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AdvancesinAppliedMathematicsA^êÆ?Ð,2023,12(3),1164-1172
PublishedOnlineMarch2023inHans.https://www.hanspub.org/journal/aam
https://doi.org/10.12677/aam.2023.123118
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²LKŠžâéÙ?1nܳÁ£nüÑ"|^FilippovXÚ ½5 ©Û nا©Û.3Ø
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JøüÑÚ•{"
'…c
Filippov§Û-½§SI.§³Á£n
DynamicsofanSIModelforPest
ManagementwithSaturated
Morbidity
PeiZhou,ShanJiang
SchoolofMathematicsandStatistics,ChangshaUniversityofScienceandTechnology,Changsha
Hunan
Received:Feb.21
st
,2023;accepted:Mar.16
th
,2023;published:Mar.23
rd
,2023
©ÙÚ^:±,öë.äkÚu¾Ç³Á£nSI.ÄåÆïÄ[J].A^êÆ?Ð,2023,12(3):1164-1172.
DOI:10.12677/aam.2023.123118
±§öë
Abstract
Inthispaper,apiecewisesmoothSIpestcontrolmodelwithsaturationincidence
rateisestablished,inordertodrawthemanagementstrategyofchemicalcontrol
onlywhenthenumberofsusceptiblepestsreachestheeconomicthreshold.Using
thequalitativeanalysistheoryofFilippovsystem,theglobaldynamicsofthemodel
indifferentthresholdsandparameterrangesareanalyzed,andtheglobalstability
ofendemicequilibriumandpseudoequilibriumisobtained.Particularly,whenthe
parametersandthresholdsareproperlyselected,thetwoendemicequilibriumpoints
willbebi-stable.Theresearchshowsthatincreasingordecreasingthedosageof
pesticides caneffectively control the number ofpestsandavoideconomiclossesunder
differenteconomicthresholdranges.
Keywords
Filippov,GlobalStability,SIModel,PestControl
Copyright
c
2023byauthor(s)andHansPublishersInc.
This work is licensed undertheCreative Commons Attribution InternationalLicense(CCBY4.0).
http://creativecommons.org/licenses/by/4.0/
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DOI:10.12677/aam.2023.1231181166A^êÆ?Ð
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1
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1
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1
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1
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0
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1
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1
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,I
1
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,
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2
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2
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)
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dt
=
β(S−S
1
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1
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1
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1
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1
)
(1+αI)(1+αI
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1
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1
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−S
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S
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1
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1
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I
I
1

.
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1
dt
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1
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DOI:10.12677/aam.2023.1231181167A^êÆ?Ð
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3.wÄåÆ©Û
Šâw•½Â,·‚Œ±Σ
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hH
z
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1
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1
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z
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2
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1
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I−
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q
1
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2
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1
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1
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2
(r−d).
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= 0.I
(2)
=
ξ−q
1
βET
q
2
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@oXÚŒU•3˜‡–²ï:Ep= [ET.I
(2)
].
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(2)
∈[I
2
,I
1
]¿‡^‡:
ϕ(I
1
) =
βq
1
(r−d)[ET(β−α(r−d)−ε−d)]
[β−α(r−d)]
2
= βq
1
I
1
(ET−S
1
),
ϕ(I
2
) =
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1
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1
)[ET(β−α(r−d−q
1
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[β−α(r−d−q
1
)]
2
= βq
1
I
2
(ET−S
2
).
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2
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1
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2
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n«œ¹?1?Ø.3XÚÛ-½5c,·‚küØXÚ•34•‚.
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s
4•‚.
y².S
2
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1
ž,–²ï:E
p
•3…ÛÜìC-½,ùL²lG
i
Ñu;‚ˆw
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I
2
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P
.dž,XÚSØ•3•¹Ü©wã4•‚.
DOI:10.12677/aam.2023.1231181168A^êÆ?Ð
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1
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22
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1
A
1
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12
ds)
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11
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12
dS)+
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1
A
1
Bf
11
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=
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1
A
1
Bf
11
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=
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3
()
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I
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−
d
I
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DOI:10.12677/aam.2023.1231181169A^êÆ?Ð
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Ó/,3D
2
¥A^‚úªk
ZZ
D
2

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22
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Z
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2
B
2
Bf
21
dI
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Z
b+δ
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()
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2
()
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I
−
β
1+αI
−
d
I
−
q
1
I
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ZZ
D
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11
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∂S
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)
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+
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D
2

∂(Bf
21
)
∂S
+
∂(Bf
22
)
αI

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=lim
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Z
a−δ
1
()
b+δ
3
()
r
I
−
β
1+αI
−
d
I
dI+
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