Mathematical Biology:
The dynamics of many models in Biology and Ecology such as: epidemic models, tumor-immune models, chemostat models, prey-predator models, competitive models, and among others can be mathematically described. The traditional mathematical models are given by ordinary differential equation (ODE).
Long-standing and important questions in mathematical biology are that: How is the longtime behavior of the system? Does one group of populations come to extinct or persistent? Under which condition, the disease will be controlled in the epidemic systems? and among others.
I focus on such problems of the biological and ecological models and take the random factors (corresponding to stochastic systems), past-dependence (corresponding to delay systems), spatial inhomogeneity (corresponding to reaction-diffusion systems) into consideration together, which are described under stochastic differential equations (SDEs), stochastic functional differential equations (SFDEs) and stochastic partial differential equations (SPDEs) framework.
Related Publications:
Hybrid stochastic SIS epidemic models with vaccination: stability of the disease-free state and applications (with T. Hieu, D. Nguyen, T. Tuong), Nonlinear Analysis: Hybrid Systems, Vol. 53 (2024), 101492. [Journal] [pdf]
Analyzing a class of stochastic SIRS models under imperfect vaccination (with N. Hieu, D. Nguyen, G. Yin), Journal of the Franklin Institute, Vol. 361 (2024), 1284-1302. [Journal] [pdf]
Stochastic Multi-group Epidemic SVIR Models: Degenerate Case (with D. Nguyen, T. Tuong), Communications in Nonlinear Science and Numerical Simulation, Vol. 128 (2024), 107588. [Journal] [pdf]
Stochastic nutrient-plankton models (with A. Hening, N. Hieu, D. Nguyen), Journal of Differential Equations, Vol. 376 (2023), 370-405. [Journal] [arXiv]
A stochastic epidemic SIR model with hidden states (with N. Du, A. Hening, G. Yin), Nonlinear Analysis: Hybrid Systems, Vol. 49 (2023), 101368. [Journal] [arXiv]
Stochastic Kolmogorov Delay Equations I: Persistence (with D. Nguyen, G. Yin), Stochastic Processes and their Applications, Vol. 142 (2021), 319-364. [Journal] [arXiv]
Stochastic Functional Kolmogorov Equations II: Extinction (with D. Nguyen, G. Yin), Journal of Differential Equations, Vol. 294 (2021), 1-39. [Journal] [arXiv]
Stochastic Lotka-Volterra Competitive Reaction-Diffusion Systems Perturbed by Space-Time White Noise: Modeling and Analysis (with G. Yin), Journal of Differential Equations, Vol. 282 (2021), 184-232. [Journal] [arXiv]
Characterization of long-term behavior of stochastic NP ecological model under regime switching (with T. Tuong), Communications in Nonlinear Science and Numerical Simulation, Vol. 93 (2021), 105497. [Journal] [pdf]
Longtime behavior of a class of stochastic tumor-immune systems (with T. Tuong, G. Yin), Systems & Control Letters, Vol. 146 (2020), 104806. [Journal] [pdf]
Permanence and Extinction for the Stochastic SIR Epidemic Model (with N. Du), Journal of Differential Equations, Vol. 269 (2020), 9619-9652. [Journal] [arXiv]
General Nonlinear Stochastic Systems Motivated by Chemostat Models: Complete Characterization of Long-Time Behavior, Optimal Controls, and Applications to Wastewater Treatment (with D. Nguyen, G. Yin), Stochastic Processes and their Applications, Vol. 130 (2020), 4608-4642. [Journal] [arXiv]
Analysis of A Spatially Inhomogeneous Stochastic Partial Differential Equation Epidemic Model (with D. Nguyen, G. Yin), Journal of Applied Probability, Vol. 57 (2020), 613-636. [Journal] [arXiv]
Stochastic Partial Differential Equation Models for Spatially Dependent Predator-Prey Equations (with G. Yin), Discrete and Continuous Dynamical Systems-Series B, Vol. 25 (2020), 117-139. [Journal] [arXiv]
Stochastic Partial Differential Equation SIS Epidemic Models: Modeling and Analysis (with G. Yin), Communication on Stochastic Analysis, Vol. 13 (2019). [Journal] [pdf]
Conditions for Permanence and Ergodicity of Certain SIR Epidemic Models (with N. Dieu, N. Du), Acta Applicandae Mathematicae, Vol. 160 (2019), 81-99. [Journal] [pdf]
Permanence and extinction of certain stochastic SIR models perturbed by a complex type of noises (with N. Du), Applied Mathematics Letters, Vol. 64 (2017), 223-230. [Journal] [pdf]