Explicit Lyapunov functions for SIR and SEIR compartmental
epidemic models with nonlinear incidence of the form
for the case
are constructed. Global stability of the models is thereby established.
Citation: Andrei Korobeinikov, Philip K. Maini. A Lyapunov function and global properties for SIR and SEIR epidemiological models with nonlinear incidence[J]. Mathematical Biosciences and Engineering, 2004, 1(1): 57-60. doi: 10.3934/mbe.2004.1.57
Related Papers:
[1]
Andrey V. Melnik, Andrei Korobeinikov .
Lyapunov functions and global stability for SIR and SEIR models withage-dependent susceptibility. Mathematical Biosciences and Engineering, 2013, 10(2): 369-378.
doi: 10.3934/mbe.2013.10.369
[2]
Yoichi Enatsu, Yukihiko Nakata .
Stability and bifurcation analysis of epidemic models with saturated incidence rates: An application to a nonmonotone incidence rate. Mathematical Biosciences and Engineering, 2014, 11(4): 785-805.
doi: 10.3934/mbe.2014.11.785
[3]
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
[4]
James M. Hyman, Jia Li .
Differential susceptibility and infectivity epidemic models. Mathematical Biosciences and Engineering, 2006, 3(1): 89-100.
doi: 10.3934/mbe.2006.3.89
[5]
Jinliang Wang, Ran Zhang, Toshikazu Kuniya .
A note on dynamics of an age-of-infection cholera model. Mathematical Biosciences and Engineering, 2016, 13(1): 227-247.
doi: 10.3934/mbe.2016.13.227
[6]
C. Connell McCluskey .
Global stability of an epidemic model with delay and general nonlinear incidence. Mathematical Biosciences and Engineering, 2010, 7(4): 837-850.
doi: 10.3934/mbe.2010.7.837
[7]
Gang Huang, Edoardo Beretta, Yasuhiro Takeuchi .
Global stability for epidemic
model with constant latency and infectious periods. Mathematical Biosciences and Engineering, 2012, 9(2): 297-312.
doi: 10.3934/mbe.2012.9.297
[8]
Abdennasser Chekroun, Mohammed Nor Frioui, Toshikazu Kuniya, Tarik Mohammed Touaoula .
Global stability of an age-structured epidemic model with general Lyapunov functional. Mathematical Biosciences and Engineering, 2019, 16(3): 1525-1553.
doi: 10.3934/mbe.2019073
[9]
Ardak Kashkynbayev, Daiana Koptleuova .
Global dynamics of tick-borne diseases. Mathematical Biosciences and Engineering, 2020, 17(4): 4064-4079.
doi: 10.3934/mbe.2020225
[10]
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
Abstract
Explicit Lyapunov functions for SIR and SEIR compartmental
epidemic models with nonlinear incidence of the form
for the case
are constructed. Global stability of the models is thereby established.
This article has been cited by:
1.
Zhipeng Qiu, Michael Y. Li, Zhongwei Shen,
Global dynamics of an infinite dimensional epidemic model with nonlocal state structures,
2018,
265,
00220396,
5262,
10.1016/j.jde.2018.06.036
2.
Samuel Bowong, Jean Jules Tewa,
Global analysis of a dynamical model for transmission of tuberculosis with a general contact rate,
2010,
15,
10075704,
3621,
10.1016/j.cnsns.2010.01.007
3.
Daihai He, David J.D. Earn,
Epidemiological effects of seasonal oscillations in birth rates,
2007,
72,
00405809,
274,
10.1016/j.tpb.2007.04.004
4.
Md Abdul Kuddus, Emma S. McBryde, Adeshina I. Adekunle, Lisa J. White, Michael T. Meehan,
Mathematical analysis of a two-strain disease model with amplification,
2021,
143,
09600779,
110594,
10.1016/j.chaos.2020.110594
5.
Divine Wanduku,
Threshold conditions for a family of epidemic dynamic models for malaria with distributed delays in a non-random environment,
2018,
11,
1793-5245,
1850085,
10.1142/S1793524518500857
6.
Hongbin Guo, Michael Y. Li,
Global dynamics of a staged-progression model with amelioration for infectious diseases,
2008,
2,
1751-3758,
154,
10.1080/17513750802120877
7.
Yong Tian, Xuejun Ding,
Rumor spreading model with considering debunking behavior in emergencies,
2019,
363,
00963003,
124599,
10.1016/j.amc.2019.124599
Junli Liu, Baoyang Peng, Tailei Zhang,
Effect of discretization on dynamical behavior of SEIR and SIR models with nonlinear incidence,
2015,
39,
08939659,
60,
10.1016/j.aml.2014.08.012
10.
Dessalegn Y. Melesse, Abba B. Gumel,
Global asymptotic properties of an SEIRS model with multiple infectious stages,
2010,
366,
0022247X,
202,
10.1016/j.jmaa.2009.12.041
11.
Yu Yang, Liguang Xu,
Stability of a fractional order SEIR model with general incidence,
2020,
105,
08939659,
106303,
10.1016/j.aml.2020.106303
12.
Muhammad Altaf Khan, Muhammad Ismail, Saif Ullah, Muhammad Farhan,
Fractional order SIR model with generalized incidence rate,
2020,
5,
2473-6988,
1856,
10.3934/math.2020124
13.
Abderrhaman Iggidr, Jean‐Claude Kamgang, Gauthier Sallet, Jean‐Jules Tewa,
Global Analysis of New Malaria Intrahost Models with a Competitive Exclusion Principle,
2006,
67,
0036-1399,
260,
10.1137/050643271
14.
R. N. Mohapatra, Donald Porchia, Zhisheng Shuai,
2015,
Chapter 51,
978-81-322-2484-6,
619,
10.1007/978-81-322-2485-3_51
15.
Zuzana Chladná, Jana Kopfová, Dmitrii Rachinskii, Samiha C. Rouf,
Global dynamics of SIR model with switched transmission rate,
2020,
80,
0303-6812,
1209,
10.1007/s00285-019-01460-2
16.
Haitao Song, Shengqiang Liu, Weihua Jiang,
Global dynamics of a multistage SIR model with distributed delays and nonlinear incidence rate,
2016,
01704214,
10.1002/mma.4130
17.
C. Connell McCluskey,
Using Lyapunov Functions to Construct Lyapunov Functionals for Delay Differential Equations,
2015,
14,
1536-0040,
1,
10.1137/140971683
18.
Paul Georgescu, Ying-Hen Hsieh,
Global Dynamics of a Predator-Prey Model with Stage Structure for the Predator,
2007,
67,
0036-1399,
1379,
10.1137/060670377
19.
Xinzhi Liu, Peter Stechlinski,
Infectious disease models with time-varying parameters and general nonlinear incidence rate,
2012,
36,
0307904X,
1974,
10.1016/j.apm.2011.08.019
20.
Modeling the effects of carriers on transmission dynamics of infectious diseases,
2011,
8,
1551-0018,
711,
10.3934/mbe.2011.8.711
21.
Sarbaz H. A. Khoshnaw, Najem A. Mohammad, Rizgar H. Salih,
Identifying Critical Parameters in SIR Model for Spread of Disease,
2017,
05,
2327-4018,
32,
10.4236/ojmsi.2017.51003
22.
Andrei Korobeinikov,
Lyapunov Functions and Global Stability for SIR and SIRS Epidemiological Models with Non-Linear Transmission,
2006,
68,
0092-8240,
615,
10.1007/s11538-005-9037-9
23.
Juping Zhang, Zhen Jin, Yuming Chen,
Analysis of sexually transmitted disease spreading in heterosexual and homosexual populations,
2013,
242,
00255564,
143,
10.1016/j.mbs.2013.01.005
24.
A. Mhlanga, C. P. Bhunu, S. Mushayabasa,
HSV-2 and Substance Abuse amongst Adolescents: Insights through Mathematical Modelling,
2014,
2014,
1110-757X,
1,
10.1155/2014/104819
25.
Zhidong Teng, Lei Wang, Linfei Nie,
Global attractivity for a class of delayed discrete SIRS epidemic models with general nonlinear incidence,
2015,
38,
01704214,
4741,
10.1002/mma.3389
26.
E.H. Elbasha, C.N. Podder, A.B. Gumel,
Analyzing the dynamics of an SIRS vaccination model with waning natural and vaccine-induced immunity,
2011,
12,
14681218,
2692,
10.1016/j.nonrwa.2011.03.015
27.
C. P. BHUNU,
MODELING THE SPREAD OF STREET KIDS IN ZIMBABWE,
2014,
22,
0218-3390,
429,
10.1142/S0218339014500168
28.
Bradley G. Wagner, David J.D. Earn,
Population dynamics of live-attenuated virus vaccines,
2010,
77,
00405809,
79,
10.1016/j.tpb.2009.08.003
29.
Liang Zhang, Zhi-Cheng Wang,
Threshold dynamics of a reaction-diffusion epidemic model with stage structure,
2017,
22,
1553-524X,
3797,
10.3934/dcdsb.2017191
30.
Gang Huang, Yasuhiro Takeuchi,
Global analysis on delay epidemiological dynamic models with nonlinear incidence,
2011,
63,
0303-6812,
125,
10.1007/s00285-010-0368-2
31.
S. Mushayabasa, C.P. Bhunu, C. Webb, M. Dhlamini,
A mathematical model for assessing the impact of poverty on yaws eradication,
2012,
36,
0307904X,
1653,
10.1016/j.apm.2011.09.022
C. P. Bhunu, A. N. Mhlanga, S. Mushayabasa,
Exploring the Impact of Prostitution on HIV/AIDS Transmission,
2014,
2014,
2356-7872,
1,
10.1155/2014/651025
34.
S.M. Ashrafur Rahman, Xingfu Zou,
Modelling the impact of vaccination on infectious diseases dynamics,
2015,
9,
1751-3758,
307,
10.1080/17513758.2014.986545
35.
Yuji Li, Rui Xu, Jiazhe Lin,
The stability analysis of an epidemic model with saturating incidence and age-structure in the exposed and infectious classes,
2018,
2018,
1687-1847,
10.1186/s13662-018-1635-6
36.
Andrei Korobeinikov,
Global Properties of SIR and SEIR Epidemic Models with Multiple Parallel Infectious Stages,
2009,
71,
0092-8240,
75,
10.1007/s11538-008-9352-z
37.
A. Elazzouzi, A. Lamrani Alaoui, M. Tilioua, A. Tridane,
Global stability analysis for a generalized delayed SIR model with vaccination and treatment,
2019,
2019,
1687-1847,
10.1186/s13662-019-2447-z
38.
Elvira Barbera, Giancarlo Consolo, Giovanna Valenti,
Spread of infectious diseases in a hyperbolic reaction-diffusion susceptible-infected-removed model,
2013,
88,
1539-3755,
10.1103/PhysRevE.88.052719
39.
Jinliang Wang, Ran Zhang, Toshikazu Kuniya,
The dynamics of an SVIR epidemiological model with infection age: Table 1.,
2016,
81,
0272-4960,
321,
10.1093/imamat/hxv039
40.
Pablo G. Barrientos, J. Ángel Rodríguez, Alfonso Ruiz-Herrera,
Chaotic dynamics in the seasonally forced SIR epidemic model,
2017,
75,
0303-6812,
1655,
10.1007/s00285-017-1130-9
41.
Samuel Bowong, Jurgen Kurths,
Modeling and analysis of the transmission dynamics of tuberculosis without and with seasonality,
2012,
67,
0924-090X,
2027,
10.1007/s11071-011-0127-y
42.
Yu Yang, Cuimei Zhang, Xunyan Jiang,
Global stability of an SEIQV epidemic model with general incidence rate,
2015,
08,
1793-5245,
1550020,
10.1142/S1793524515500205
43.
Zhisheng Shuai, P. van den Driessche,
Global Stability of Infectious Disease Models Using Lyapunov Functions,
2013,
73,
0036-1399,
1513,
10.1137/120876642
44.
Yijun Lou, Jianhong Wu,
Tick seeking assumptions and their implications for Lyme disease predictions,
2014,
17,
1476945X,
99,
10.1016/j.ecocom.2013.11.003
45.
Global properties of a delayed SIR epidemic
model with multiple parallel infectious stages,
2012,
9,
1551-0018,
685,
10.3934/mbe.2012.9.685
46.
Swarnali Sharma, G. P. Samanta,
A ratio-dependent predator-prey model with Allee effect and disease in prey,
2015,
47,
1598-5865,
345,
10.1007/s12190-014-0779-0
47.
Jinliang Wang, Min Guo, Xianning Liu, Zhitao Zhao,
Threshold dynamics of HIV-1 virus model with cell-to-cell transmission, cell-mediated immune responses and distributed delay,
2016,
291,
00963003,
149,
10.1016/j.amc.2016.06.032
JEAN M. TCHUENCHE, CHRISTINAH CHIYAKA,
STABILITY ANALYSIS OF A TRITROPHIC FOOD CHAIN MODEL WITH AN ADAPTIVE PARAMETER FOR THE PREDATOR,
2008,
22,
08908575,
237,
10.1111/j.1939-7445.2008.00035.x
50.
Xichao Duan, Sanling Yuan, Zhipeng Qiu, Junling Ma,
Global stability of an SVEIR epidemic model with ages of vaccination and latency,
2014,
68,
08981221,
288,
10.1016/j.camwa.2014.06.002
51.
Luju Liu, Yicang Zhou, Jianhong Wu,
Global Dynamics in a TB Model Incorporating Case Detection And Two Treatment Stages,
2008,
38,
0035-7596,
10.1216/RMJ-2008-38-5-1541
52.
S. M. Ashrafur Rahman, Xingfu Zou,
Flu epidemics: a two-strain flu model with a single vaccination,
2011,
5,
1751-3758,
376,
10.1080/17513758.2010.510213
53.
Gilberto C. González-Parra, Diego F. Aranda, Benito Chen-Charpentier, Miguel Díaz-Rodríguez, Jaime E. Castellanos,
Mathematical Modeling and Characterization of the Spread of Chikungunya in Colombia,
2019,
24,
2297-8747,
6,
10.3390/mca24010006
54.
S M O'Regan,
Impact of seasonality upon the dynamics of a novel pathogen in a seabird colony,
2008,
138,
1742-6596,
012017,
10.1088/1742-6596/138/1/012017
55.
Hongquan Sun, Jin Li,
A numerical method for a diffusive virus model with general incidence function, cell-to-cell transmission and time delay,
2020,
545,
03784371,
123477,
10.1016/j.physa.2019.123477
56.
Dan Li, Wanbiao Ma, Zhichao Jiang,
An Epidemic Model for Tick-Borne Disease with Two Delays,
2013,
2013,
1110-757X,
1,
10.1155/2013/427621
57.
Gang Huang, Yueping Dong,
A note on global properties for a stage structured predator–prey model with mutual interference,
2018,
2018,
1687-1847,
10.1186/s13662-018-1767-8
58.
Nicholas Kwasi-Do Ohene Opoku, Cecilia Afriyie,
The Role of Control Measures and the Environment in the Transmission Dynamics of Cholera,
2020,
2020,
1085-3375,
1,
10.1155/2020/2485979
59.
Impact of heterogeneity on the dynamics of an SEIR epidemic model,
2012,
9,
1551-0018,
393,
10.3934/mbe.2012.9.393
60.
Swarnali Sharma, G. P. Samanta,
Stability analysis and optimal control of an epidemic model with vaccination,
2015,
08,
1793-5245,
1550030,
10.1142/S1793524515500308
61.
Samuel Bowong, Jean Jules Tewa,
Mathematical analysis of a tuberculosis model with differential infectivity,
2009,
14,
10075704,
4010,
10.1016/j.cnsns.2009.02.017
62.
Yijun Lou, Xiao-Qiang Zhao,
Modelling Malaria Control by Introduction of Larvivorous Fish,
2011,
73,
0092-8240,
2384,
10.1007/s11538-011-9628-6
63.
Ellina V. Grigorieva, Evgenii N. Khailov, Andrei Korobeinikov,
Optimal Controls of the Highly Active Antiretroviral Therapy,
2020,
2020,
1085-3375,
1,
10.1155/2020/8107106
64.
Hai-Feng Huo, Shuai-Jun Dang, Yu-Ning Li,
Stability of a Two-Strain Tuberculosis Model with General Contact Rate,
2010,
2010,
1085-3375,
1,
10.1155/2010/293747
65.
Gang Huang, Anping Liu,
A note on global stability for a heroin epidemic model with distributed delay,
2013,
26,
08939659,
687,
10.1016/j.aml.2013.01.010
66.
Jinliang Wang, Xianning Liu,
Modeling diseases with latency and nonlinear incidence rates: global dynamics of a multi-group model,
2016,
39,
01704214,
1964,
10.1002/mma.3613
67.
Yanan Zhao, Xiaoying Zhang, Donal O'Regan,
THRESHOLD DYNAMICS IN A STOCHASTIC SIRS EPIDEMIC MODEL WITH NONLINEAR INCIDENCE RATE,
2019,
9,
2156-907X,
2096,
10.11948/20180041
68.
Zhisheng Shuai, Joseph H. Tien, P. van den Driessche,
Cholera Models with Hyperinfectivity and Temporary Immunity,
2012,
74,
0092-8240,
2423,
10.1007/s11538-012-9759-4
69.
Xiaoming Fan, Zhigang Wang, Xuelian Xu,
Global Stability of Two-Group Epidemic Models with Distributed Delays and Random Perturbation,
2012,
2012,
1085-3375,
1,
10.1155/2012/132095
70.
Elamin H. Elbasha,
Global Stability of Equilibria in a Two-Sex HPV Vaccination Model,
2008,
70,
0092-8240,
10.1007/s11538-007-9283-0
71.
Xiaomei Ren, Tiansi Zhang,
Global Analysis of an SEIR Epidemic Model with a Ratio-Dependent Nonlinear Incidence Rate,
2017,
05,
2327-4352,
2311,
10.4236/jamp.2017.512188
72.
Wang Shaoli, Feng Xinlong, He Yinnian,
Global asymptotical properties for a diffused HBV infection model with CTL immune response and nonlinear incidence,
2011,
31,
02529602,
1959,
10.1016/S0252-9602(11)60374-3
73.
Hongquan Sun, Jinliang Wang,
Dynamics of a diffusive virus model with general incidence function, cell-to-cell transmission and time delay,
2019,
77,
08981221,
284,
10.1016/j.camwa.2018.09.032
Andrei Korobeinikov,
Global Properties of Infectious Disease Models with Nonlinear Incidence,
2007,
69,
0092-8240,
1871,
10.1007/s11538-007-9196-y
76.
Ram Singh, Madhu Jain, Shoket Ali,
2016,
Mathematical analysis of transmission dynamics of tuberculosis with recurrence based on treatment,
978-1-4673-9939-5,
2990,
10.1109/ICEEOT.2016.7755248
77.
Haitao Song, Weihua Jiang, Shengqiang Liu,
Global dynamics of two heterogeneous SIR models with nonlinear incidence and delays,
2016,
09,
1793-5245,
1650046,
10.1142/S1793524516500467
78.
C. P. Bhunu, S. Mushayabasa, J. M. Tchuenche,
A Theoretical Assessment of the Effects of Smoking on the Transmission Dynamics of Tuberculosis,
2011,
73,
0092-8240,
1333,
10.1007/s11538-010-9568-6
79.
Global stability for epidemic
model with constant latency and infectious periods,
2012,
9,
1551-0018,
297,
10.3934/mbe.2012.9.297
80.
Muhammad Altaf Khan, Qaisar Badshah, Saeed Islam, Ilyas Khan, Sharidan Shafie, Sher Afzal Khan,
Global dynamics of SEIRS epidemic model with non-linear generalized incidences and preventive vaccination,
2015,
2015,
1687-1847,
10.1186/s13662-015-0429-3
81.
C.Y. Chen, J.P. Ward, W.B. Xie,
Modelling the outbreak of infectious disease following mutation from a non-transmissible strain,
2019,
126,
00405809,
1,
10.1016/j.tpb.2018.08.002
82.
Hongbin Guo, Michael Y. Li,
Global dynamics of a staged-progression model for HIV/AIDS with amelioration,
2011,
12,
14681218,
2529,
10.1016/j.nonrwa.2011.02.021
83.
Sveir epidemiological model with varying infectivity and distributed delays,
2011,
8,
1551-0018,
875,
10.3934/mbe.2011.8.875
84.
Jonathan Horrocks, Chris T. Bauch,
Algorithmic discovery of dynamic models from infectious disease data,
2020,
10,
2045-2322,
10.1038/s41598-020-63877-w
85.
Aadil Lahrouz, Lahcen Omari, Driss Kiouach, Aziza Belmaâti,
Complete global stability for an SIRS epidemic model with generalized non-linear incidence and vaccination,
2012,
218,
00963003,
6519,
10.1016/j.amc.2011.12.024
86.
v b,
Test high volume of citations,
2012,
4,
0037-7333,
28,
10.5555/20120925-a1
87.
Lei Wang, Zhidong Teng, Long Zhang,
Global Behaviors of a Class of Discrete SIRS Epidemic Models with Nonlinear Incidence Rate,
2014,
2014,
1085-3375,
1,
10.1155/2014/249623
88.
Jean M. Tchuenche, Chris T. Bauch,
Dynamics of an Infectious Disease Where Media Coverage Influences Transmission,
2012,
2012,
2090-7702,
1,
10.5402/2012/581274
89.
Zhisheng Shuai, P. van den Driessche,
Global dynamics of cholera models with differential infectivity,
2011,
234,
00255564,
118,
10.1016/j.mbs.2011.09.003
90.
N.H. AlShamrani, A.M. Elaiw, H. Batarfi, A.D. Hobiny, H. Dutta,
Global stability analysis of a general nonlinear scabies dynamics model,
2020,
138,
09600779,
110133,
10.1016/j.chaos.2020.110133
91.
Abderrazak Nabti, Behzad Ghanbari,
Global stability analysis of a fractional SVEIR epidemic model,
2021,
0170-4214,
10.1002/mma.7285
92.
Guanghua Chen, Huizhang Shen, Guangming Chen, Teng Ye, Xiangbin Tang, Naphtali Kerr,
A new kinetic model to discuss the control of panic spreading in emergency,
2015,
417,
03784371,
345,
10.1016/j.physa.2014.09.055
93.
Swarnali Sharma, G.P. Samanta,
A Leslie–Gower predator–prey model with disease in prey incorporating a prey refuge,
2015,
70,
09600779,
69,
10.1016/j.chaos.2014.11.010
94.
Z. Mukandavire, W. Garira, J.M. Tchuenche,
Modelling effects of public health educational campaigns on HIV/AIDS transmission dynamics,
2009,
33,
0307904X,
2084,
10.1016/j.apm.2008.05.017
95.
D. Okuonghae,
Lyapunov functions and global properties of some tuberculosis models,
2015,
48,
1598-5865,
421,
10.1007/s12190-014-0811-4
Joaquim P. Mateus, César M. Silva,
Existence of periodic solutions of a periodic SEIRS model with general incidence,
2017,
34,
14681218,
379,
10.1016/j.nonrwa.2016.09.013
98.
Xia Wang, Yuming Chen, Shengqiang Liu,
Dynamics of an age‐structured host‐vector model for malaria transmission,
2018,
41,
0170-4214,
1966,
10.1002/mma.4723
99.
S M O'Regan, T C Kelly, A Korobeinikov, M J A O'Callaghan, A V Pokrovskii,
Qualitative and numerical investigations of the impact of a novel pathogen on a seabird colony,
2008,
138,
1742-6596,
012018,
10.1088/1742-6596/138/1/012018
100.
K. Nudee, S. Chinviriyasit, W. Chinviriyasit,
The effect of backward bifurcation in controlling measles transmission by vaccination,
2019,
123,
09600779,
400,
10.1016/j.chaos.2019.04.026
101.
Ling Zhang, Jingmei Pang, Jinliang Wang,
Stability Analysis of a Multigroup Epidemic Model with General Exposed Distribution and Nonlinear Incidence Rates,
2013,
2013,
1085-3375,
1,
10.1155/2013/354287
102.
Suzanne M. O’Regan, Thomas C. Kelly, Andrei Korobeinikov, Michael J.A. O’Callaghan, Alexei V. Pokrovskii,
Lyapunov functions for SIR and SIRS epidemic models,
2010,
23,
08939659,
446,
10.1016/j.aml.2009.11.014
103.
Shu Liao, Jin Wang,
Global stability analysis of epidemiological models based on Volterra–Lyapunov stable matrices,
2012,
45,
09600779,
966,
10.1016/j.chaos.2012.03.009
104.
Jean Claude Kamgang, Christopher Penniman Thron,
Analysis of Malaria Control Measures’ Effectiveness Using Multistage Vector Model,
2019,
81,
0092-8240,
4366,
10.1007/s11538-019-00637-6
105.
Ricardo Almeida, Artur M. C. Brito da Cruz, Natália Martins, M. Teresa T. Monteiro,
An epidemiological MSEIR model described by the Caputo fractional derivative,
2019,
7,
2195-268X,
776,
10.1007/s40435-018-0492-1
106.
GLOBAL DYNAMICS OF A REACTION AND DIFFUSION MODEL FOR AN HTLV-I INFECTION WITH MITOTIC DIVISION OF ACTIVELY INFECTED CELLS,
2017,
7,
2156-907X,
899,
10.11948/2017057
107.
Piu Samui, Jayanta Mondal, Subhas Khajanchi,
A mathematical model for COVID-19 transmission dynamics with a case study of India,
2020,
140,
09600779,
110173,
10.1016/j.chaos.2020.110173
108.
C. P. Bhunu, W. Garira, G. Magombedze,
Mathematical Analysis of a Two Strain HIV/AIDS Model with Antiretroviral Treatment,
2009,
57,
0001-5342,
361,
10.1007/s10441-009-9080-2
109.
Shuyu Han, Chengxia Lei,
Global stability of equilibria of a diffusive SEIR epidemic model with nonlinear incidence,
2019,
98,
08939659,
114,
10.1016/j.aml.2019.05.045
110.
Aberrahman Iggidr, Gauthier Sallet, Max O. Souza,
On the dynamics of a class of multi-group models for vector-borne diseases,
2016,
441,
0022247X,
723,
10.1016/j.jmaa.2016.04.003
111.
C. Connell McCluskey,
Global stability for a class of mass action systems allowing for latency in tuberculosis,
2008,
338,
0022247X,
518,
10.1016/j.jmaa.2007.05.012
112.
Cong Jin, Xiao-Yan Wang,
Analysis and control stratagems of flash disk virus dynamic propagation model,
2012,
5,
19390114,
226,
10.1002/sec.310
113.
Hongbin Guo, Michael Yi Li,
Impacts of migration and immigration on disease transmission dynamics in heterogeneous populations,
2012,
17,
1553-524X,
2413,
10.3934/dcdsb.2012.17.2413
114.
C. Connell McCluskey,
Global stability for an model of infectious disease with age structure and immigration of infecteds,
2016,
13,
1551-0018,
381,
10.3934/mbe.2015008
115.
P. Magal, C.C. McCluskey, G.F. Webb,
Lyapunov functional and global asymptotic stability for an infection-age model,
2010,
89,
0003-6811,
1109,
10.1080/00036810903208122
116.
Jean Claude Kamgang, Vivient Corneille Kamla, Stéphane Yanick Tchoumi,
Modeling the Dynamics of Malaria Transmission with Bed Net Protection Perspective,
2014,
05,
2152-7385,
3156,
10.4236/am.2014.519298
117.
Xinzhi Liu, Peter Stechlinski,
Transmission dynamics of a switched multi-city model with transport-related infections,
2013,
14,
14681218,
264,
10.1016/j.nonrwa.2012.06.003
118.
B. Bonzi, A. A. Fall, A. Iggidr, G. Sallet,
Stability of differential susceptibility and infectivity epidemic models,
2011,
62,
0303-6812,
39,
10.1007/s00285-010-0327-y
119.
Muhammad Altaf Khan, Yasir Khan, Taj Wali Khan, Saeed Islam,
Dynamical system of a SEIQV epidemic model with nonlinear generalized incidence rate arising in biology,
2017,
10,
1793-5245,
1750096,
10.1142/S1793524517500966
120.
Paul Georgescu, Ying‐Hen Hsieh,
Global Stability for a Virus Dynamics Model with Nonlinear Incidence of Infection and Removal,
2007,
67,
0036-1399,
337,
10.1137/060654876
121.
N Anggriani, A K Supriatna, E Soewono,
The Existence and Stability Analysis of the Equilibria in Dengue Disease Infection Model,
2015,
622,
1742-6588,
012039,
10.1088/1742-6596/622/1/012039
122.
Mohamed El Fatini, Aziz Laaribi, Roger Pettersson, Regragui Taki,
Lévy noise perturbation for an epidemic model with impact of media coverage,
2019,
91,
1744-2508,
998,
10.1080/17442508.2019.1595622
123.
Soufiane Bentout, Abdennasser Chekroun, Toshikazu Kuniya,
Parameter estimation and prediction for coronavirus disease outbreak 2019 (COVID-19) in Algeria,
2020,
7,
2327-8994,
306,
10.3934/publichealth.2020026
124.
Dan Li, Wanbiao Ma,
Dynamical Analysis of a Stage-Structured Model for Lyme Disease with Two Delays,
2016,
59,
0008-4395,
363,
10.4153/CMB-2015-063-x
125.
C.P. Bhunu, S. Mushayabasa, R.J. Smith,
Assessing the effects of poverty in tuberculosis transmission dynamics,
2011,
0307904X,
10.1016/j.apm.2011.11.046
126.
Muhammad Altaf Khan, Sajjad Ullah, Saif Ullah, Muhammad Farhan,
Fractional order SEIR model with generalized incidence rate,
2020,
5,
2473-6988,
2843,
10.3934/math.2020182
127.
Jean Jules Tewa, Jean Luc Dimi, Samuel Bowong,
Lyapunov functions for a dengue disease transmission model,
2009,
39,
09600779,
936,
10.1016/j.chaos.2007.01.069
128.
Tzy-Wei Hwang, Feng-Bin Wang,
Dynamics of a dengue fever transmission model with crowding effect in human population and spatial variation,
2013,
18,
1553-524X,
147,
10.3934/dcdsb.2013.18.147
129.
GLOBAL DYNAMICS IN A MULTI-GROUP EPIDEMIC MODEL FOR DISEASE WITH LATENCY SPREADING AND NONLINEAR TRANSMISSION RATE,
2016,
6,
2156-907X,
47,
10.11948/2016005
130.
Ying Yang, Yanan Zhao, Daqing Jiang,
The dynamics of the stochastic multi-molecule biochemical reaction model,
2014,
52,
0259-9791,
1477,
10.1007/s10910-014-0324-2
131.
Ram P. Sigdel, C. Connell McCluskey,
Global stability for an SEI model of infectious disease with immigration,
2014,
243,
00963003,
684,
10.1016/j.amc.2014.06.020
132.
Shangbing Ai, Jia Li, Junliang Lu,
Mosquito-Stage-Structured Malaria Models and Their Global Dynamics,
2012,
72,
0036-1399,
1213,
10.1137/110860318
133.
Ram Singh, Madhu Jain, Shoket Ali,
2016,
Mathematical analysis of transmission dynamics of tuberculosis with recurrence based on treatment,
978-1-4673-9939-5,
3995,
10.1109/ICEEOT.2016.7755464
134.
Da-peng Gao, Nan-jing Huang,
Threshold dynamics of an SEIR epidemic model with a nonlinear incidence rate and a discontinuous treatment function,
2020,
114,
1578-7303,
10.1007/s13398-019-00751-z
135.
Jean Jules Tewa, Samuel Bowong, Boulchard Mewoli,
Mathematical analysis of two-patch model for the dynamical transmission of tuberculosis,
2012,
36,
0307904X,
2466,
10.1016/j.apm.2011.09.004
136.
Xia Wang, Youde Tao, Xinyu Song,
Global stability of a virus dynamics model with Beddington–DeAngelis incidence rate and CTL immune response,
2011,
66,
0924-090X,
825,
10.1007/s11071-011-9954-0
137.
J. Demongeot, O. Hansen, H. Hessami, A. S. Jannot, J. Mintsa, M. Rachdi, C. Taramasco,
Random Modelling of Contagious Diseases,
2013,
61,
0001-5342,
141,
10.1007/s10441-013-9176-6
138.
Huawen Ye, Weihua Gui, Honglei Xu,
Global convergence analysis of a class of epidemic models,
2017,
47,
0307904X,
442,
10.1016/j.apm.2017.03.013
139.
Tanuja Das, Prashant K. Srivastava, Anuj Kumar,
Nonlinear dynamical behavior of an SEIR mathematical model: Effect of information and saturated treatment,
2021,
31,
1054-1500,
043104,
10.1063/5.0039048
140.
Shubhankar Saha, Priti Kumar Roy,
A Comparative Study Between Two Systems with and Without Awareness in Controlling HIV/AIDS,
2017,
27,
2083-8492,
337,
10.1515/amcs-2017-0024
141.
Antonín Slavík,
Reaction–diffusion equations on graphs: stationary states and Lyapunov functions,
2021,
34,
0951-7715,
1854,
10.1088/1361-6544/abd52c
142.
Anupam Khatua, Debprasad Pal, Tapan Kumar Kar,
Global Dynamics of a Diffusive Two-Strain Epidemic Model with Non-Monotone Incidence Rate,
2022,
46,
1028-6276,
859,
10.1007/s40995-022-01287-5
143.
Md Abdul Kuddus, Azizur Rahman,
Analysis of COVID-19 using a modified SLIR model with nonlinear incidence,
2021,
27,
22113797,
104478,
10.1016/j.rinp.2021.104478
144.
Ardak Kashkynbayev, Daiana Koptleuova,
Global dynamics of tick-borne diseases,
2020,
17,
1551-0018,
4064,
10.3934/mbe.2020225
145.
Tianyu Cheng, Xingfu Zou,
A new perspective on infection forces with demonstration by a DDE infectious disease model,
2022,
19,
1551-0018,
4856,
10.3934/mbe.2022227
146.
Jana Kopfová, Petra Nábělková, Dmitrii Rachinskii, Samiha C. Rouf,
Dynamics of SIR model with vaccination and heterogeneous behavioral response of individuals modeled by the Preisach operator,
2021,
83,
0303-6812,
10.1007/s00285-021-01629-8
147.
Abderrahman Iggidr, Max O. Souza,
On the limits of the Volterra function in the Lyapunov method: The Anderson-May-Gupta model as a cautionary example,
2023,
517,
0022247X,
126465,
10.1016/j.jmaa.2022.126465
148.
Attiq ul Rehman, Ram Singh, Praveen Agarwal,
On Fractional Lyapunov Functions of Nonlinear Dynamic Systems and Mittag-Leffler Stability Thereof,
2022,
2,
2673-9321,
209,
10.3390/foundations2010013
149.
Kuldeep Chaudhary, Pradeep Kumar, Sudipa Chauhan, Vijay Kumar,
Optimal promotional policy of an innovation diffusion model incorporating the brand image in a segment-specific market,
2022,
9,
2327-0012,
120,
10.1080/23270012.2021.1978883
150.
Hongquan Sun, Hong Li, Jin Li, Zhangsheng Zhu,
Dynamics of an SIRS model with age structure and two delays,
2021,
14,
1793-5245,
10.1142/S179352452150056X
151.
A. Lamrani Alaoui, M. Tilioua, M. R. Sidi Ammi, P. Agarwal,
2021,
Chapter 2,
978-981-16-2449-0,
17,
10.1007/978-981-16-2450-6_2
152.
Alfonso Ruiz-Herrera,
Stable and unstable endemic solutions in the seasonally forced SIR epidemic model,
2023,
0,
1531-3492,
0,
10.3934/dcdsb.2023046
153.
S. Bowong, A. Temgoua, Y. Malong, J. Mbang,
Mathematical Study of a Class of Epidemiological Models with Multiple Infectious Stages,
2020,
21,
2191-0294,
259,
10.1515/ijnsns-2017-0244
154.
Ion Bica, Zhichun Zhai, Rui Hu,
A modified Susceptible-Infected-Recovered epidemiological model,
2022,
49,
12236934,
291,
10.52846/ami.v49i2.1560
155.
Jagan Mohan Jonnalagadda,
Epidemic Analysis and Mathematical Modelling of H1N1 (A) with Vaccination,
2022,
9,
2353-0626,
1,
10.1515/msds-2020-0143
156.
Weixin Wu, Zhidong Teng,
Periodic wave propagation in a diffusive SIR epidemic model with nonlinear incidence and periodic environment,
2022,
63,
0022-2488,
122701,
10.1063/5.0109312
Ardak Kashkynbayev, Fathalla A. Rihan,
Dynamics of Fractional-Order Epidemic Models with General Nonlinear Incidence Rate and Time-Delay,
2021,
9,
2227-7390,
1829,
10.3390/math9151829
159.
Santosh Ansumali, Shaurya Kaushal, Aloke Kumar, Meher K. Prakash, M. Vidyasagar,
Modelling a pandemic with asymptomatic patients, impact of lockdown and herd immunity, with applications to SARS-CoV-2,
2020,
50,
13675788,
432,
10.1016/j.arcontrol.2020.10.003
160.
Linhe Zhu, Xuewei Wang, Zhengdi Zhang, Chengxia Lei,
Spatial dynamics and optimization method for a rumor propagation model in both homogeneous and heterogeneous environment,
2021,
105,
0924-090X,
3791,
10.1007/s11071-021-06782-9
161.
Walid Ben Aribi, Bechir Naffeti, Kaouther Ayouni, Hamadi Ammar, Henda Triki, Slimane Ben Miled, Amira Kebir,
Global Stability and Numerical Analysis of a Compartmental Model of the Transmission of the Hepatitis A Virus (HAV): A Case Study in Tunisia,
2022,
8,
2349-5103,
10.1007/s40819-022-01326-0
162.
Ke Qi, Zhijun Liu, Lianwen Wang, Yuming Chen,
Global dynamics of a diffusive SEICR HCV model with nonlinear incidences,
2023,
206,
03784754,
181,
10.1016/j.matcom.2022.11.017
163.
Yu Gu, Mohabat Khan, Rahat Zarin, Amir Khan, Abdullahi Yusuf, Usa Wannasingha Humphries,
Mathematical analysis of a new nonlinear dengue epidemic model via deterministic and fractional approach,
2023,
67,
11100168,
1,
10.1016/j.aej.2022.10.057
164.
Santosh Ansumali, Shaurya Kaushal, Aloke Kumar, Meher K. Prakash, M. Vidyasagar,
Modelling the COVID-19 Pandemic: Asymptomatic Patients, Lockdown and Herd Immunity,
2020,
53,
24058963,
823,
10.1016/j.ifacol.2021.04.223
165.
Guodong Liu, Xiaoyan Zhang,
Asymptotic dynamics of a logistic SIS epidemic reaction-diffusion model with nonlinear incidence rate,
2023,
520,
0022247X,
126866,
10.1016/j.jmaa.2022.126866
166.
Divine Wanduku,
ESTIMATING WHITE NOISE INTENSITY REGIONS FOR COMPARABLE PROPERTIES OF A CLASS OF SEIRS STOCHASTIC AND DETERMINISTIC EPIDEMIC MODELS,
2021,
11,
2156-907X,
1095,
10.11948/20190372
167.
Modeste N'zi, Gérard Kanga,
Global analysis of a deterministic and stochastic nonlinear SIRS epidemic model with saturated incidence rate,
2016,
24,
0926-6364,
65,
10.1515/rose-2016-0005
168.
Xiaogang Liu, Yuming Chen, Xiaomin Li, Jianquan Li,
Global stability of latency-age/stage-structured epidemic models with differential infectivity,
2023,
86,
0303-6812,
10.1007/s00285-023-01918-4
169.
Liancheng WANG, Xiaoqin WU,
Stability and Hopf Bifurcation for an SEIR Epidemic Model with Delay,
2018,
2,
2587-2648,
113,
10.31197/atnaa.380970
170.
Svetozar Margenov, Nedyu Popivanov, Iva Ugrinova, Tsvetan Hristov,
Differential and Time-Discrete SEIRS Models with Vaccination: Local Stability, Validation and Sensitivity Analysis Using Bulgarian COVID-19 Data,
2023,
11,
2227-7390,
2238,
10.3390/math11102238
171.
Florian Nill,
Endemic oscillations for SARS-CoV-2 Omicron—A SIRS model analysis,
2023,
173,
09600779,
113678,
10.1016/j.chaos.2023.113678
172.
Zviiteyi Chazuka, Edinah Mudimu, Dephney Mathebula,
Stability and bifurcation analysis of an HIV model with pre-exposure prophylaxis and treatment interventions,
2024,
23,
24682276,
e01979,
10.1016/j.sciaf.2023.e01979
173.
Daudel Tchatat, Gabriel Guilsou Kolaye, Amadou Alioum, Samuel Bowong, Céline Maïrousgou,
Mathematical modelling of the impact of poverty on cholera outbreaks,
2023,
0170-4214,
10.1002/mma.9727
174.
Patrick Noah Okolo, Christiana Gideon Makama, Roseline Toyin Abah,
A MATHEMATICAL MODEL FOR TUBERCULOSIS INFECTION TRANSMISSION DYNAMICS IN THE PRESENCE OF TESTING AND THERAPY, ISOLATION AND TREATMENT,
2023,
7,
2616-1370,
103,
10.33003/fjs-2023-0706-2108
175.
Moreen Brenda Gatwiri, Marilyn Ronoh, Cyrus Gitonga Ngari, Dominic Makaa Kitavi, Firdous A. Shah,
Mathematical Modelling of Host-Pest Interaction in the Presence of Insecticides and Resistance: A Case of Fall Armyworm,
2024,
2024,
2314-4785,
1,
10.1155/2024/2886786
176.
Summer Atkins, Michael Malisoff,
Robustness of feedback control for SIQR epidemic model under measurement uncertainty,
2023,
0,
2156-8472,
0,
10.3934/mcrf.2023043
177.
Huicong Li, Tian Xiang,
On an SIS epidemic model with power‐like nonlinear incidence and with/without cross‐diffusion,
2024,
0022-2526,
10.1111/sapm.12683
178.
J. A. Akingbade, R. A. Adetona, B. S Ogundare,
Mathematical model for the study of transmission and control of measles with immunity at initial stage,
2018,
6,
23193786,
823,
10.26637/MJM0604/0019
179.
Jinlong Lv, Wanbiao Ma,
Delay induced stability switch in a mathematical model of CD8 T-cell response to SARS-CoV-2 mediated by receptor ACE2,
2024,
34,
1054-1500,
10.1063/5.0187872
180.
Saida Id Ouaziz, Mohammed El Khomssi,
Mathematical approaches to controlling COVID-19: optimal control and financial benefits,
2024,
4,
2791-8564,
1,
10.53391/mmnsa.1373093
181.
Mohammed Azoua, Marouane Karim, Abderrahim Azouani, Imad Hafidi,
Improved parameter estimation in epidemic modeling using continuous data assimilation methods,
2024,
1598-5865,
10.1007/s12190-024-02145-w
182.
Shan Yang, Shihan Liu, Kaijun Su, Jianhong Chen,
A Rumor Propagation Model Considering Media Effect and Suspicion Mechanism under Public Emergencies,
2024,
12,
2227-7390,
1906,
10.3390/math12121906
183.
Rattiya Sungchasit, I.-Ming Tang, Puntani Pongsumpun,
Sensitivity analysis and global stability of epidemic between Thais and tourists for Covid -19,
2024,
14,
2045-2322,
10.1038/s41598-024-71009-x
184.
Sacrifice Nana-Kyere, Baba Seidu, Kwara Nantomah,
Optimal control and cost-effectiveness analysis of nonlinear deterministic Zika virus model,
2024,
2363-6203,
10.1007/s40808-024-02130-z
185.
Suvankar Majee, Soovoojeet Jana, T. K. Kar, Bidhan Bhunia,
Complex dynamics of a fractional-order delayed epidemic model incorporating waning immunity and optimal control,
2024,
1951-6355,
10.1140/epjs/s11734-024-01221-3
186.
Xiaoqing Mu,
Stability analysis of a conventional SEIR epidemic model with relapse and general nonlinear incidence,
2024,
2905,
1742-6588,
012036,
10.1088/1742-6596/2905/1/012036
Benjamin Wacker,
Revisiting the classical target cell limited dynamical within-host HIV model - Basic mathematical properties and stability analysis,
2024,
21,
1551-0018,
7805,
10.3934/mbe.2024343
189.
Bechir Naffeti, Zeineb Ounissi, Akhil Kumar Srivastav, Nico Stollenwerk, Joseba Bidaurrazaga Van-Dierdonck, Maíra Aguiar,
Modeling COVID-19 dynamics in the Basque Country: characterizing population immunity profile from 2020 to 2022,
2025,
25,
1471-2334,
10.1186/s12879-024-10342-y
190.
Sumana Ghosh, Jayanta Mondal, Subhas Khajanchi,
Effect of media awareness in the spread of infectious diseases,
2025,
1598-5865,
10.1007/s12190-025-02387-2
Andrei Korobeinikov, Philip K. Maini. A Lyapunov function and global properties for SIR and SEIR epidemiological models with nonlinear incidence[J]. Mathematical Biosciences and Engineering, 2004, 1(1): 57-60. doi: 10.3934/mbe.2004.1.57
Andrei Korobeinikov, Philip K. Maini. A Lyapunov function and global properties for SIR and SEIR epidemiological models with nonlinear incidence[J]. Mathematical Biosciences and Engineering, 2004, 1(1): 57-60. doi: 10.3934/mbe.2004.1.57