Dynamical Study of a Vector Host Epidemic Model With Non-Monotone Incidence

Raut, Seema; Janardhan, Sujatha; Khekare, Ganesh

doi:10.1080/1726037X.2021.1945724

Open Access Research Article

Dynamical Study of a Vector Host Epidemic Model With Non-Monotone Incidence

^*Seema RautCorresponding authorseema.ssk83@yahoo.inDepartment of Applied MathematicsG. H. Raisoni. Institute of Engineering & TechnologyNagpur, Maharashtra, IndiaView full profile → , Sujatha Janardhansujata_jana@yahoo.comDepartment of MathematicsSt. Francis De Sales CollegeNagpur, Maharashtra, IndiaView full profile → , Ganesh Khekarekhekare.123@gmail.comDepartment of Information TechnologyG.H. Raisoni College of EngineeringNagpur, Maharashtra, IndiaView full profile →

* Corresponding author · click or hover a name for details

pp. 77–94Vol. 19Issue 1January 2021DOI: 10.1080/1726037X.2021.1945724XML

Received:: 05 Jun 2020
Accepted:: 29 Dec 2020
Published Online:: 29 Sep 2021
Article type:: Research Article
Language:: EN
Article no.:: 1726037X.2021.1945724
Pages:: 77–94

Abstract

Epidemics of vector borne disease studied in this paper when disease incidence rate is non- monotone. Non monotonic behaviors of infected hosts as well as infected vectors are studied for influence of increase in disease on susceptible host population and effect of repellents and insecticides on vectors, respectively. Suitable Liapunov functions are constructed to discuss the global asymptotic stabilities at the equilibrium points. Results are verified by conducting numerical simulation. Mechanism of disease spread by vectors and hosts during the epidemic can be better understood with the help of this model.

Keywords

Vector borne diseasesDisease free equilibriumEndemic equilibriumStability

Subject Classifications

92B0593C15

References

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LindahlJ. F., GraceD., The consequences of human actions on risks for infectious diseases: a review , Infection Ecology and Epidemiology , 5 : 30048 , ( 2015 ). doi: 10.3402/iee.v5.30048
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OzairM., LashariA. A., I. H.Jung, K. O.Okosun, Stability analysis and optimal control of a vector-borne disease with nonlinear incidence , Discrete Dynamics in Nature and Society , doi: 10.1155/2012/595487 , 1 - 21 , ( 2012 ).
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QuiZ., Dynamical behavior of a vector-host epidemic model with demographic structure , Computers and Mathematics with Applications , Vol. 56 , Number 12 , 3118 - 3129 , ( 2008 ). doi: 10.1016/j.camwa.2008.09.002
RossR., The Prevention of Malaria , Murray, London, ( 1911 ).
WeiH. M., LiX. Z. and MartchevaM., An epidemic model of a vector-borne disease with direct transmission and time delay , Journal of Mathematical Analysis and Applications , Vol. 342 , 895908 , ( 2008 ). doi: 10.1016/j.jmaa.2007.12.058
XiaoD., RuanS., Global Analysis of an epidemic model with non-monotone incidence rate , Math Biosci ., Vol. 208 , 419 - 429 , ( 2007 ). doi: 10.1016/j.mbs.2006.09.025

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[1] BrauerF., ChavezC. C., MubayiA., TowersS., Some models for epidemics of vector- transmitted diseases , Infectious Disease Modelling , Vol. 1 ,Number 1 , 79 - 87 , ( 2016 ). doi: 10.1016/j.idm.2016.08.001

[2] CaiL., GuoS., LiX. and GhoshM., Global dynamics of a dengue epidemic mathematical model, Chaos , Solitions and fractals , Vol. 42 , 2297 - 2304 , ( 2009 ). doi: 10.1016/j.chaos.2009.03.130

[3] CaiL., LiX., Global analysis of a vector host epidemic model with nonlinear incidences , Applied Mathematics and Computation , Vol. 217 , 3531 - 3541 , ( 2010 ). doi: 10.1016/j.amc.2010.09.028

[4] GratzN. G., Emerging and Resurging Vector Borne Diseases , Annual Review of Entomology , Vol. 44 , 51 - 75 , ( 1999 ). doi: 10.1146/annurev.ento.44.1.51

[5] GuoS., LiX. and GhoshM., Analysis of a dengue disease model with nonlinear incidence , Discrete Dynamics in Nature and Society , doi: 10.1155/2013/320581 , 1 - 10 , ( 2013 ).

[6] LiM.Y. and MuldowneyJ.S., Global stability for the SEIR model in epidemiology , Mathematical Biosciences , Vol. 125 , 155164 , ( 1995 ).

[7] LindahlJ. F., GraceD., The consequences of human actions on risks for infectious diseases: a review , Infection Ecology and Epidemiology , 5 : 30048 , ( 2015 ). doi: 10.3402/iee.v5.30048

[8] MaZ., LiJ., Dynamical Modeling and Analysis of Epidemics , World Scientific Publishing Co. Pte. Ltd. , Singapore, ( 2009 ).

[9] OkosunK. O., MakindeO. D., Optimal Control Analysis of Malaria in the Presence of Nonlinear Incidence Rate , Appl. Comput. Math ., Vol. 12 , 20 - 32 , ( 2013 ).

[10] OzairM., LashariA. A., I. H.Jung, K. O.Okosun, Stability analysis and optimal control of a vector-borne disease with nonlinear incidence , Discrete Dynamics in Nature and Society , doi: 10.1155/2012/595487 , 1 - 21 , ( 2012 ).

[11] PerkoL., Differential Equations and Dynamical Systems , Vol. 7 , Springer-Verlag , New York, ( 1996 ).

[12] QuiZ., Dynamical behavior of a vector-host epidemic model with demographic structure , Computers and Mathematics with Applications , Vol. 56 , Number 12 , 3118 - 3129 , ( 2008 ). doi: 10.1016/j.camwa.2008.09.002

[13] RossR., The Prevention of Malaria , Murray, London, ( 1911 ).

[14] WeiH. M., LiX. Z. and MartchevaM., An epidemic model of a vector-borne disease with direct transmission and time delay , Journal of Mathematical Analysis and Applications , Vol. 342 , 895908 , ( 2008 ). doi: 10.1016/j.jmaa.2007.12.058

[15] XiaoD., RuanS., Global Analysis of an epidemic model with non-monotone incidence rate , Math Biosci ., Vol. 208 , 419 - 429 , ( 2007 ). doi: 10.1016/j.mbs.2006.09.025

Journal of Dynamical Systems and Geometric Theories

WoS JIF 2026 : 0.5 (Q3)

Dynamical Study of a Vector Host Epidemic Model With Non-Monotone Incidence

Abstract

Keywords

Subject Classifications

References