Skip to main content
SpringerLink
Log in

Stability and bifurcation analysis of Japanese encephalitis model with/without effects of some control parameters

  • Published:
Computational and Applied Mathematics Aims and scope Submit manuscript

Abstract

In this paper, a mathematical model on transmission of Japanese Encephalitis disease has been developed considering some control parameters and time-dependent environmental-carrying capacity. Here, the total vector population is divided into two subpopulations such as susceptible mosquito and infected mosquito. Here also, total reservoir population (i.e., the population in which the encephalitis virus grows) such as pig, horse, etc., has been considered which is divided into three subpopulations such as susceptible reservoir, infected reservoir and recovered reservoir. Total human population is also divided into three subpopulations such as susceptible human, infected human and recovered human. The dynamical behaviors of the system have been investigated. Here, the basic reproduction number associated with the system has been analyzed with respect to control parameters both theoretically and numerically. The biological feasible equilibria and their stability properties have been discussed and the existence condition of the disease has been illustrated numerically. For a certain set of parametric values, effectiveness of control parameters of our proposed model has been checked numerically. At last, Hopf bifurcations have been made numerically without considering control parameters for the case of constant environmental-carrying capacity of mosquito.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

References

  • Bandyopadhyay B, Bhattacharyya I, Adhikary S, Mondal S, Konar J, Dawar N, Biswas A, Bhattacharya N (2013) Incidence of Japanese Encephalitis among acute encephalitis syndrome cases in West Bengal, India. BioMed Res Int 2013:1–5. doi:10.1155/2013/896749

    Article  Google Scholar 

  • Erlanger TE, Weiss S, Keiser J, Utzinger J, Wiedenmayer K (2009) Past, present, and future of Japanese Encephalitis. Emerg Infect Dis 15(1):1–7

    Article  Google Scholar 

  • Freedman HI, Ruan S, Tang M (1994) Uniform persistence and flows near a closed positively invariant set. J Dyn Diff Equ 6(4):583–600

    Article  MathSciNet  MATH  Google Scholar 

  • Gromowski GD (2014) Japanese encephalitis virus vaccine candidates generated bychimerization with dengue virus type 4. Vaccine 32:3010–3018

    Article  Google Scholar 

  • Keiser J (2005) Effect of irrigated rice agriculture on Japanese encephalitis, including challenges and opportunities for integrated vector management. Acta Trop 95(1):40–57

    Article  Google Scholar 

  • Le Flohic G, Porphyre V, Barbazan P, Gonzalez JP (2013) Review of climate, landscape, and viral genetics as drivers of the Japanese Encephalitis virus ecology. Plos Neg Trop Dis 7(9):e2208

    Article  Google Scholar 

  • Li MY, Muldowney JS (1996) A geometric approach global stability problems. SIAM J Math Anal 27(4):1070–1083

    Article  MathSciNet  MATH  Google Scholar 

  • Lindahl JF, Stahl K, Chirico J, Boqvist S, Thu HTV, Magnusson U (2013) Circulation of Japanese encephalitis virus in pigs and mosquito vectors within Can Tho City, Vietnam. Plos Neg Trop Dis 7(4):e2153

    Article  Google Scholar 

  • Lutambi AM, Penny MA, Smith T, Chitnis N (2013) Mathematical modelling of mosquito dispersal in a heterogeneous environment. Math Biosci 241(2):198–216

    Article  MathSciNet  MATH  Google Scholar 

  • Mukhopadhyay BB, Tapaswi PK, Chatterjee A, Mukherjee B (1993) A mathematical model for the occurence of japanese Encephalititis. Math Comput Model 17:99–103

    Article  MATH  Google Scholar 

  • Mukhopadhyay BB, Tapaswi PK (1994) An SIRS epidemic model of Japanese Encephalitis. Int J Math Math Sci 17(2):347–356

    Article  MATH  Google Scholar 

  • Naresh R, Pandey S (2009) Modelling and analysis of the spread of Japanese encephalitis with environmental effects. App App Math 4(1):155–175

    MATH  Google Scholar 

  • Sengupta N, Basu A (2013) Japanese encephalitis virus infection: effect on brain development and repair. Curr Sci India 105(6):815–820

    Google Scholar 

  • Sharma J, Kr Baruah M, Pathak A, Khan SA, Dutta P (2014) Epidemiology of Japanese encephalitis cases in Dhemaji district of Assam, India. Ann Biol Res 5(1):50–54

    Google Scholar 

  • Singh A, Saxena SK, Srivastava AK, Mathur A (2012) Japanese Encephalitis: a persistent threat. Proc Natl Acad Sci Sect B Biol Sci 82(1):55–68

    Article  Google Scholar 

  • Tapaswi PK, Ghosh AK, Mukhopadhyay BB (1995) Transmission of Japanese Encephalitis in a 3-population model. Ecol Model 83:295–309

    Article  Google Scholar 

  • Thenmozhi V (2014) A first note on Japanese encephalitis virus isolation from Culex quinquefasciatus Say in Northern West Bengal. Int J Mosq Res 1(1):1–4

    Google Scholar 

  • Thieme HR (1992) Epidemic and demographic interaction in the spread of potentially fatal diseases in growing populations. Math Biosci 111(1):99–130

    Article  MathSciNet  MATH  Google Scholar 

  • Upadhyayula SM, Rao MS, Nayanoori HK, Natarajan A, Goswami P (2012) Impact of weather variables on mosquitoes infected with Japanese encephalitis virus in Kurnool district, Andhra Pradesh. Asian Pac J Trop Med 5(5):337–341

    Article  Google Scholar 

  • Van den Driessche P, Watmough J (2002) Reproduction number and subthreshold endemic equilibrium for compartmental models of disease transmission. Math Biosci 180:29–48

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore, WB, 721 102, India

    Prabir Panja & Shyamal Kumar Mondal

  2. Agricultural and Ecological Research Unit, ISI Kolkata, 203 B.T. Road, Kolkata, India

    Joydev Chattopadhyay

Authors
  1. Prabir Panja
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Shyamal Kumar Mondal
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Joydev Chattopadhyay
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Prabir Panja.

Additional information

Communicated by Eduardo Souza de Cursi.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Panja, P., Mondal, S.K. & Chattopadhyay, J. Stability and bifurcation analysis of Japanese encephalitis model with/without effects of some control parameters. Comp. Appl. Math. 37, 1330–1351 (2018). https://doi.org/10.1007/s40314-016-0400-2

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40314-016-0400-2

Keywords

Mathematics Subject Classification

Search

Navigation