Global dynamics of humoral immunity Chikungunya virus with two routes of infection and Holling type-II
-
1915
Downloads
-
4266
Views
Authors
A. M. Elaiw
- Department of Mathematics, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia.
S. E. Almalki
- Jeddah College of Technology, Technical and Vocational Training Corporation, P. O. Box 17608, Jeddah 21494, Saudi Arabia.
A. D. Hobiny
- Department of Mathematics, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia.
Abstract
In this work, we analyze the global dynamics of within-host Chikungunya virus
(CHIKV) infection model with humoral immune response. We incorporate two
modes of infections, attaching a CHIKV to a host monocyte, and contacting an
infected monocyte with an uninfected monocyte. The infection incident rate is
given by Holling type-II. The basic reproduction number \(\mathcal{R}_{0}\) is
used to prove that the CHIKV-free equilibrium \(E_{0}\) is globally
asymptotically stable when \(\mathcal{R}_{0}\leq1\) and the infected equilibrium
\(E_{1}\) is globally asymptotically stable when \(\mathcal{R}_{0}>1\). Numerical
simulations have been performed to confirm the theoretical results.
Share and Cite
ISRP Style
A. M. Elaiw, S. E. Almalki, A. D. Hobiny, Global dynamics of humoral immunity Chikungunya virus with two routes of infection and Holling type-II, Journal of Mathematics and Computer Science, 19 (2019), no. 2, 65--73
AMA Style
Elaiw A. M., Almalki S. E., Hobiny A. D., Global dynamics of humoral immunity Chikungunya virus with two routes of infection and Holling type-II. J Math Comput SCI-JM. (2019); 19(2):65--73
Chicago/Turabian Style
Elaiw, A. M., Almalki, S. E., Hobiny, A. D.. "Global dynamics of humoral immunity Chikungunya virus with two routes of infection and Holling type-II." Journal of Mathematics and Computer Science, 19, no. 2 (2019): 65--73
Keywords
- Chikungunya virus
- holling type-II
- global stability
- Lyapunov function
- viral and cellular infections
MSC
References
-
[1]
A. Abdelrazec, J. Belair, C. H. Shan, H. P. Zhu, Modeling the spread and control of dengue with limited public health resources, Math. Biosci., 271 (2016), 136--145
-
[2]
F. B. Agusto, S. Bewick, W. F. Fagan, Mathematical model of Zika virus with vertical transmission, Infectious Disease Modelling, 2 (2017), 244--267
-
[3]
E. Beretta, V. Capasso, D. G. Garao, A mathematical model for malaria transmission with asymptomatic carriers and two age groups in the human population, Math. Biosci., 300 (2018), 87--101
-
[4]
E. Bonyah, K. O. Okosun, Mathematical modeling of Zika virus, Asian Pacific J. Tropical Disease, 6 (2016), 673--679
-
[5]
N. Chitnis, J. M. Cushing, J. M. Hyman, Bifurcation analysis of a mathematical model for malaria transmission, SIAM J. Appl. Math., 67 (2006), 24--45
-
[6]
N. Chitnis, J. M. Hyman, J. M. Cushing, Determining important parameters in the spread of malaria through the sensitivity analysis of a mathematical model, Bull. Math. Biol., 70 (2008), 1272--1296
-
[7]
E. Dantas, M. Tosin, A. Cunha, Calibration of a SEIR-SEI epidemic model to describe the Zika virus outbreak in Brazil, Appl. Math. Comput., 338 (2018), 249--259
-
[8]
Y. Dumont, F. Chiroleu, Vector control for the chikungunya disease, Math. Biosci. Eng., 7 (2010), 313--345
-
[9]
Y. Dumont, F. Chiroleu, C. Domerg, On a temporal model for the chikungunya disease: modeling, theory and numerics, Math. Biosci., 213 (2008), 80--91
-
[10]
Y. Dumont, J. M. Tchuenche, Mathematical studies on the sterile insect technique for the chikungunya disease and aedes albopictus, J. Math. Biol., 65 (2012), 809--854
-
[11]
A. M. Elaiw, Global properties of a class of HIV models, Nonlinear Anal. Real World Appl., 11 (2010), 2253--2263
-
[12]
A. M. Elaiw, Global properties of a class of virus infection models with multitarget cells, Nonlinear Dynam., 69 (2012), 423--435
-
[13]
A. M. Elaiw, T. O. Alade, S. M. Alsulami, Analysis of latent CHIKV dynamics models with general incidence rate and time delays, J. Biol. Dyn., 12 (2018), 700--730
-
[14]
A. M. Elaiw, T. O. Alade, S. M. Alsulami, Analysis of within-host CHIKV dynamics models with general incidence rate, Int. J. Biomath., 11 (2018), 25 pages
-
[15]
A. M. Elaiw, S. E. Almalki, A. D. Hobiny, Stability of CHIKV infection models with CHIKV-monocyte and infected-monocyte saturated incidences, AIP Advances, 9 (2019), 12 pages
-
[16]
A. M. Elaiw, N. A. Almuallem, Global properties of delayed-HIV dynamics models with differential drug efficacy in cocirculating target cells, Appl. Math. Comput., 265 (2015), 1067--1089
-
[17]
A. M. Elaiw, N. A. Almuallem, Global dynamics of delay-distributed HIV infection models with differential drug efficacy in cocirculating target cells, Math. Methods Appl. Sci., 39 (2016), 4--31
-
[18]
A. M. Elaiw, N. H. AlShamrani, Global stability of humoral immunity virus dynamics models with nonlinear infection rate and removal, Nonlinear Anal. Real World Appl., 26 (2015), 161--190
-
[19]
A. M. Elaiw, N. H. AlShamrani, Stability of a general delay-distributed virus dynamics model with multi-staged infected progression and immune response, Math. Methods Appl. Sci., 40 (2017), 699--719
-
[20]
A. M. Elaiw, N. H. AlShamrani, Stability of an adaptive immunity pathogen dynamics model with latency and multiple delays, Math. Methods Appl. Sci., 41 (2018), 6645--6672
-
[21]
A. M. Elaiw, S. A. Azoz, Global properties of a class of HIV infection models with Beddington-DeAngelis functional response, Math. Methods Appl. Sci., 36 (2013), 383--394
-
[22]
A. M. Elaiw, E. K. Elnahary, A. A. Raezah, Effect of cellular reservoirs and delays on the global dynamics of HIV, Adv. Difference Equ., 2018 (2018), 36 pages
-
[23]
A. M. Elaiw, I. Hassanien, S. A. Azoz, Global stability of HIV infection models with intracellular delays, J. Korean Math. Soc., 49 (2012), 779--794
-
[24]
A. M. Elaiw, A. A. Raezah, Stability of general virus dynamics models with both cellular and viral infections and delays, Math. Methods Appl. Sci., 40 (2017), 5863--5880
-
[25]
A. M. Elaiw, A. A. Raezah, B. S. Alofi, Dynamics of delayed pathogen infection models with pathogenic and cellular infections and immune impairment, AIP Advances, 8 (2018), 14 pages
-
[26]
A. M. Elaiw, A. A. Raezah, S. A. Azoz, Stability of delayed HIV dynamics models with two latent reservoirs and immune impairment, Adv. Difference Equ., 2018 (2018), 25 pages
-
[27]
L. Esteva, C. Vargas, A model for dengue disease with variable human population, J. Math. Biol., 38 (1999), 220--240
-
[28]
A. D. Hobiny, A. M. Elaiw, A. A. Almatrafi, Stability of delayed pathogen dynamics models with latency and two routes of infection, Adv. Difference Equ., 2018 (2018), 26 pages
-
[29]
G. Huang, Y. Takeuchi, W. Ma, Lyapunov functionals for delay differential equations model of viral infections, SIAM J. Appl. Math., 70 (2010), 2693--2708
-
[30]
A. Korobeinikov, Global properties of basic virus dynamics models, Bull. Math. Biol., 66 (2004), 879--883
-
[31]
X. L. Lai, X. F. Zou, Modelling HIV-1 virus dynamics with both virus-to-cell infection and cell-to-cell transmission, SIAM J. Appl. Math., 74 (2014), 898--917
-
[32]
X. L. Lai, X. F. Zou, Modeling cell-to-cell spread of HIV-1 with logistic target cell growth, J. Math. Anal. Appl., 426 (2015), 563--584
-
[33]
F. Li, J. L. Wang, Analysis of an HIV infection model with logistic target cell growth and cell-to-cell transmission, Chaos Solitons Fractals, 81 (2015), 136--145
-
[34]
X. Z. Liu, P. Stechlinski, Application of control strategies to a seasonal model of chikungunya disease, Appl. Math. Model., 39 (2015), 3194--3220
-
[35]
K. M. Long, M. T. Heise, Protective and pathogenic responses to chikungunya virus infection, Curr. Trop. Med. Rep., 2 (2015), 13--21
-
[36]
S. Mandal, R. R. Sarkar, S. Sinha, Mathematical models of malaria-a review, Malaria J., 10 (2011), 19 pages
-
[37]
C. A. Manore, K. S. Hickmann, S. Xu, H. J. Wearing, J. M. Hyman, Comparing dengue and chikungunya emergence and endemic transmission in A. aegypti and A. albopictus, J. Theoret. Biol., 356 (2014), 174--191
-
[38]
D. Moulay, M. Aziz-Alaoui, M. Cadivel, The chikungunya disease: modeling, vector and transmission global dynamics, Math. Biosci., 229 (2011), 50--63
-
[39]
D. Moulay, M. Aziz-Alaoui, H.-D. Kwon, Optimal control of chikungunya disease: larvae reduction, treatment and prevention, Math. Biosci. Eng., 9 (2012), 369--392
-
[40]
S. M. Raimundo, M. Amaku, E. Massad, Equilibrium analysis of a yellow fever dynamical model with vaccination, Comput. Math. Methods Med., 2015 (2015), 12 pages
-
[41]
H. Y. Shu, Y. M. Chen, L. Wang, Impacts of the cell-free and cell-to-cell infection modes on viral dynamics, J. Dynam. Differential Equations, 30 (2018), 1817--1736
-
[42]
H. Y. Shu, L. Wang, J. Watmough, Global stability of a nonlinear viral infection model with infinitely distributed intracellular delays and CTL immune responses, SIAM J. Appl. Math., 73 (2013), 1280--1302
-
[43]
J. J. Tewaa, J. L. Dimi, S. Bowong, Lyapunov functions for a dengue disease transmission model, Chaos Solitons Fractals, 39 (2009), 936--941
-
[44]
J. L. Wang, J. Y. Lang, X. F. Zou, Analysis of an age structured HIV infection model with virus-to-cell infection and cell-to-cell transmission, Nonlinear Anal. Real World Appl., 34 (2017), 75--96
-
[45]
Y. Wang, X. N. Liu, Stability and Hopf bifurcation of a within-host chikungunya virus infection model with two delays, Math. Comput. Simulation, 138 (2017), 31--48
-
[46]
L. Yakob, A. C. Clements, A mathematical model of chikungunya dynamics and control: the major epidemic on Reunion Island, PLoS One, 8 (2013), 6 pages
-
[47]
Y. Yang, L. Zou, S. G. Ruan, Global dynamics of a delayed within-host viral infection model with both virus-to-cell and cell-to-cell transmissions, Math. Biosci., 270 (2015), 183--191
-
[48]
M. Zhu, Y. Xu, A time-periodic dengue fever model in a heterogeneous environment, Math. Comput. Simulation, 155 (2019), 115--129
