ABSTRACT
Dengue is the transmission disease occurred by biting of infected Aedes aegypti and infected Aedes albopictus. The temperature of each area influences to the transmission of this disease. In this paper, we describe the transmission of this disease by using mathematical model. We separate the human population into susceptible, exposed, infectious and recovered classes. The vector population is divided into Aedes aegypti and Aedes albopictus. The mosquito population is separated into susceptible, exposed and infectious classes. We analyzed our mathematical model by finding the equilibrium points and determined the stability of each steady state. The numerical solutions are shown. The difference of temperatures is shown to describe the behaviors of human and vector populations. From the results, we will see that the temperature influences to the transmission of dengue disease.
- Marinho, R.A., Beserra, E.B., ,Bezerra-M.A., Porto V.S.,Olinda R.A. and Santos C. 2016. Effects of temperature on the life cycle, expansion, and dispersion of Aedesaegypti (Diptera: Culicidae) in three cities in Paraiba, Brazil. Journal of Vector Ecology.41(1), pp.1-10.Google ScholarCross Ref
- Ponlawat A., Harrington L.C. 2005. Blood feeding patterns of Aedes aegypti and Aedes albopictus in Thailand. 2005. Journal of Medical Entomology. 42(5), pp.844-849.Google ScholarCross Ref
- Morin C.W., Comrie A.C., Ernst K. 2013. Climate and dengue transmission: evidence and implications. Environmental Health Perspective.121, pp.1264-1272.Google ScholarCross Ref
- Dengue. Available from https://www.honestdocs.co/dengue-symptoms-and-prevention/Google Scholar
- Reinhold,J.,Lazzari, C. and Lahondère, C.2018.Effects of the Environmental Temperature on Aedes aegypti and Aedes albopictus Mosquitoes: A Review. Insects,9(4):158. doi: 10.3390/insects9040158.Google ScholarCross Ref
- Joanna, M., Reinhold, Claudio, R. Lazzari and ChloéLahondère. 2018. Effects of the Environmental Temperature on Aedes aegypti and Aedesalbopictus Mosquitoes: A Review, Insects. 9, 158; doi:10.3390/insects9040158.Google Scholar
- Rowley, W.A.; Graham, C.L. 1968. The effect of temperature and relative humidity on the flight performance of female Aedes aegypti. J. Insect Physiol. 14, 1251–1257.Google ScholarCross Ref
- LöwenbergNeto, P.; Navarro-Silva, M.A. 2004. Development, longevity, gonotrophic cycle and oviposition of Aedes albopictusSkuse (Diptera: Culicidae) under cyclic temperatures. Neotrop.Entomol. 33, 29–33.Google ScholarCross Ref
- Corfas,R.A.;Vosshall,L.B. 2015. ThecationchannelTRPA1tunesmosquitothermotaxistohosttemperatures. eLife,4, e11750.Google Scholar
- Ross, R. 1911. The Prevention of Malaria. John Murray, London.Google Scholar
- Wongkoon, S., Jaroensutasinee, M.,Jaroensutasinee K., 2012. Development of temporal modelingfor prediction of dengue infection in Northeastern Thailand. Asian Pacific Journal of TropicalMedicine. Asian Pacific Journal of Tropical Medicine.pp.249-252.Google Scholar
- Wongkoon,S., Jaroensutasinee,M. and Jaroensutasinee, K., 2016. Spatio-temporal climate-based model of dengue infection in Southern, Thailand. Tropical Biomedicine, 33(1), 55–70.Google Scholar
- Phaijoo, G.R. and Gurung, D.B., 2017. Modeling Impact of Temperature and Human Movement on the Persistence of Dengue Disease.Computational and Mathematical Methods in Medicine, Article ID 1747134, pp.1-9.Google Scholar
- Chanprasopchai, P., Pongsumpun, P. and Tang, I.M.,2017. Effect of rainfall for the dynamical transmission model of the dengue disease in Thailand.Computational and Mathematical Methods in Medicine.Article ID 2541862, pp.1-17.Google Scholar
- Pongsumpun,P., Tang,I.M. and Wongvanich, N., 2019, Optimal control of the dengue dynamical transmission with vertical transmission. Advances in Difference Equations, 176,https://doi.org/10.1186/s13662-019-2120-6.Google Scholar
- Sungchasit R. and Pongsumpun,P, 2019. Mathematical Model of Dengue Virus with Primary andSecondary Infection. Current Applied Science and Technology, 19(2),pp.154-176.Google Scholar
- van den Driesschea, P.,Watmough, J. Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. 2002. Mathematical Biosciences, Volume 180, Issues 1–2, 29-48.Google ScholarCross Ref
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