The sedentary behavior among college students has become one of the most important factors affecting the development of physical and mental health. Chronic lack of physical activity may lead to health problems such as decreased physical fitness, and increased psychological disorders. In the post-epidemic era, it is necessary for college students to have a strong immune system, and a strong body cannot be achieved without regular leisure physical activity. Therefore, it is necessary to explore the relationship between relevant health factors and physical activity. This paper presents an optimized COM-B model. And the experimental results show that the optimized model is well applied in describing the current situation of physical activity participation among college students, analyzing the distribution characteristics of socio-demographic variables related to physical activity, and exploring the correlation between physical activity and the subhealth status of college students.
Citation: Hanying Zhang, Zhongqiu Xu. The correlation between physical inactivity and students' health based on data mining and related influencing factors[J]. Mathematical Biosciences and Engineering, 2023, 20(4): 6735-6750. doi: 10.3934/mbe.2023290
[1] | Ke Guo, Wanbiao Ma . Global dynamics of an SI epidemic model with nonlinear incidence rate, feedback controls and time delays. Mathematical Biosciences and Engineering, 2021, 18(1): 643-672. doi: 10.3934/mbe.2021035 |
[2] | Yu Ji . Global stability of a multiple delayed viral infection model with general incidence rate and an application to HIV infection. Mathematical Biosciences and Engineering, 2015, 12(3): 525-536. doi: 10.3934/mbe.2015.12.525 |
[3] | Ardak Kashkynbayev, Daiana Koptleuova . Global dynamics of tick-borne diseases. Mathematical Biosciences and Engineering, 2020, 17(4): 4064-4079. doi: 10.3934/mbe.2020225 |
[4] | Xinran Zhou, Long Zhang, Tao Zheng, Hong-li Li, Zhidong Teng . Global stability for a class of HIV virus-to-cell dynamical model with Beddington-DeAngelis functional response and distributed time delay. Mathematical Biosciences and Engineering, 2020, 17(5): 4527-4543. doi: 10.3934/mbe.2020250 |
[5] | Pengyan Liu, Hong-Xu Li . Global behavior of a multi-group SEIR epidemic model with age structure and spatial diffusion. Mathematical Biosciences and Engineering, 2020, 17(6): 7248-7273. doi: 10.3934/mbe.2020372 |
[6] | A. M. Elaiw, N. H. AlShamrani . Analysis of an HTLV/HIV dual infection model with diffusion. Mathematical Biosciences and Engineering, 2021, 18(6): 9430-9473. doi: 10.3934/mbe.2021464 |
[7] | N. H. AlShamrani, A. M. Elaiw . Stability of an adaptive immunity viral infection model with multi-stages of infected cells and two routes of infection. Mathematical Biosciences and Engineering, 2020, 17(1): 575-605. doi: 10.3934/mbe.2020030 |
[8] | Ning Bai, Rui Xu . Mathematical analysis of an HIV model with latent reservoir, delayed CTL immune response and immune impairment. Mathematical Biosciences and Engineering, 2021, 18(2): 1689-1707. doi: 10.3934/mbe.2021087 |
[9] | Jinliang Wang, Jingmei Pang, Toshikazu Kuniya . A note on global stability for malaria infections model with latencies. Mathematical Biosciences and Engineering, 2014, 11(4): 995-1001. doi: 10.3934/mbe.2014.11.995 |
[10] | A. M. Elaiw, N. H. AlShamrani . Stability of HTLV/HIV dual infection model with mitosis and latency. Mathematical Biosciences and Engineering, 2021, 18(2): 1077-1120. doi: 10.3934/mbe.2021059 |
The sedentary behavior among college students has become one of the most important factors affecting the development of physical and mental health. Chronic lack of physical activity may lead to health problems such as decreased physical fitness, and increased psychological disorders. In the post-epidemic era, it is necessary for college students to have a strong immune system, and a strong body cannot be achieved without regular leisure physical activity. Therefore, it is necessary to explore the relationship between relevant health factors and physical activity. This paper presents an optimized COM-B model. And the experimental results show that the optimized model is well applied in describing the current situation of physical activity participation among college students, analyzing the distribution characteristics of socio-demographic variables related to physical activity, and exploring the correlation between physical activity and the subhealth status of college students.
As we know, one of the most common ways to study the asymptotic stability for a system of delay differential equations (DDEs) is the Lyapunov functional method. For DDEs, the Lyapunov-LaSalle theorem (see [6,Theorem 5.3.1] or [11,Theorem 2.5.3]) is often used as a criterion for the asymptotic stability of an autonomous (possibly nonlinear) delay differential system. It can be applied to analyse the dynamics properties for lots of biomathematical models described by DDEs, for example, virus infection models (see, e.g., [2,3,10,14]), microorganism flocculation models (see, e.g., [4,5,18]), wastewater treatment models (see, e.g., [16]), etc.
In the Lyapunov-LaSalle theorem, a Lyapunov functional plays an important role. But how to construct an appropriate Lyapunov functional to investigate the asymptotic stability of DDEs, is still a very profound and challenging topic.
To state our purpose, we take the following microorganism flocculation model with time delay in [4] as example:
{˙x(t)=1−x(t)−h1x(t)y(t),˙y(t)=rx(t−τ)y(t−τ)−y(t)−h2y(t)z(t),˙z(t)=1−z(t)−h3y(t)z(t), | (1.1) |
where
G={ϕ=(ϕ1,ϕ2,ϕ3)T∈C+:=C([−τ,0],R3+) : ϕ1≤1, ϕ3≤1}. |
In model (1.1), there exists a forward bifurcation or backward bifurcation under some conditions [4]. Thus, it is difficult to use the research methods that some virus models used to study the dynamics of such model.
Clearly, (1.1) always has a microorganism-free equilibrium
L(ϕ)=ϕ2(0)+r∫0−τϕ1(θ)ϕ2(θ)dθ, ϕ∈G. | (1.2) |
The derivative of
˙L(ut)=(rx(t)−1−h2z(t))y(t)≤(r−1−h2z(t))y(t). | (1.3) |
Obviously, if
However, we can not get
lim inft→∞z(t)≥h1h1+rh3. | (1.4) |
If
˙V(ut)≤[r−1−h1h2ε(h1+rh3)]y(t)≤0, t≥T. |
Obviously, for all
In this paper, we will expand the view of constructing Lyapunov functionals, namely, we first give a new understanding of Lyapunov-LaSalle theorem (including its modified version [9,15,19]), and based on it establish some global stability criteria for an autonomous delay differential system.
Let
˙u(t)=g(ut), t≥0, | (2.1) |
where
˙L(ϕ)=˙L(ϕ)|(2.1)=lim sups→0+L(us(ϕ))−L(ϕ)s. |
Let
u(t)=u(t,ϕ):=(u1(t,ϕ),u2(t,ϕ),⋯,un(t,ϕ))T |
denote a solution of system (2.1) satisfying
U(t):=ut(⋅):X→X (which also satisfies U(t):¯X→¯X), |
and for
OT(ϕ):={ut(ϕ):t≥T}. |
Let
The following Definition 2.1 and Theorem 2.1 (see, e.g., [6,Theorem 5.3.1], [11,Theorem 2.5.3]) can be utilized in dynamics analysis of lots of biomathematical models in the form of system (2.1).
Definition 2.1. We call
(ⅰ)
(ⅱ)
Theorem 2.1 (Lyapunov-LaSalle theorem [11]). Let
In Theorem 2.1, a Lyapunov functional
X={ϕ=(ϕ1,ϕ2,⋯,ϕn)T∈C:ϕi(0)>0}, | (2.2) |
which can ensure
However, we will assume that
Corollary 2.1. Let the solution
Proof. It is clear that if
Remark 2.1. It is not difficult to find that in the modified Lyapunov-LaSalle theorem (see, e.g., [9,15,19]), if
Remark 2.2. In fact, we can see that a bounded
From Corollary 2.1, we may consider the global properties of system (2.1) on the larger space than
Let
Theorem 3.1. Suppose that the following conditions hold:
(ⅰ) Let
˙L(φ)≤−w(φ)b(φ), | (3.1) |
where
(ⅱ) There exist
k1≤φ≤k2, w(φ)≥(w01,w02,⋯,w0k)≡w0=w0(k1,k2)≫0, |
and
Then
Proof. To obtain
lim inft→∞w(ut(ϕ)):=(lim inft→∞w1(ut(ϕ)),lim inft→∞w2(ut(ϕ)),⋯,lim inft→∞wk(ut(ϕ)))=(limm→∞f1(t1m),limm→∞f2(t2m),⋯,limm→∞fk(tkm)). |
For each sequence
lim inft→∞wi(ut(ϕ))=limm→∞wi(utim(ϕ))=wi(ϕi). |
By the condition (ⅱ),
˙L(φ)≤−w(φ)b(φ)≤−w0b(φ)2≤0. |
Hence,
Next, we show that
˙L(ut(ψ))≤−w(ut(ψ))b(ut(ψ)), ∀t≥0. |
By (ⅱ),
Remark 3.1. By
Next, we will give an illustration for Theorem 3.1. Now, we reconsider the global stability for the infection-free equilibrium
{˙x(t)=s−dx(t)−cx(t)y(t)−βx(t)v(t),˙y(t)=e−μτβx(t−τ)v(t−τ)−py(t),˙v(t)=ky(t)−uv(t), | (3.2) |
where
In [1], we know
G={ϕ∈C([−τ,0],R3+):ϕ1≤x0}⊂C+:=C([−τ,0],R3+). |
Indeed, by Theorem 3.1, we can extend the result of [1] to the larger set
Corollary 3.1. If
Proof. It is not difficult to obtain
L(ϕ)=ϕ1(0)−x0−x0lnϕ1(0)x0+a1ϕ2(0)+a1e−μτ∫0−τβϕ1(θ)ϕ3(θ)dθ+a2ϕ3(0), | (3.3) |
where
a1=2(kβx0+ucx0)pu−e−μτkβx0,a2=2(pβx0+e−μτcβx20)pu−e−μτkβx0. |
Let
w(φ)≡(dφ1(0),a1p−a2k−cx0,a2u−a1e−μτβφ1(0)−βx0)≥(dx0,a1p−a2k−cx0,a2u−a1e−μτβx0−βx0)=(dx0,cx0,βx0)≡w0≫0, |
where
The derivative of
˙L1(ut)=d(x0−x(t))(1−x0x(t))+x0(cy(t)+βv(t))−x(t)(cy(t)+βv(t))+a1e−μτβx(t)v(t)−a1py(t)+a2ky(t)−a2uv(t)≤−dx(t)(x0−x(t))2−(a1p−a2k−cx0)y(t)−(a2u−a1e−μτβx(t)−βx0)v(t)=−w(ut)b(ut). |
Therefore, it follows from Theorem 3.1 that
In [3,Theorem 3.1], the infection-free equilibrium
Theorem 3.2. In the condition (ii) of Theorem 3.1, if the condition that
Proof. In the foundation of the similar argument as in the proof of Theorem 3.1, we have that
˙L(ut(ψ))≤−w0b(ut(ψ))≤0. |
Hence,
Next, by using Theorem 3.2, we will give the global stability of the equilibrium
˙L(ut)≤−w(ut)b(ut), | (3.4) |
where
w(ut)=1+h2zt(0)−r=1+h2z(t)−r,b(ut)=yt(0)=y(t). |
Let
p(t)=rh1xt(−τ)+yt(0)=rh1x(t−τ)+y(t), t≥τ. |
Then we have
lim inft→∞x(t)≥1r+1, lim inft→∞z(t)≥h1h1+rh3. | (3.5) |
Thus, for any
(1/(r+1),0,h1/(h1+rh3))T≤φ≤(1,r/h1,1)T,w(φ)=1+h2φ3(0)−r≥1+h1h2/(h1+rh3)−r≡w0>0, |
and
Thus, we only need to obtain the solutions of a system are bounded and then may establish the upper- and lower-bound estimates of
Corollary 3.2. Let
a(φ(0))≤L(φ), ˙L(φ)≤−w0b(φ), 0≪wT0∈Rk, | (3.6) |
where
Proof. Since
a(u(t,ϕ))≤L(ut(ϕ))≤L(uT(ϕ)), t∈[T,εϕ), |
and the fact that
Corollary 3.3. Assume that
a(|φ(0)−E|)≤L(φ), ˙L(φ)≤−w0b(φ), 0≪wT0∈Rk, | (3.7) |
where
Proof. It follows from Corollary 3.2 that the boundedness of
ut(ϕ)∈B(ut(E),ε)=B(E,ε), |
where
a(|u(t,ϕ)−E|)≤L(ut(ϕ))≤L(uT(ϕ))<a(ε), |
which yields
Lemma 3.1. ([13,Lemma 1.4.2]) For any infinite positive definite function
By Lemma 3.1, we have the following remark.
Remark 3.2. If there exists an infinite positive definite function
Corollary 3.4. In Corollary 3.2, if the condition
For a dissipative system (2.1), we will give the upper- and lower-bound estimates of
Lemma 3.2. Let
Proof. For any
Theorem 3.3. Suppose that there exist
k1≤lim inft→∞ut(ϕ)(θ)≤lim supt→∞ut(ϕ)(θ)≤k2, ∀ϕ∈X, ∀θ∈[−τ,0], | (3.8) |
where
lim inft→∞ut(ϕ)(θ):=(lim inft→∞u1t(ϕ)(θ),⋯,lim inft→∞unt(ϕ)(θ))T,lim supt→∞ut(ϕ)(θ):=(lim supt→∞u1t(ϕ)(θ),⋯,lim supt→∞unt(ϕ)(θ))T. |
Then
Proof. Clearly,
|˙u(t,φ)|≤M1, ∀t≥0, ∀φ∈M. |
It follows from the invariance of
In this paper, we first give a variant of Theorem 2.1, see Corollary 2.1. In fact, the modified version of Lyapunov-LaSalle theorem (see, e.g., [9,15,19]) is to expand the condition (ⅰ) of Definition 2.1, while Corollary 2.1 is mainly to expand the condition (ⅱ) of Definition 2.1. More specifically, we assume that
As a result, the criteria for the global attractivity of equilibria of system (2.1) are given in Theorem 3.1 and Theorem 3.2, respectively. As direct consequences, we also give the corresponding particular cases of Theorem 3.1 and Theorem 3.2, see Corollaries 3.2, 3.3 and 3.4, respectively. The developed theory can be utilized in many models (see, e.g., [2,3,9,10,14]). The compactness and the upper- and lower-bound estimates of
This work was supported in part by the General Program of Science and Technology Development Project of Beijing Municipal Education Commission (No. KM201910016001), the Fundamental Research Funds for Beijing Universities (Nos. X18006, X18080 and X18017), the National Natural Science Foundation of China (Nos. 11871093 and 11471034). The authors would like to thank Prof. Xiao-Qiang Zhao for his valuable suggestions.
The authors declare there is no conflict of interest in this paper.
[1] |
A. K. Ghrouz, M. M. Noohu, D. Manzar, D. W. Spence, A. S. BaHammam, S. R. Pandi-Perumal, Physical activity and sleep quality in relation to mental health among college students, Sleep Breathing, 23 (2019), 627–634. https://doi.org/10.1007/s11325-019-01780-z doi: 10.1007/s11325-019-01780-z
![]() |
[2] |
C. Romero-Blanco, J. Rodríguez-Almagro, M. D. Onieva-Zafra, M. L. Parra-Fernández, M. D. C. Prado-Laguna, A. Hernández-Martínez, Physical activity and sedentary lifestyle in university students: changes during confinement due to the COVID-19 pandemic, Int. J. Environ. Res. Public Health, 17 (2020), 6567. https://doi.org/10.3390/ijerph17186567 doi: 10.3390/ijerph17186567
![]() |
[3] |
T. R. Snedden, J. Scerpella, S. A. Kliethermes, R. S. Norman, L. Blyholder, J. Sanfilippo, et al., Sport and physical activity level impacts health-related quality of life among collegiate students, Am. J. Health Promot., 33 (2019), 675–682. https://doi.org/10.1177/0890117118817715 doi: 10.1177/0890117118817715
![]() |
[4] |
Y. Zhang, H. Zhang, X. Ma, Q. Di, Mental health problems during the COVID-19 pandemics and the mitigation effects of exercise: a longitudinal study of college students in China, Int. J. Environ. Res. Public Health, 17 (2020), 3722. https://doi.org/10.3390/ijerph17103722 doi: 10.3390/ijerph17103722
![]() |
[5] |
L. Bertrand, K. A. Shaw, J. Ko, D. Deprez, P. D. Chilibeck, G. A. Zello, The impact of the coronavirus disease 2019 (COVID-19) pandemic on university students' dietary intake, physical activity, and sedentary behaviour, Appl. Physiol. Nutr. Metab., 46 (2021), 265–272. https://doi.org/10.1139/apnm-2020-0990 doi: 10.1139/apnm-2020-0990
![]() |
[6] |
N. E. Peterson, J. R. Sirard, P. A. Kulbok, M. D. DeBoer, J. M. Erickson, Sedentary behavior and physical activity of young adult university students, Res. Nurs. Health, 41 (2018), 30–38. https://doi.org/10.1002/nur.21845 doi: 10.1002/nur.21845
![]() |
[7] |
S. Sukys, V. J. Cesnaitiene, A. Emeljanovas, B. Mieziene, I. Valantine, Z. M. Ossowski, Reasons and barriers for university students' leisure-time physical activity: moderating effect of health education, Perceptual Motor Skills, 126 (2019), 1084–1100. https://doi.org/10.1177/0031512519869089 doi: 10.1177/0031512519869089
![]() |
[8] |
V. Violant-Holz, M. G. Gallego-Jiménez, C. S. González-González, S. Muñoz-Violant, M. J. Rodríguez, O. Sansano-Nadal, et al., Psychological health and physical activity levels during the COVID-19 pandemic: a systematic review, Int. J. Environ. Res. Public Health, 17 (2020), 9419. https://doi.org/10.3390/ijerph17249419 doi: 10.3390/ijerph17249419
![]() |
[9] |
M. H. Murphy, A. Carlin, C. Woods, A. Nevill, C. MacDonncha, K. Ferguson, et al., Active students are healthier and happier than their inactive peers: the results of a large representative cross-sectional study of university students in Ireland, J. Phys. Act. Health, 15 (2018), 737–746. https://doi.org/10.1123/jpah.2017-0432 doi: 10.1123/jpah.2017-0432
![]() |
[10] |
D. Schultchen, J. Reichenberger, T. Mittl, T. R. Weh, J. M. Smyth, J. Blechert, et al., Bidirectional relationship of stress and affect with physical activity and healthy eating, Br. J. Health Psychol., 24 (2019), 315–333. https://doi.org/10.1111/bjhp.12355 doi: 10.1111/bjhp.12355
![]() |
[11] |
Z. Zhang, W. Chen, A systematic review of the relationship between physical activity and happiness, J. Happiness Stud., 2 (2019), 1305–1322. https://doi.org/10.1007/s10902-018-9976-0 doi: 10.1007/s10902-018-9976-0
![]() |
[12] |
F. Wang, S. Boros, The effect of physical activity on sleep quality: a systematic review, Eur. J. Physiother., 23 (2021), 11–18. https://doi.org/10.1080/21679169.2019.1623314 doi: 10.1080/21679169.2019.1623314
![]() |
[13] |
F. Zurita-Ortega, S. San Román-Mata, R. Chacón-Cuberos, M. Castro-Sánchez, J. J. Muros, Adherence to the mediterranean diet is associated with physical activity, self-concept and sociodemographic factors in university student, Nutrients, 10 (2018), 966. https://doi.org/10.3390/nu10080966 doi: 10.3390/nu10080966
![]() |
[14] |
S. Dogra, L. MacIntosh, C. O'Neill, C. D'Silva, H. Shearer, K. Smith, et al., The association of physical activity with depression and stress among post-secondary school students: A systematic review, Mental Health Phys. Act., 14 (2018), 146–156. https://doi.org/10.1016/j.mhpa.2017.11.001 doi: 10.1016/j.mhpa.2017.11.001
![]() |
[15] |
E. Sharara, C. Akik, H. Ghattas, C. Makhlouf Obermeyer, Physical inactivity, gender and culture in Arab countries: a systematic assessment of the literature, BMC Public Health, 18 (2018), 1–19. https://doi.org/10.1186/s12889-018-5472-z doi: 10.1186/s12889-017-4524-0
![]() |
[16] |
E. L. Caputo, F. F. Reichert, Studies of physical activity and COVID-19 during the pandemic: a scoping review, J. Phys. Act. Health, 17 (2020), 1275–1284. https://doi.org/10.1123/jpah.2020-0406 doi: 10.1123/jpah.2020-0406
![]() |
[17] |
M. Pascoe, A. P. Bailey, M. Craike, T. Carter, R. Patten, N. Stepto, et al., Physical activity and exercise in youth mental health promotion: A scoping review, BMJ Open Sport Exercise Med., 6 (2020), e000677. https://doi.org/10.1136/bmjsem-2019-000677 doi: 10.1136/bmjsem-2019-000677
![]() |
[18] |
G. Maugeri, P. Castrogiovanni, G. Battaglia, R. Pippi, V. D'Agata, A. Palma, et al., The impact of physical activity on psychological health during Covid-19 pandemic in Italy, Heliyon, 6 (2020), e04315. https://doi.org/10.1016/j.heliyon.2020.e04315 doi: 10.1016/j.heliyon.2020.e04315
![]() |
[19] |
S. Stockwell, M. Trott, M. Tully, J. Shint, Y. Barnet, L. Butler, et al., Changes in physical activity and sedentary behaviours from before to during the COVID-19 pandemic lockdown: a systematic review, BMJ Open Sport Exercise Med., 7 (2021), e000960. https://doi.org/10.1136/bmjsem-2020-000960 doi: 10.1136/bmjsem-2020-000960
![]() |
[20] |
M. J. Savage, R. James, D. Magistro, J. Donaldson, L. C. Healy, M. Nevill, et al., Mental health and movement behaviour during the COVID-19 pandemic in UK university students: Prospective cohort study, Mental Health Phys. Act., 19 (2020), 100357. https://doi.org/10.1016/j.mhpa.2020.100357 doi: 10.1016/j.mhpa.2020.100357
![]() |
[21] |
B. Sañudo, C. Fennell, A. J. Sánchez-Oliver, Objectively-assessed physical activity, sedentary behavior, smartphone use, and sleep patterns pre-and during-COVID-19 quarantine in young adults from Spain, Sustainability, 12 (2020), 5890. https://doi.org/10.3390/su12155890 doi: 10.3390/su12155890
![]() |
[22] |
H. A. Alzamil, M. A. Alhakbany, N. A. Alfadda, S. M. Almusallam, H. M. Al-Hazzaa, A profile of physical activity, sedentary behaviors, sleep, and dietary habits of Saudi college female students, J. Fam. Community Med., 26 (2019), 1. https://doi.org/10.4103/jfcm.JFCM_58_18 doi: 10.4103/jfcm.JFCM_58_18
![]() |
[23] |
S. Panahi, A. Tremblay, Sedentariness and health: is sedentary behavior more than just physical inactivity, Front. Public Health, 6 (2018), 258. https://doi.org/10.3389/fpubh.2018.00258 doi: 10.3389/fpubh.2018.00258
![]() |
[24] |
Ó. Martínez-de-Quel, D. Suárez-Iglesias, M. López-Flores, C. A. Pérez, Physical activity, dietary habits and sleep quality before and during COVID-19 lockdown: A longitudinal study, Appetite, 158 (2021), 105019. https://doi.org/10.1016/j.appet.2020.105019 doi: 10.1016/j.appet.2020.105019
![]() |
[25] |
P. J. Puccinelli, T. S. da Costa, A. Seffrin, C. A. B. de Lira, R. L. Vancini, P. T. Nikolaidis, et al., Reduced level of physical activity during COVID-19 pandemic is associated with depression and anxiety levels: an internet-based survey, BMC Public Health, 21 (2021), 1–11. https://doi.org/10.1186/s12889-021-10684-1 doi: 10.1186/s12889-020-10013-y
![]() |
[26] |
J. Zhou, D. Zhang, W. Ren, W. Zhang, Auto color correction of underwater images utilizing depth information, IEEE Geosci. Remote Sens. Lett., 19 (2022), 1–5. https://doi.org/10.1109/LGRS.2022.3170702 doi: 10.1109/LGRS.2022.3170702
![]() |
[27] |
Y. Sun, J. Xu, H. Wu, G. Lin, S. Mumtaz, Deep learning based semi-supervised control for vertical security of maglev vehicle with guaranteed bounded airgap, IEEE Trans. Intell. Transp. Syst., 22 (2021), 4431–4442. https://doi.org/10.1109/TITS.2020.3045319 doi: 10.1109/TITS.2020.3045319
![]() |
1. | Jing-An Cui, Shifang Zhao, Songbai Guo, Yuzhen Bai, Xiaojing Wang, Tianmu Chen, Global dynamics of an epidemiological model with acute and chronic HCV infections, 2020, 103, 08939659, 106203, 10.1016/j.aml.2019.106203 | |
2. | Jinlong Lv, Songbai Guo, Jing-An Cui, Jianjun Paul Tian, Asymptomatic transmission shifts epidemic dynamics, 2021, 18, 1551-0018, 92, 10.3934/mbe.2021005 | |
3. | Yunzhe Su, Yajun Yang, Xuerong Yang, Wei Ye, Attitude tracking control for observation spacecraft flying around the target spacecraft, 2021, 15, 1751-8644, 1868, 10.1049/cth2.12165 | |
4. | Yujie Sheng, Jing-An Cui, Songbai Guo, The modeling and analysis of the COVID-19 pandemic with vaccination and isolation: a case study of Italy, 2023, 20, 1551-0018, 5966, 10.3934/mbe.2023258 | |
5. | Yu-zhen Bai, Xiao-jing Wang, Song-bai Guo, Global Stability of a Mumps Transmission Model with Quarantine Measure, 2021, 37, 0168-9673, 665, 10.1007/s10255-021-1035-7 | |
6. | Song-bai Guo, Min He, Jing-an Cui, Global Stability of a Time-delayed Malaria Model with Standard Incidence Rate, 2023, 0168-9673, 10.1007/s10255-023-1042-y | |
7. | Iasson Karafyllis, Pierdomenico Pepe, Antoine Chaillet, Yuan Wang, 2022, Uniform Global Asymptotic Stability for Time-Invariant Delay Systems, 978-1-6654-6761-2, 6875, 10.1109/CDC51059.2022.9992709 | |
8. | Iasson Karafyllis, Pierdomenico Pepe, Antoine Chaillet, Yuan Wang, Is Global Asymptotic Stability Necessarily Uniform for Time-Invariant Time-Delay Systems?, 2022, 60, 0363-0129, 3237, 10.1137/22M1485887 | |
9. | Leilei Xue, Liping Sun, Songbai Guo, Dynamic effects of asymptomatic infections on malaria transmission, 2023, 214, 03784754, 172, 10.1016/j.matcom.2023.07.004 | |
10. | 勇盛 赵, Dynamical Analysis of a COVID-19 Transmission Model with Vaccination, 2024, 13, 2324-7991, 1187, 10.12677/aam.2024.134109 | |
11. | Ke Guo, Songbai Guo, Lyapunov functionals for a general time-delayed virus dynamic model with different CTL responses, 2024, 34, 1054-1500, 10.1063/5.0204169 | |
12. | Songbai Guo, Min He, Fuxiang Li, Threshold dynamics of a time-delayed dengue virus infection model incorporating vaccination failure and exposed mosquitoes, 2025, 161, 08939659, 109366, 10.1016/j.aml.2024.109366 | |
13. | Songbai Guo, Qianqian Pan, Jing‐An Cui, P. Damith Nilanga Silva, Global behavior and optimal control of a dengue transmission model with standard incidence rates and self‐protection, 2024, 0170-4214, 10.1002/mma.10351 | |
14. | Songbai Guo, Xin Yang, Zuohuan Zheng, Global dynamics of a time-delayed malaria model with asymptomatic infections and standard incidence rate, 2023, 31, 2688-1594, 3534, 10.3934/era.2023179 | |
15. | Dongfang Li, Yilong Zhang, Wei Tong, Ping Li, Rob Law, Xin Xu, Limin Zhu, Edmond Q. Wu, Anti-Disturbance Path-Following Control for Snake Robots With Spiral Motion, 2023, 19, 1551-3203, 11929, 10.1109/TII.2023.3254534 | |
16. | 欣 李, Dynamic Analysis of a Syphilis Infectious Disease Model with Early Screening, 2024, 13, 2324-7991, 3722, 10.12677/aam.2024.138355 | |
17. | Songbai Guo, Yuling Xue, Rong Yuan, Maoxing Liu, An improved method of global dynamics: Analyzing the COVID-19 model with time delays and exposed infection, 2023, 33, 1054-1500, 10.1063/5.0144553 | |
18. | Xiaojing Wang, Jiahui Li, Songbai Guo, Maoxing Liu, Dynamic analysis of an Ebola epidemic model incorporating limited medical resources and immunity loss, 2023, 69, 1598-5865, 4229, 10.1007/s12190-023-01923-2 |