A mathematical model for Dengue and Chikungunya in Mexico

Abstract

We present a model that incorporates two co-circulating viral diseases, Dengue and Chikungunya, where we allow secondary infections from either of the two diseases. We only consider one vector population, Ae. aegypti since in the Mexican region where we set our scenarios, only this species has been reported to transmit both viruses. We estimate the basic reproduction number and perform numerical simulations for dierent scenarios where we may observe coexistence of Dengue and Chikungunya; we also compare the results of the model with Dengue and Chikungunya data from Mexico 2015 and we obtain a good model t. To complete our ndings we perform a sensitivity analysis, and calculate the partial rank correlation coecients (PRCCs) to determine the parameter values inuence on the reproduction numbers and predict fate of the diseases.We show that R0 for each one of the viruses is highly sensitive to the mosquito biting rate and the transmission rates for both diseases with positive inuence and the average lifespan of mosquito along with the human recovery rate with negative inuence on both diseases. Our results are consistent with those of previous authors.

A mathematical analysis of the dynamics of chikungunya virus transmission

“…Age structured deterministic model also proposed, analyzed theoritically and numerically [32]. Authors in [33], formulate a model that incorporate the dynamics of two circulating viral disease: dengue and chikungunya by considering variable population size and infection in sub-acute and chronic phase but not analyzed the model qualitatively. The spatio-temporal transmission of chikungunya is analysed in [34] and it is shown that the prevention of moving symptomatic individuals is not sufficient mechanisms to control the outbreak, since the presence of asymptomatic individuals spread the disease silently within the population.…”

Prioritizing Water Security in the Management of Vector‐Borne Diseases: Lessons From Oaxaca, Mexico

“…Human demographic trends and insufficient mosquito management are major factors contributing to increases in dengue transmission, and climatic conditions conducive to the survival and expansion of Ae. aegypti also contribute (Baez‐Harnandez et al, ; Dick et al, ). Human migration, population density, and inadequate water management facilitate residential mosquito populations, particularly in arid regions where they were previously absent (Akanda & Hossain, ).…”

Mathematical Modelling and Analysis of Dengue Transmission in Bangladesh with Saturated Incidence Rate and Constant Treatment Function

“…Based on the classical SIR model, the transmission has been studied in [4], [7], [8], [9], [10], [11], [12], [13], [14]. The authors in [15], [16], [17] have used the SEIR model for the study of the dynamics of dengue. In [5], [18] the authors have introduced migrated and treatment class for human population and aquatic class for vector population.…”