An example from the world of tsetse flies

John Hargrove; John Hargrove

doi:10.3934/mbe.2013.10.691

Mathematical Biosciences and Engineering

2013, Volume 10, Issue 3: 691-704. doi: 10.3934/mbe.2013.10.691

Previous Article Next Article

An example from the world of tsetse flies

John Hargrove

1.
SACEMA, (DST/NRF Centre of Excellence, in Epidemiological Modelling and Analysis), 19 Jonkershoek Road,Stellenbosch 7600

Received: 01 October 2012 Accepted: 29 June 2018 Published: 01 April 2013
MSC : Primary: 92.

In biomathematics, communication between mathematicians and biologists is crucial. This matter is illustrated using studies aimed at estimating mortality rates of tsetse flies (Glossina spp.). Examples are provided of apparently sound pieces of mathematics which, when applied to real data, provide obviously erroneous results. More serious objections arise when mathematical models make no attempt to address the real world in such a way that they can be tested. Unless models account for the known biology of the problem under investigation, and are challenged with data, the existence and nature of imperfections in the models will likely not be detected.

Keywords:

Tsetse Glossina mortality estimation communication.

Citation: John Hargrove. An example from the world of tsetse flies[J]. Mathematical Biosciences and Engineering, 2013, 10(3): 691-704. doi: 10.3934/mbe.2013.10.691

Related Papers:

[1]	Jinliang Wang, Hongying Shu . Global analysis on a class of multi-group SEIR model with latency and relapse. Mathematical Biosciences and Engineering, 2016, 13(1): 209-225. doi: 10.3934/mbe.2016.13.209
[2]	Pengyan Liu, Hong-Xu Li . Global behavior of a multi-group SEIR epidemic model with age structure and spatial diffusion. Mathematical Biosciences and Engineering, 2020, 17(6): 7248-7273. doi: 10.3934/mbe.2020372
[3]	Hamdy M. Youssef, Najat A. Alghamdi, Magdy A. Ezzat, Alaa A. El-Bary, Ahmed M. Shawky . A new dynamical modeling SEIR with global analysis applied to the real data of spreading COVID-19 in Saudi Arabia. Mathematical Biosciences and Engineering, 2020, 17(6): 7018-7044. doi: 10.3934/mbe.2020362
[4]	Gang Huang, Edoardo Beretta, Yasuhiro Takeuchi . Global stability for epidemic model with constant latency and infectious periods. Mathematical Biosciences and Engineering, 2012, 9(2): 297-312. doi: 10.3934/mbe.2012.9.297
[5]	Andrei Korobeinikov, Philip K. Maini . A Lyapunov function and global properties for SIR and SEIR epidemiological models with nonlinear incidence. Mathematical Biosciences and Engineering, 2004, 1(1): 57-60. doi: 10.3934/mbe.2004.1.57
[6]	Andrey V. Melnik, Andrei Korobeinikov . Lyapunov functions and global stability for SIR and SEIR models withage-dependent susceptibility. Mathematical Biosciences and Engineering, 2013, 10(2): 369-378. doi: 10.3934/mbe.2013.10.369
[7]	Jun Zhai, Bilin Xu . Research on meme transmission based on individual heterogeneity. Mathematical Biosciences and Engineering, 2021, 18(5): 5176-5193. doi: 10.3934/mbe.2021263
[8]	Cheng-Cheng Zhu, Jiang Zhu, Xiao-Lan Liu . Influence of spatial heterogeneous environment on long-term dynamics of a reaction-diffusion SVIR epidemic model with relaps. Mathematical Biosciences and Engineering, 2019, 16(5): 5897-5922. doi: 10.3934/mbe.2019295
[9]	Shanjing Ren . Global stability in a tuberculosis model of imperfect treatment with age-dependent latency and relapse. Mathematical Biosciences and Engineering, 2017, 14(5&6): 1337-1360. doi: 10.3934/mbe.2017069
[10]	Junyuan Yang, Rui Xu, Xiaofeng Luo . Dynamical analysis of an age-structured multi-group SIVS epidemic model. Mathematical Biosciences and Engineering, 2019, 16(2): 636-666. doi: 10.3934/mbe.2019031

Abstract

References

[1]	John Wiley & Sons, Chichester, 1977
[2]	Bulletin de la Société de Pathologie Exotique, 58 (1965), 250-259.
[3]	Bulletin of Entomological Research, 59 (1968), 651-658.
[4]	Medical and Veterinary Entomology, 3 (1989), 83-95.
[5]	Insect Science and its Application, 11 (1990), 323-330.
[6]	in "Management of Insect Pests: Nuclear and Related Molecular and Genetic Techniques", International Atomic Energy Agency, Vienna, (1993), 549-556.
[7]	Medical and Veterinary Entomology, 13 (1999), 165-176.
[8]	Entomologia Experimentalis et Applicata, 92 (1999), 89-99.
[9]	Entomologia Experimentalis et Applicata, 100 (2001), 151-164.
[10]	DFID Animal Health Programme, Edinburgh, UK, (2003), 133 + ix pp.
[11]	PowerPoint Presentation of a Talk Delivered at: Mathematical Methods in Systems Biology and Population Dynamics (4-7 January 2012, Cape Town, South Africa). Available from: http://www.sacema.com
[12]	Medical and Veterinary Entomology, 25 (2011), 385-394.
[13]	Acta Biotheoretica, 44 (1996), 317-33.
[14]	Bulletin of Entomological Research, 89 (1999), 515-521.
[15]	Biometrika, 52 (1965), 225-247.
[16]	Bulletin of Entomological Research, 58 (1968), 399-410.
[17]	Bulletin of the World Health Organisation, 46 (1972), 33-38.
[18]	Bulletin of Entomological Research, 62 (1973), 423-438.
[19]	Entomologia Experimentalis et Applicata, 12 (1969), 33-43.
[20]	Bulletin of Entomological Research, 64 (1974), 313-324.
[21]	Biometrika, 52 (1965), 249-259.
[22]	Charles Griffin & Co, London, 1982.
[23]	Bulletin of Entomological Research, 64 (1974), 545-588.
[24]	Bulletin of Entomological Research, 72 (1982), 71-93.
[25]	Bulletin of Entomological Research, 78 (1988), 51-61.

This article has been cited by:

1.	Ling Zhang, Jingmei Pang, Jinliang Wang, Stability Analysis of a Multigroup Epidemic Model with General Exposed Distribution and Nonlinear Incidence Rates, 2013, 2013, 1085-3375, 1, 10.1155/2013/354287
2.	Lianwen Wang, Zhijun Liu, Xingan Zhang, Global dynamics of an SVEIR epidemic model with distributed delay and nonlinear incidence, 2016, 284, 00963003, 47, 10.1016/j.amc.2016.02.058
3.	Wei Duan, Zhichao Song, Xiaogang Qiu, Heterogeneous edge weights promote epidemic diffusion in weighted evolving networks, 2016, 30, 0217-9849, 1650300, 10.1142/S0217984916503000
4.	Aberrahman Iggidr, Gauthier Sallet, Max O. Souza, On the dynamics of a class of multi-group models for vector-borne diseases, 2016, 441, 0022247X, 723, 10.1016/j.jmaa.2016.04.003
5.	Lin Zhao, Zhi-Cheng Wang, Shigui Ruan, Traveling wave solutions in a two-group SIR epidemic model with constant recruitment, 2018, 77, 0303-6812, 1871, 10.1007/s00285-018-1227-9
6.	Haitao Song, Weihua Jiang, Shengqiang Liu, Global dynamics of two heterogeneous SIR models with nonlinear incidence and delays, 2016, 09, 1793-5245, 1650046, 10.1142/S1793524516500467
7.	Jinliang Wang, Xianning Liu, Modeling diseases with latency and nonlinear incidence rates: global dynamics of a multi-group model, 2016, 39, 01704214, 1964, 10.1002/mma.3613
8.	Jinhu Xu, Yicang Zhou, Global stability of a multi-group model with vaccination age, distributed delay and random perturbation, 2015, 12, 1551-0018, 1083, 10.3934/mbe.2015.12.1083
9.	GLOBAL DYNAMICS IN A MULTI-GROUP EPIDEMIC MODEL FOR DISEASE WITH LATENCY SPREADING AND NONLINEAR TRANSMISSION RATE, 2016, 6, 2156-907X, 47, 10.11948/2016005
10.	F. Capone, V. De Cataldis, R. De Luca, On the Stability of a SEIR Reaction Diffusion Model for Infections Under Neumann Boundary Conditions, 2014, 132, 0167-8019, 165, 10.1007/s10440-014-9899-7
11.	Matthias Ehrhardt, Ján Gašper, Soňa Kilianová, SIR-based mathematical modeling of infectious diseases with vaccination and waning immunity, 2019, 37, 18777503, 101027, 10.1016/j.jocs.2019.101027
12.	Florinda Capone, Valentina De Cataldis, Roberta De Luca, Influence of diffusion on the stability of equilibria in a reaction–diffusion system modeling cholera dynamic, 2015, 71, 0303-6812, 1107, 10.1007/s00285-014-0849-9
13.	R. N. Mohapatra, Donald Porchia, Zhisheng Shuai, 2015, Chapter 51, 978-81-322-2484-6, 619, 10.1007/978-81-322-2485-3_51
14.	F. Capone, V. De Cataldis, R. De Luca, On the nonlinear stability of an epidemic SEIR reaction-diffusion model, 2013, 62, 0035-5038, 161, 10.1007/s11587-013-0151-y
15.	Xiaomei Feng, Zhidong Teng, Fengqin Zhang, Global dynamics of a general class of multi-group epidemic models with latency and relapse, 2015, 12, 1551-0018, 99, 10.3934/mbe.2015.12.99
16.	Huicong Li, Rui Peng, An SIS epidemic model with mass action infection mechanism in a patchy environment, 2022, 0022-2526, 10.1111/sapm.12553
17.	Lin Zhao, Propagation dynamics for a time-periodic reaction-diffusion two group SIR epidemic model, 2024, 0, 1531-3492, 0, 10.3934/dcdsb.2024114
18.	Hyukpyo Hong, Eunjin Eom, Hyojung Lee, Sunhwa Choi, Boseung Choi, Jae Kyoung Kim, Overcoming bias in estimating epidemiological parameters with realistic history-dependent disease spread dynamics, 2024, 15, 2041-1723, 10.1038/s41467-024-53095-7

Reader Comments

Your name:*

Email:*
© 2013 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)