arXiv subjects

Huaiping Zhu

Publications and source records attributed to Huaiping Zhu.

10 recordsLinked to original sources

arXiv2026

On a nonlocal dengue model with moving boundaries: The impact of dry-wet season and impulsive intervention

Seasonal succession and human intervention profoundly influence dengue fever transmission, and both humans and mosquito vectors can disperse over long distances. This paper proposes a nonlocal reaction-diffusion dengue model with moving boundaries that incorporates dry-wet seasonality and impulsive intervention. We first present the existence and uniqueness of the global solution to the model, then introduce the definition of the generalized principal eigenvalue, prove its uniqueness when the kernel functions coincide via the method of separation of variables, and further discuss its associated properties. Using this eigenvalue as an index, we obtain a spreading-vanishing dichotomy and derive two criteria that characterize the spreading and vanishing states, respectively. Our results extend both the nonlocal diffusion model without impulsive intervention and the model with impulsive intervention but without seasonal succession. Finally, we validate our theoretical findings and investigate how various factors affect dengue transmission through numerical simulations. The numerical results indicate that a shorter dry season makes disease containment more difficult, whereas more intensive impulsive intervention enhances control efficacy.

math.AP↗

arXiv2025

Universal differential equations for optimal control problems and its application on cancer therapy

This paper highlights a parallel between the forward backward sweeping method for optimal control and deep learning training procedures. We reformulate a classical optimal control problem, constrained by a differential equation system, into an optimization framework that uses neural networks to represent control variables. We demonstrate that this deep learning method adheres to Pontryagin Maximum Principle and mitigates numerical instabilities by employing backward propagation instead of a backward sweep for the adjoint equations. As a case study, we solve an optimal control problem to find the optimal combination of immunotherapy and chemotherapy. Our approach holds significant potential across various fields, including epidemiology, ecological modeling, engineering, and financial mathematics, where optimal control under complex dynamic constraints is crucial.

math.OC↗

arXiv2023

On an age-structured juvenile-adult model with harvesting pulse in moving and heterogeneous environment

This paper concerns an age-structured juvenile-adult model with harvesting pulse and moving boundaries in a heterogeneous environment, in which the moving boundaries describe the natural expanding front of species and human periodic pulse intervention is carried on the adults. The principal eigenvalue is firstly defined and its properties involving the intensity of harvesting and length of habitat sizes are analysed. Then the criteria to determine whether the species spread or vanish is discussed, and some relevant sufficient conditions characterized by pulse are established. Our results reveal that the co-extinction or coexistence of species is influenced by internal expanding capacities from species itself and external harvesting pulse from human intervention, in which the intensity and timing of harvesting play key roles. The final numerical approximations indicate that the larger the harvesting rate and the shorter the harvesting period, the worse the survival of all individuals due to the cooperation among juveniles and adults, and such harvesting pulse can even alter the situation of species, from persistence to extinction. In addition, expanding capacities also affect or alter the outcomes of spreading-vanishing

math.AP↗

arXiv2021

Detection of bistable structures via the Conley index and applications to biological systems

Bistability is a ubiquitous phenomenon in life sciences. In this paper, two kinds of bistable structures in dynamical systems are studied: One is two one-point attractors, another is a one-point attractor accompanied by a cycle attractor. By the Conley index theory, we prove that there exist other isolated invariant sets besides the two attractors, and also obtain the possible components and their configuration. Moreover, we find that there is always a separatrix or cycle separatrix, which separates the two attractors. Finally, the biological meanings and implications of these structures are given and discussed.

math.DS↗

arXiv2020

Four-tier response system and spatial propagation of COVID-19 in China by a network model

In order to investigate the effectiveness of lockdown and social distancing restrictions, which have been widely carried out as policy choice to curb the ongoing COVID-19 pandemic around the world, we formulate and discuss a staged and weighed networked system based on a classical SEAIR epidemiological model. Five stages have been taken into consideration according to four-tier response to Public Health Crisis, which comes from the National Contingency Plan in China. Staggered basic reproduction number has been derived and we evaluate the effectiveness of lockdown and social distancing policies under different scenarios among 19 cities/regions in mainland China. Further, we estimate the infection risk associated with the sequential release based on population mobility between cities and the intensity of some non-pharmaceutical interventions. Our results reveal that Level I public health emergency response is necessary for high-risk cities, which can flatten the COVID-19 curve effectively and quickly. Moreover, properly designed staggered-release policies are extremely significant for the prevention and control of COVID-19, furthermore, beneficial to economic activities and social stability and development.

physics.soc-ph↗

arXiv2020

A Data-Driven Network Model for the Emerging COVID-19 Epidemics in Wuhan, Toronto and Italy

The ongoing Coronavirus Disease 2019 (COVID-19) pandemic threatens the health of humans and causes great economic losses. Predictive modelling and forecasting the epidemic trends are essential for developing countermeasures to mitigate this pandemic. We develop a network model, where each node represents an individual and the edges represent contacts between individuals where the infection can spread. The individuals are classified based on the number of contacts they have each day (their node degrees) and their infection status. The transmission network model was respectively fitted to the reported data for the COVID-19 epidemic in Wuhan (China), Toronto (Canada), and the Italian Republic using a Markov Chain Monte Carlo (MCMC) optimization algorithm. Our model fits all three regions well with narrow confidence intervals and could be adapted to simulate other megacities or regions. The model projections on the role of containment strategies can help inform public health authorities to plan control measures.

q-bio.PE↗

arXiv2018

The spatial-temporal risk index and spreading dynamics for a time-periodic diffusive WNv model

This paper is concerned with a simplified epidemic model for West Nile virus in a heterogeneous time-periodic environment. By means of the model, we will explore the impact of spatial heterogeneity of environment and temporal periodicity on the persistence and eradication of West Nile virus. The free boundary is employed to represent the moving front of the infected region. The basic reproduction number $R_0^D$ and the spatial-temporal risk index $R_0^F(t)$, which depend on spatial heterogeneity, temporal periodicity and spatial diffusion, are defined by considering the associated linearized eigenvalue problem. Sufficient conditions for the spreading and vanishing of West Nile virus are presented for the spatial dynamics of the virus.

math.AP↗

arXiv2017

Spatial spreading model and dynamics of West Nile virus in birds and mosquitoes with free boundary

In this paper, a reaction-diffusion system is proposed to model the spatial spreading of West Nile virus in vector mosquitoes and host birds in North America. Infection dynamics are based on a simplified model for cross infection between mosquitoes and birds, and the free boundary is introduced to model and explore the expanding front of the infective region. The spatial-temporal risk index $R_0^F(t)$, which involves time and characters of the region, is defined for the simplified model with the free boundary to compare with other related threshold values, including the usual basic reproduction number $R_0$. Sufficient conditions for the virus to vanish or spread are given. Our results suggest that the virus will be in a scenario of vanishing if $R_0\leq 1$, and the virus will spread to the whole region if $R_{0}^F(t_0)\geq 1$ for some $t_0\geq 0$, while if $R^F_0(0)<1<R_0$, the spreading or vanishing of the virus depends on the initial numbers of infected mosquitoes and birds, the area of the infected region and diffusion rates. Moreover, some remarks on the basic reproduction numbers and the spreading speed are presented and compared.

math.AP↗

arXiv2015

A SIS reaction-diffusion-advection model in a low-risk and high-risk domain

A simplified SIS reaction-diffusion-advection model is proposed and investigated to understand the impact of spatial heterogeneity of environment and advection on the persistence and eradication of an infectious disease. The free boundary is introduced to model the contact transmission at the spreading front of the disease. The behavior of positive solutions to a reaction-diffusion-advection system are discussed. The basic reproduction number $R_0^F(t)$ associated with the diseases in the spatial setting is introduced for this diffusive SIS model with the free boundary, we prove that fast diffusion, small expanding rate and small initial infected domain are benefit for the control of the spatial spread of the disease. Sufficient conditions for the disease to be eradicated or to spread are also given, our result shows that the disease will spread to the whole area if there exists a $t_0\geq 0$ such that $R_{0}^F(t_0)\geq 1$, that is, if the spreading domain is high-risk at some time, the disease will continue to spread till the whole area is infected; while if $R_{0}^F(0)<1$, the disease may be vanishing or keep spreading depends on the expanding rate and the initial number of the infective individuals. The spreading speeds are also given when spreading happens, and numerical simulations are also given to illustrate the impacts of the advection and the expanding rate on the spreading fronts.

math.AP↗

arXiv2015

Finite cyclicity of some graphics through a nilpotent point of saddle type inside quadratic systems

In this paper we show the finite cyclicity of the two graphics $(I_{12}^1)$ and $(I_{13}^1)$ through a triple nilpotent point of saddle type inside quadratic vector fields. These results contribute to the program launched in 1994 by Dumortier, Roussarie and Rousseau (DRR program) to show the existence of a uniform upper bound for the number of limit cycles for planar quadratic vector fields.

math.CA↗