Mathematical modelling of vector-borne diseases

Vector-borne diseases account for approximately 17% of all infectious diseases in the word and cause about 700 000 deaths each year. Vector-borne diseases are transmitted by vectors, which include mosquitoes, ticks, and fleas. In our work we mainly focus on diseases transmitted by mosquitoes like dengue, zika and chikungunya. We extend classical SISUV model [4] to fractional-order system given by fractional-order differential equations [2] .This type of model better characterizes the virus transmission process as it involves memory and hereditary properties. We also consider fractional version of SIRUV model [3]. We investigate asymptotic stability for both models and perform numerical simulations.

References: [1] P. van den Driessche, J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Mathematical Biosciences 2002, pp. 29–48, 180.
[2] Matigon D. Stability Results For Fractional Differential Equations With Applications To Control Processing Compput Eng Syst Appl, Vol.2, Citeseer, 1996, pp 963–968
[3] Rocha, F., Aguiar M, Souza M., Stollenwerk N. Time-scale separation and centre manifold analysis describing vector-borne disease dynamics, International Journal of Computer Mathematics , 2013, pp. 2105–2125, https://doi.org/10.1080/00207160.2013.783208
[4] Rocha, F., Mateus L., Skwara U. Aguiar M., Stollenwerk N., Understanding dengue fever dynamics: a study of seasonality in vector-borne disease models, International Journal of Computer Mathematics 2015, pp. 1405-1422 , https://doi.org/10.1080/00207160.2015.1050961
[5] WHO. www.who.int/news-room/fact-sheets/detail/vector-borne-diseases