In this article, the qualitative properties of a stochastic dual virus parallel transmission model with immunity delay are analyzed. First, we use Lyapunov theory to study the existence and uniqueness of the global positive solution of the proposed model. Second, the threshold values of the persistence and extinction of two viruses were obtained. Finally, the numerical simulation verifies the theoretical results. The results show that the immunity delay and the intensity of noise have important effects on the two diseases spreading in parallel.
Get full access to this article
View all access options for this article.
References
1.
AmadorJ, ArmestoD, Gómez-CorralA, et al.Extreme values in sir epidemic models with two strains and cross-immunity. Math Biosci Eng, 2019; 16(4):1992–2022.
2.
BabaIA, KaymakamzadeB, HincalE, et al.Two-strain epidemic model with two vaccinations. Chaos, Solitons and Fractals, 2018; 106:342–348.
3.
BoukanjimeB, El FatiniM, LaaribiA, et al.Analysis of a deterministic and a stochastic epidemic model with two distinct epidemics hypothesis. Physica A, 2019; 534:122321.
4.
ChangY, LiuC. A stochastic multi-strain sir model with two-dose vaccination rate. Mathematics, 2022; 10(11):1804.
5.
DinA, AmineS, AllaliA. A stochastically perturbed co-infection epidemic model for covid-19 and hepatitis b virus. Nonlinear Dyn, 2023; 111(2):1921–1945.
6.
FanH, WangK, ZhuY, et al.Stability and asymptotic properties of the seqir epidemic model. Applied Mathematics Letters, 2023; 141:108604.
7.
FanL, QuanxinZ, ZhengWX, et al.Stability analysis of switched stochastic nonlinear systems with state-dependent delay. IEEE Transactions on Automatic Control, 2023.
8.
FudoligM, HowardR. The local stability of a modified multi-strain sir model for emerging viral strains. PLoS One, 2020; 15(12):e0243408.
9.
HouT, LanG, YuanS, et al.Threshold dynamics of a stochastic sihr epidemic model of covid-19 with general population-size dependent contact rate. Math Biosci Eng, 2022; 19(4):4217–4236.
10.
JiC, JiangD, ShiN, et al.Multigroup sir epidemic model with stochastic perturbation. Physica A: Statistical Mechanics and Its Applications, 2011; 390(10):1747–1762.
11.
KhanA, ShahK, AbdeljawadT, et al.Existence of results and computational analysis of a fractional order two strain epidemic model. Results in Physics, 2022; 39:105649.
12.
KhyarO, AllaliK. Global dynamics of a multi-strain seir epidemic model with general incidence rates: Application to covid-19 pandemic. Nonlinear Dyn, 2020; 102(1):489–509.
13.
KumarS, GhildayalN, YangM, et al.Social media effectiveness as a humanitarian response to mitigate influenza epidemic and covid-19 pandemic. Ann Oper Res, 2022; 319(1):823–851.
14.
LahrouzA, OmariL. Extinction and stationary distribution of a stochastic sirs epidemic model with non-linear incidence. Statistics and Probability Letters, 2013; 83(4):960–968.
15.
LiC-L, ChengC-Y, LiC-H, et al.Global dynamics of two-strain epidemic model with single-strain vaccination in complex networks. Nonlinear Anal Real World Appl, 2023; 69:103738.
16.
LiuQ, ChenQ. Analysis of the deterministic and stochastic sirs epidemic models with nonblinear incidence. Physica A: Statistical Mechanics and Its Applications, 2015; 428:140–153.
17.
LiuQ, JiangD. Stationary distribution and probability density for a stochastic seir-type model of coronavirus (covid-19) with asymptomatic carriers. Chaos Solitons Fractals, 2023; 169:113256.
18.
MajumderA, AdakD, BairagiN, et al.Phytoplankton-zooplankton interaction under environmental stochasticity: Survival, extinction and stability. Applied Mathematical Modelling, 2021b;89:1382–1404.
19.
MajumderA, AdakD, BairagiN, et al.Persistence and extinction of species in a disease-induced ecological system under environmental stochasticity. Phys Rev E, 2021a;103(3–1):32412.
20.
MassardM, EftimieR, PerassoA, et al.A multi-strain epidemic model for covid-19 with infected and asymptomatic cases: Application to french data. J Theor Biol, 2022; 545:111117.
21.
MeehanMT, CocksDG, TrauerJM, et al.Coupled, multi-strain epidemic models of mutating pathogens. Math Biosci, 2018; 296:82–92.
22.
MeskafA, KhyarO, DananeJ, et al.Global stability analysis of a two-strain epidemic model with non-monotone incidence rates. Chaos, Solitons and Fractals, 2022; 133:109647.
23.
OtunugaO. Analysis of multi-strain infection of vaccinated and recovered population through epidemic model: Application to covid-19. PLoS One, 2022; 17(7):e0271446.
24.
ParéPE, LiuJ, BeckCL, et al.Multi-competitive viruses over time-varying networks with mutations and human awareness. Automatica, 2021; 123:109330.
25.
RajasekarS, PitchaimaniM. Qualitative analysis of stochastically perturbed sirs epidemic model with two viruses. Chaos, Solitons and Fractals, 2019; 118:207–221.
26.
SardanyésJ, AlcaideC, GómezP, et al.Modelling temperature-dependent dynamics of single and mixed infections in a plant virus. Applied Mathematical Modelling, 2022; 102:694–705.
27.
ShamiL, LazebnikT. Economic aspects of the detection of new strains in a multi-strain epidemiologicalcmathematical model. Chaos, Solitons and Fractals, 2022; 165:112823.
28.
SinghA, ArquamM. Epidemiological modeling for covid-19 spread in india with the effect of testing. Physica A: Statistical Mechanics and Its Applications, 2022; 592:126774.
29.
TakiR, El FatiniM, El KhalifiM, et al.Understanding death risks of covid-19 under media awareness strategy: A stochastic approach. J Anal, 2022; 30(1):79–99.
30.
WangS, ZhangJ, XuF, et al.Dynamics of virus infection models with density-dependent diffusion. Computers and Mathematics with Applications, 2017; 74(10):2403–2422.
31.
WangX, HuangC, HaoY, et al.A stochastic mathematical model of two different infectious epidemic under vertical transmission. Math Biosci Eng, 2022a;19(3):2179–2192.
32.
WangL, ZhangQ, LiuJ. On the dynamical model for covid-19 with vaccination and time-delay effects: A model analysis supported by yangzhou epidemic in 2021. Appl Math Lett, 2022b;125:107783.
33.
XuC, LiX. The threshold of a stochastic delayed sirs epidemic model with temporary immunity and vaccination. Chaos, Solitons and Fractals, 2018; 111:227–234.
34.
YaagoubZ, AllaliK. Global stability of multi-strain seir epidemic model with vaccination strategy. MCA, 2023; 28(1):9.
35.
YangJ, XuR, LuoX. Dynamical analysis of an age-structured multi-group sivs epidemic model. Math Biosci Eng, 2019; 16(2):636–666.
36.
YuJ, JiangD, ShiN, et al.Global stability of two-group sir model with random perturbation. Journal of Mathematical Analysis and Applications, 2009; 360(1):235–244.
37.
ZhangJ, WangX, ChenS, et al.Study on the interaction between information dissemination and infectious disease dissemination under government prevention and management. Chaos, Solitons and Fractals, 2023; 173:113601.
38.
ZhaoL, WangZ-C, RuanS, et al.Dynamics of a time-periodic two-strain sis epidemic model with diffusion and latent period. Nonlinear Analysis: Real World Applications, 2020; 51:102966.
39.
ZhuQ. Stabilization of stochastic nonlinear delay systems with exogenous disturbances and the event-triggered feedback control. IEEE Trans Automat Contr, 2019; 64(9):3764–3771.
