transmission. Further, when treatment fails, mutation-driven mechanisms tend to favor the selection of fully resistant bacterial strains. We also investigated the efficacy of different treatment strategies based on these mechanisms, finding that a twice-daily regimen consistently outperforms a once-daily regimen in terms of infection clearance. Additionally, our simulations with short half-life antibiotics indicate that the "catch-up" strategy outperforms the "compensatory double-dose" approach after a missed dose, a finding that aligns with general pharmaceutical advice for short-half-life drugs.

q-bio.PE↗

arXiv2025

Quantifying the Risk of Long Term Chikungunya Persistence in Miami Dade County

Chikungunya virus is a mosquito-borne arbovirus with the potential to establish sustained transmission in subtropical regions like Florida, where climatic and ecological conditions support vector proliferation. In this study, we develop a Continuous Time Markov Chain model to assess the probability of long-term Chikungunya establishment in Miami-Dade County following repeated introductions of external infectious individuals. This work aims to identify seasonal windows of heightened endemic risk and evaluates the impact of vector control strategies on mitigating the likelihood of persistent transmission. These results generate insights into the dynamics of Chikungunya virus infections and inform targeted interventions to prevent its transition from minor sporadic outbreaks to endemic circulation.

q-bio.PE↗

arXiv2025

On the Geographic Spread of Chikungunya between Brazil and Florida: A Multi-patch Model with Time Delay

Chikungunya (CHIK) is a viral disease transmitted to humans through the bites of {\it Aedes} mosquitoes infected with the chikungunya virus (CHIKV). CHIKV has been imported annually to Florida in the last decade due to Miami's crucial location as a hub for international travel, particularly from Central and South America including Brazil, where CHIK is endemic. This work addresses to the geographic spread of CHIK, incorporating factors such as human movement, temperature dependency, as well as vertical transmission, and incubation periods, for different patches. Central to the model is the integration of a multi-patch framework, and in the numerical analysis it is considered human movement between endemic Brazilian states and Florida. We establish crucial correlations between the mosquito reproduction number $\mathcal{R}_{m}$ and the disease reproduction number $\mathcal{R}_{0}$ with the disease dynamics in a multi-patch environment, encompassing not only a numerical analysis but also from a theoretical perspective. Through numerical simulations, validated with real population and temperature data, it is possible to understand the disease dynamics under many different scenarios and make future projections, offering insights for potential effective control strategies, as well as addressing the timing for these strategies to be adopted.

q-bio.PE↗

arXiv2022

Age-structured Models with Nonlocal Diffusion of Dirichlet Type, I: Principal Spectral Theory and Limiting Properties

Age-structured models with nonlocal diffusion arise naturally in describing the population dynamics of biological species and the transmission dynamics of infectious diseases in which individuals disperse nonlocally and interact each other and the age structure of individuals matters. In the first part of our series papers, we study the principal spectral theory of age-structured models with nonlocal diffusion of Dirichlet type. First, we provide two criteria on the existence of principal eigenvalues by using the theory of resolvent positive operators with their perturbations. Then we define the generalized principal eigenvalue and use it to investigate the influence of diffusion rate on the principal eigenvalue. In addition, we establish the strong maximum principle for age-structured nonlocal diffusion operators. In the second part \cite{Ducrot2022Age-structuredII} we will investigate the effects of principal eigenvalues on the global dynamics of the model with monotone nonlinearity in the birth rate and show that the principal eigenvalue being zero is critical.

math.AP↗

arXiv2020

Spatial Propagation in Nonlocal Dispersal Fisher-KPP Equations

In this paper we focus on three problems about the spreading speeds of nonlocal dispersal Fisher-KPP equations. First, we study the signs of spreading speeds and find that they are determined by the asymmetry level of the nonlocal dispersal and $f'(0)$, where $f$ is the reaction function. This indicates that asymmetric dispersal can influence the spatial dynamics in three aspects: it can determine the spatial propagation directions of solutions, influence the stability of equilibrium states, and affect the monotone property of solutions. Second, we give an improved proof of the spreading speed result by constructing new lower solutions and using the new "forward-backward spreading" method. Third, we establish the relationship between spreading speed and exponentially decaying initial data. Our result demonstrates that when dispersal is symmetric, spreading speed decreases along with the increase of the exponentially decaying rate. In addition, the results on the signs of spreading speeds are applied to two special cases where we present more details of the influence of asymmetric dispersal.

math.AP↗

arXiv2020

Spatial Propagation in an Epidemic Model with Nonlocal Diffusion: the Influences of Initial Data and Dispersals

This paper studies an epidemic model with nonlocal dispersals. We focus on the influences of initial data and nonlocal dispersals on its spatial propagation. Here the initial data stand for the spatial concentrations of infectious agent and infectious human population when the epidemic breaks out and the nonlocal dispersals mean their diffusion strategies. Two types of initial data decaying to zero exponentially or faster are considered. For the first type, we show that the spreading speeds are two constants whose signs change with the number of elements in some set. Moreover, we find an interesting phenomenon: the asymmetry of nonlocal dispersals can influence the propagating directions of solutions and the stability of steady states. For the second type, we show that the spreading speed is decreasing with respect to the exponentially decaying rate of initial data, and further, its minimum value coincides with the spreading speed for the first type. In addition, we give some results about the nonexistence of traveling wave solutions and the monotone property of solutions. Finally, some applications are presented to illustrate the theoretical results.

math.AP↗

arXiv2019

Relaxation Oscillations and the Entry-Exit Function in Multi-Dimensional Slow-Fast Systems

For a slow-fast system of the form $\dot{p}=εf(p,z,ε)+h(p,z,ε)$, $\dot{z}=g(p,z,ε)$ for $(p,z)\in \mathbb R^n\times \mathbb R^m$, we consider the scenario that the system has invariant sets $M_i=\{(p,z): z=z_i\}$, $1\le i\le N$, linked by a singular closed orbit formed by trajectories of the limiting slow and fast systems. Assuming that the stability of $M_i$ changes along the slow trajectories at certain turning points, we derive criteria for the existence and stability of relaxation oscillations for the slow-fast system. Our approach is based on a generalization of the entry-exit relation to systems with multi-dimensional fast variables. We then apply our criteria to several predator-prey systems with rapid ecological evolutionary dynamics to show the existence of relaxation oscillations in these models.

math.DS↗

arXiv2016

Prevention and control of Zika fever as a mosquito-borne and sexually transmitted disease

The ongoing Zika virus (ZIKV) epidemic poses a major global public health emergency. It is known that ZIKV is spread by \textit{Aedes} mosquitoes, recent studies show that ZIKV can also be transmitted via sexual contact and cases of sexually transmitted ZIKV have been confirmed in the U.S., France, and Italy. How sexual transmission affects the spread and control of ZIKV infection is not well-understood. We presented a mathematical model to investigate the impact of mosquito-borne and sexual transmission on spread and control of ZIKV and used the model to fit the ZIKV data in Brazil, Colombia, and El Salvador. Based on the estimated parameter values, we calculated the median and confidence interval of the basic reproduction number R0=2.055 (95% CI: 0.523-6.300), in which the distribution of the percentage of contribution by sexual transmission is 3.044 (95% CI: 0.123-45.73). Our study indicates that R0 is most sensitive to the biting rate and mortality rate of mosquitoes while sexual transmission increases the risk of infection and epidemic size and prolongs the outbreak. In order to prevent and control the transmission of ZIKV, it must be treated as not only a mosquito-borne disease but also a sexually transmitted disease.

q-bio.PE↗

arXiv2014

Traveling Wave Solutions for Delayed Reaction-Diffusion Systems and Applications to Lotka-Volterra Competition-Diffusion Models with Distributed Delays

This paper is concerned with the traveling wave solutions of delayed reaction-diffusion systems. By using Schauder's fixed point theorem, the existence of traveling wave solutions is reduced to the existence of generalized upper and lower solutions. Using the technique of contracting rectangles, the asymptotic behavior of traveling wave solutions for delayed diffusive systems is obtained. To illustrate our main results, the existence, nonexistence and asymptotic behavior of positive traveling wave solutions of diffusive Lotka-Volterra competition systems with distributed delays are established. The existence of nonmonotone traveling wave solutions of diffusive Lotka-Volterra competition systems is also discussed. In particular, it is proved that if there exists instantaneous self-limitation effect, then the large delays appearing in the intra-specific competitive terms may not affect the existence and asymptotic behavior of traveling wave solutions.

math.DS↗

arXiv2011

The decay rates of Traveling Waves for a class of Nonlocal Evolution Equations

We obtain the precise decay rates of traveling wave for a class of nonlocal evolution equations arising in the theory of phase transitions. We also investigate the spectrum of the operator obtained by linearizing at such a traveling wave. The detailed description of the spectrum is established.

math.CA↗

arXiv2009

Modelling hematopoiesis mediated by growth factors with applications to periodic hematological diseases

Hematopoiesis is a complex biological process that leads to the production and regulation of blood cells. It is based upon differentiation of stem cells under the action of growth factors. A mathematical approach of this process is proposed to carry out explanation on some blood diseases, characterized by oscillations in circulating blood cells. A system of three differential equations with delay, corresponding to the cell cycle duration, is analyzed. The existence of a Hopf bifurcation for a positive steady-state is obtained through the study of an exponential polynomial characteristic equation with delay-dependent coefficients. Numerical simulations show that long period oscillations can be obtained in this model, corresponding to a destabilization of the feedback regulation between blood cells and growth factors. This stresses the localization of periodic hematological diseases in the feedback loop.

math.CA↗

arXiv2009

Stability and Hopf bifurcation in a mathematical model of pluripotent stem cell dynamics

We study a mathematical model describing the dynamics of a pluripotent stem cell population involved in the blood production process in the bone marrow. This model is a differential equation with a time delay. The delay describes the cell cycle duration and is uniformly distributed on an interval. We obtain stability conditions independent of the delay. We also show that the distributed delay can destabilize the entire system. In particularly, it is shown that Hopf bifurcations can occur.

math.AP↗

arXiv2009

A mathematical study of the hematopoiesis process with applications to chronic myelogenous leukemia

This paper is devoted to the analysis of a mathematical model of blood cells production in the bone marrow (hematopoiesis). The model is a system of two age-structured partial differential equations. Integrating these equations over the age, we obtain a system of two nonlinear differential equations with distributed time delay corresponding to the cell cycle duration. This system describes the evolution of the total cell populations. By constructing a Lyapunov functional, it is shown that the trivial equilibrium is globally asymptotically stable if it is the only equilibrium. It is also shown that the nontrivial equilibrium, the most biologically meaningful one, can become unstable via a Hopf bifurcation. Numerical simulations are carried out to illustrate the analytical results. The study maybe helpful in understanding the connection between the relatively short cell cycle durations and the relatively long periods of peripheral cell oscillations in some periodic hematological diseases.

math.AP↗