Control of Nipah virus outbreak in commercial pig-farm with biosecurity and culling

Samhita Das¹ ; Pritha Das¹ ; Parthasakha Das ¹

¹ Department of Mathematics, Indian Institute of Engineering Science & Technology, Shibpur, Howrah 711103, India.

Mathematical modelling of natural phenomena, Tome 15 (2020), article no. 64.

Résumé

A coupled pig-human Nipah virus disease model is studied in a commercial farm to understand dynamics of disease spillover from pig to human. To portray the specific scenario, two parameters representing biosecurity level and selective culling are included in the system. Along with standard equilibrium analysis, backward and Hopf bifurcation phenomena are demonstrated analytically and numerically. Optimal control of culling alone and also with other controls for the minimization of loss are discussed. It is observed that, irrespective of its application rate, culling is more effective in presence of other controls. Parameter sensitivity analysis of system solution has been used to identify significant parameters for the change of disease dynamics. Sensitivity test is also performed on the objective function of optimal control problem, which singled out crucial parameters influencing the economic loss of farm-owner. Based on this study, some strategies regarding application of various controls are suggested.

Détail

DOI : 10.1051/mmnp/2020047

Bibliographie

[1] F.B. Agusto Mathematical model of Ebola transmission dynamics with relapse and reinfection Math. Biosci 2017 48 59

[2] M.E. Alexander, C. Bowman, S.M. Moghadas, R. Summers, A.B. Gumel, B.M. Sahai A vaccination model for transmission dynamics of influenza SIAM J. Appl. Dyn. Syst 2004 503 524

[3] M.H.A. Biswas Optimal control of Nipah virus (NIV) infections: A Bangladesh scenario J. Pure Appl. Math 2014 77 104

[4] M.H.A. Biswas, M.M. Haque, G. Duvvuru A mathematical model for understanding the spread of Nipah fever epidemic in Bangladesh 2015 International Conference on Industrial Engineering and Operations Management (IEOM) 2015 1 8

[5] C. Castillo-Chavez, B. Song Dynamical models of Tuberculosis and their applications Math. Biosci. Eng 2004 361 404

[6] N.S. Chong, R.J. Smith Modeling avian influenza using Filippov systems to determine culling of infected birds and quarantine Nonlinear Anal.: Real World Appl 2015 196 218

[7] E.M.C. Dágata, G.F. Webb, J. Pressley Rapid emergence of co-colonization with community-acquired and hospital-acquired methicillin-resistant Staphylococcus aureus strains in the hospital setting MMNP 2010 76 93

[8] E.M.C. D’Agata, M. Horn, G. Webb Quantifying the impact of bacterial fitness and repeated antimicrobial exposure on the emergence of multidrug-resistant gram-negative bacilli MMNP 2007 129 142

[9] S. Das, P. Das, P. Das Dynamics and control of multidrug-resistant bacterial infection in hospital with multiple delays Commun. Nonlinear Sci. Numer. Simul 2020 105279

[10] P. Das, P. Das, S. Das Effects of delayed immune-activation in the dynamics of tumor-immune interactions MMNP 2020 45

[11] E. De Wit, V.J. Munster, Animal models of disease shed light on Nipah virus pathogenesis and transmission J. Pathol 2015 196 205

[12] M. Deka, N. Morshed Mapping disease transmission risk of Nipah virus in south and Southeast Asia Trop. Med. Infect. Disease 2018 05

[13] G. Djatcha Yaleu, S. Bowong, E. Houpa Danga, J. Kurths Mathematical analysis of the dynamical transmission of Neisseria meningitidis serogroup A Int. J. Comput. Math 2017 2409 2434

[14] P.R. Epstein Climate change and emerging infectious diseases Microb. Infection 2001 747 754

[15] W.H. Fleming and R.W. Rishel, Deterministic and stochastic optimal control. Applications of mathematics. Springer-Verlag (1975).

[16] Food and Agriculture Organization of the United Nations. Farmer’s Hand Book on Pig Production (2009).

[17] B. Gomero, Latin hypercube sampling and partial rank correlation coefficient analysis applied to an optimal control problem. Master’s thesis, University of Tennessee, Knoxville (2012).

[18] J. Guckenheimer and P. Holmes, Nonlinear Oscillations Dynamical Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer, New York (1983).

[19] A.B. Gumel Global dynamics of a two-strain Avian influenza model Int. J. Comput. Math 2009 85 108

[20] H. Gulbudak, M. Martcheva Forward hysteresis and backward bifurcation caused by culling in an Avian influenza model Math. Biosci 2013 202 212

[21] E.V. Grigorieva, E.N. Khailov Optimal vaccination, treatment, and preventive campaigns in regard to the SIR epidemic model MMNP 2014 105 121

[22] E.V. Grigorieva, E.N. Khailov, A. Korobeinikov Optimal control for a SIR epidemic model with nonlinear incidence rate MMNP 2016 89 104

[23] J.M. Hassell, M. Begon, M.J. Ward, E.M. Fèver Urbanization and disease emergence: Dynamics at the wildlife-livestock-human interface Trends Ecol. Evol 2017 55 67

[24] J.M. Hughes, M.E. Wilson, E.S. Gurley, M. Jahangir Hossain, S.P. Luby Transmission of Human Infection with Nipah Virus Clin. Infect. Dis 2009 1743 1748

[25] T.T.T. Huynh, A. Aarnink, A. Drucker, M. Verstegen Pig production in Cambodia, Laos, Philippines, and Vietnam: a review Asian J. Agric. Dev 2007

[26] Q. Hu, X. Zou Optimal vaccination strategies for an influenza epidemic model J. Biol. Syst 2013 1340006

[27] A.B. Jamaluddin, A.B. Adzhar Nipah virus infection-Malaysia experience 2011 2019

[28] S. Lenhart and J.T. Workman, Optimal Control Applied to Biological Models. CRC Press (2007).

[29] B. Levy, C. Edholm, O. Gaoue, R. Kaondera-Shava, M. Kgosimore, S. Lenhart, B. Lephodisa, E. Lungu, T. Marijani, F. Nyabadza Modeling the role of public health education in Ebola virus disease outbreaks in Sudan Infect. Dis. Model 2017 323 340

[30] L.-M. Looi, K.-B. Chua Lessons from the Nipah virus outbreak in Malaysia Malaysian J. Pathol 2007 63 67

[31] S. Marino, I. Hogue, C. Ray, D. Kirschner A methodology for performing global uncertainty and sensitivity analysis in systems biology J. Theor. Biol 2008 178 196

[32] M.K. Mondal, M. Hanif, Md. Haider Ali Biswas A mathematical analysis for controlling the spread of Nipah virus infection Int. J. Model. Simul 2017 185 197

[33] V. Pitzer, R. Aguas, S. Riley, W. Loeffen, J. Wood, B.T. Grenfell High turnover drives prolonged persistence of influenza in managed pig herds J. Royal Soc. Interface 2016 20160138

[34] L.S. Pontryagin, V.G. Boltyanskii, R.V. Gamkrelidze and E.F. Mishchenko, The Mathematical Theory of Optimal Processes. John Wiley Sons (1962).

[35] B.A. Satterfield, B.E. Dawes, G.N. Milligan Status of vaccine research and development of vaccines for Nipah virus Vaccine 2016 2971 2975

[36] H.J. Shimozako, J. Wu, E. Massad Mathematical modelling for zoonotic Visceral Leishmaniasis dynamics: a new analysis considering updated parameters and notified human Brazilian data Infectious Disease Model 2017 143 160

[37] P. van den Driessche and J. Watmough, Further Notes on the Basic Reproduction Number. Springer Berlin Heidelberg, Berlin, Heidelberg (2008).

[38] L. Wang, G.S. Crameri Emerging zoonotic viral diseases Rev. Sci. Tech 2014 569 581

[39] H. Weingartl Hendra and Nipah viruses: pathogenesis, animal models and recent breakthroughs in vaccination Vaccine: Dev. Therapy 2015 09

[40] A.K. Wiethoelter, D. Beltrán-Alcrudo, R. Kock, S.M. Mor Global trends in infectious diseases at the wildlife-livestock interface Proc. Natl. Acad. Sci 2015 9662 9667

[41] A. Wiratsudakul, P. Suparit, C. Modchang Dynamics of Zika virus outbreaks: an overview of mathematical modeling approaches PeerJ 2018 e4526