Models for the spread and persistence of  hantavirus infection in rodents with direct and  indirect transmission

Curtis L. Wesley; Linda J. S. Allen; Michel Langlais; Curtis L. Wesley; Linda J. S. Allen; Michel Langlais

doi:10.3934/mbe.2010.7.195

Mathematical Biosciences and Engineering

2010, Volume 7, Issue 1: 195-211. doi: 10.3934/mbe.2010.7.195

Previous Article Next Article

Models for the spread and persistence of hantavirus infection in rodents with direct and indirect transmission

1.
Louisiana State University in Shreveport, Department of Mathematics, Shreveport, LA 71115
2.
Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX 79409-1042
3.
Université Victor Segalen Bordeaux 2, IMB UMR CNRS 5251 & INRIA Bordeaux Sud Ouest projet Anubis, case 36, UFR Sciences et Modelisation, 3 ter place de la Victoire, 33076 Bordeaux Cedex

Received: 01 March 2009 Accepted: 29 June 2018 Published: 01 January 2010
MSC : Primary: 37N25, 34C25; Secondary: 37M99, 37B25.

Hantavirus, a zoonotic disease carried by wild rodents, is spread among rodents via direct contact and indirectly via infected rodent excreta in the soil. Spillover to humans is primarily via the indirect route through inhalation of aerosolized viral particles. Rodent-hantavirus models that include direct and indirect transmission and periodically varying demographic and epidemiological parameters are studied in this investigation. Two models are analyzed, a nonautonomous system of differential equations with time-periodic coefficients and an autonomous system, where the coefficients are taken to be the time-average. In the nonautonomous system, births, deaths, transmission rates and viral decay rates are assumed to be periodic. For both models, the basic reproduction numbers are calculated. The models are applied to two rodent populations, reservoirs for a New World and for an Old World hantavirus. The numerical examples show that periodically varying demographic and epidemiological parameters may substantially increase the basic reproduction number. Also, large variations in the viral decay rate in the environment coupled with an outbreak in rodent populations may lead to spillover infection in humans.

Keywords:

Citation: Curtis L. Wesley, Linda J. S. Allen, Michel Langlais. Models for the spread and persistence of hantavirus infection in rodents with direct and indirect transmission[J]. Mathematical Biosciences and Engineering, 2010, 7(1): 195-211. doi: 10.3934/mbe.2010.7.195

Related Papers:

[1]	Junli Liu . Threshold dynamics of a time-delayed hantavirus infection model in periodic environments. Mathematical Biosciences and Engineering, 2019, 16(5): 4758-4776. doi: 10.3934/mbe.2019239
[2]	Raimund BÜrger, Gerardo Chowell, Elvis GavilÁn, Pep Mulet, Luis M. Villada . Numerical solution of a spatio-temporal gender-structured model for hantavirus infection in rodents. Mathematical Biosciences and Engineering, 2018, 15(1): 95-123. doi: 10.3934/mbe.2018004
[3]	Chandrani Banerjee, Linda J. S. Allen, Jorge Salazar-Bravo . Models for an arenavirus infection in a rodent population: consequences of horizontal, vertical and sexual transmission. Mathematical Biosciences and Engineering, 2008, 5(4): 617-645. doi: 10.3934/mbe.2008.5.617
[4]	Danfeng Pang, Yanni Xiao . The SIS model with diffusion of virus in the environment. Mathematical Biosciences and Engineering, 2019, 16(4): 2852-2874. doi: 10.3934/mbe.2019141
[5]	Rajanish Kumar Rai, Pankaj Kumar Tiwari, Yun Kang, Arvind Kumar Misra . Modeling the effect of literacy and social media advertisements on the dynamics of infectious diseases. Mathematical Biosciences and Engineering, 2020, 17(5): 5812-5848. doi: 10.3934/mbe.2020311
[6]	Jingli Xie, Hongli Guo, Meiyang Zhang . Dynamics of an SEIR model with media coverage mediated nonlinear infectious force. Mathematical Biosciences and Engineering, 2023, 20(8): 14616-14633. doi: 10.3934/mbe.2023654
[7]	Xi-Chao Duan, Xue-Zhi Li, Maia Martcheva . Dynamics of an age-structured heroin transmission model with vaccination and treatment. Mathematical Biosciences and Engineering, 2019, 16(1): 397-420. doi: 10.3934/mbe.2019019
[8]	Xia Wang, Yuming Chen . An age-structured vector-borne disease model with horizontal transmission in the host. Mathematical Biosciences and Engineering, 2018, 15(5): 1099-1116. doi: 10.3934/mbe.2018049
[9]	Jianxin Yang, Zhipeng Qiu, Xue-Zhi Li . Global stability of an age-structured cholera model. Mathematical Biosciences and Engineering, 2014, 11(3): 641-665. doi: 10.3934/mbe.2014.11.641
[10]	Sarafa A. Iyaniwura, Musa Rabiu, Jummy F. David, Jude D. Kong . Assessing the impact of adherence to Non-pharmaceutical interventions and indirect transmission on the dynamics of COVID-19: a mathematical modelling study. Mathematical Biosciences and Engineering, 2021, 18(6): 8905-8932. doi: 10.3934/mbe.2021439

Abstract

Hantavirus, a zoonotic disease carried by wild rodents, is spread among rodents via direct contact and indirectly via infected rodent excreta in the soil. Spillover to humans is primarily via the indirect route through inhalation of aerosolized viral particles. Rodent-hantavirus models that include direct and indirect transmission and periodically varying demographic and epidemiological parameters are studied in this investigation. Two models are analyzed, a nonautonomous system of differential equations with time-periodic coefficients and an autonomous system, where the coefficients are taken to be the time-average. In the nonautonomous system, births, deaths, transmission rates and viral decay rates are assumed to be periodic. For both models, the basic reproduction numbers are calculated. The models are applied to two rodent populations, reservoirs for a New World and for an Old World hantavirus. The numerical examples show that periodically varying demographic and epidemiological parameters may substantially increase the basic reproduction number. Also, large variations in the viral decay rate in the environment coupled with an outbreak in rodent populations may lead to spillover infection in humans.

This article has been cited by:

1.	Dionysios Christos Watson, Maria Sargianou, Anna Papa, Paraskevi Chra, Ioannis Starakis, George Panos, Epidemiology of Hantavirus infections in humans: A comprehensive, global overview, 2014, 40, 1040-841X, 261, 10.3109/1040841X.2013.783555
2.	Hyun Mo Yang, The basic reproduction number obtained from Jacobian and next generation matrices – A case study of dengue transmission modelling, 2014, 126, 03032647, 52, 10.1016/j.biosystems.2014.10.002
3.	S. Madec, C. Wolf, A multi-structured epidemic problem with direct and indirect transmission in heterogeneous environments, 2012, 6, 1751-3758, 235, 10.1080/17513758.2011.553392
4.	Nicolas Bacaër, El Hadi Ait Dads, On the biological interpretation of a definition for the parameter R 0 in periodic population models, 2012, 65, 0303-6812, 601, 10.1007/s00285-011-0479-4
5.	Zhenguo Bai, Yicang Zhou, Addendum, 2011, 15, 1553-524X, 915, 10.3934/dcdsb.2011.15.915
6.	Verónica Anaya, Mostafa Bendahmane, Michel Langlais, Mauricio Sepúlveda, A convergent finite volume method for a model of indirectly transmitted diseases with nonlocal cross-diffusion, 2015, 70, 08981221, 132, 10.1016/j.camwa.2015.04.021
7.	Cong Jin, Dexin Li, 2015, 9781118644713, 43, 10.1002/9781118644843.ch3
8.	Jie Lou, Yijun Lou, Jianhong Wu, Threshold virus dynamics with impulsive antiretroviral drug effects, 2012, 65, 0303-6812, 623, 10.1007/s00285-011-0474-9
9.	Maia Martcheva, Xue-Zhi Li, Competitive exclusion in an infection-age structured model with environmental transmission, 2013, 408, 0022247X, 225, 10.1016/j.jmaa.2013.05.064
10.	Jonas Reijniers, Katrien Tersago, Benny Borremans, Nienke Hartemink, Liina Voutilainen, Heikki Henttonen, Herwig Leirs, Why Hantavirus Prevalence Does Not Always Increase With Host Density: Modeling the Role of Host Spatial Behavior and Maternal Antibodies, 2020, 10, 2235-2988, 10.3389/fcimb.2020.536660
11.	Colleen B. Jonsson, Luiz Tadeu Moraes Figueiredo, Olli Vapalahti, A Global Perspective on Hantavirus Ecology, Epidemiology, and Disease, 2010, 23, 0893-8512, 412, 10.1128/CMR.00062-09
12.	L. J. S. ALLEN, V. L. BROWN, C. B. JONSSON, S. L. KLEIN, S. M. LAVERTY, K. MAGWEDERE, J. C. OWEN, P. VAN DEN DRIESSCHE, MATHEMATICAL MODELING OF VIRAL ZOONOSES IN WILDLIFE, 2012, 25, 08908575, 5, 10.1111/j.1939-7445.2011.00104.x
13.	Wei Ye, Yongni Xu, Yuan Wang, Yangchao Dong, Qianqian Xi, Mengyuan Cao, Lan Yu, Liang Zhang, Linfeng Cheng, Xingan Wu, Zhikai Xu, Yingfeng Lei, Fanglin Zhang, Hantaan virus can infect human keratinocytes and activate an interferon response through the nuclear translocation of IRF-3, 2015, 29, 15671348, 146, 10.1016/j.meegid.2014.11.009
14.	Alison Adams, Quiyana M. Murphy, Owen P. Dougherty, Aubrey M. Sawyer, Fan Bai, Christina J. Edholm, Evan P. Williams, Linda J.S. Allen, Colleen B. Jonsson, Data-driven models for replication kinetics of Orthohantavirus infections, 2022, 349, 00255564, 108834, 10.1016/j.mbs.2022.108834
15.	Juan Pablo Gutiérrez Jaraa, María Teresa Quezada, Modeling of hantavirus cardiopulmonary syndrome, 2022, 22, 07176384, e002526, 10.5867/medwave.2022.03.002526
16.	Torsten Thalheim, Tyll Krüger, Jörg Galle, Indirect Virus Transmission via Fomites Can Counteract Lock-Down Effectiveness, 2022, 19, 1660-4601, 14011, 10.3390/ijerph192114011
17.	Briana Spruill-Harrell, Anna Pérez-Umphrey, Leonardo Valdivieso-Torres, Xueyuan Cao, Robert D. Owen, Colleen B. Jonsson, Impact of Predator Exclusion and Habitat on Seroprevalence of New World Orthohantavirus Harbored by Two Sympatric Rodents within the Interior Atlantic Forest, 2021, 13, 1999-4915, 1963, 10.3390/v13101963
18.	Dorcus C. A. Omoga, David P. Tchouassi, Marietjie Venter, Edwin O. Ogola, Gilbert Rotich, Joseph N. Muthoni, Dickens O. Ondifu, Baldwyn Torto, Sandra Junglen, Rosemary Sang, Divergent Hantavirus in Somali Shrews (Crocidura somalica) in the Semi-Arid North Rift, Kenya, 2023, 12, 2076-0817, 685, 10.3390/pathogens12050685
19.	Juan Pablo Gutiérrez-Jara, María Teresa Muñoz-Quezada, Fernando Córdova-Lepe, Alex Silva-Guzmán, Mathematical Model of the Spread of Hantavirus Infection, 2023, 12, 2076-0817, 1147, 10.3390/pathogens12091147
20.	Asep K. Supriatna, Herlina Napitupulu, Meksianis Z. Ndii, Bapan Ghosh, Ryusuke Kon, Chung-Min Liao, A Mathematical Model for Transmission of Hantavirus among Rodents and Its Effect on the Number of Infected Humans, 2023, 2023, 1748-6718, 1, 10.1155/2023/9578283
21.	Natalia Shartova, Fedor Korennoy, Svetlana Zelikhina, Varvara Mironova, Li Wang, Svetlana Malkhazova, Spatial and temporal patterns of haemorrhagic fever with renal syndrome (HFRS) and the impact of environmental drivers in a border area of the Russian Far East, 2024, 1863-1959, 10.1111/zph.13118

Reader Comments

Your name:*

Email:*
© 2010 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)