Mathematical Modeling and Characterization of the Spread of Chikungunya in Colombia

Abstract

The Chikungunya virus is the cause of an emerging disease in Asia and Africa, and also in America, where the virus was first detected in 2006. In this paper, we present a mathematical model of the Chikungunya epidemic at the population level that incorporates the transmission vector. The epidemic threshold parameter R 0 for the extinction of disease is computed using the method of the next generation matrix, which allows for insights about what are the most relevant model parameters. Using Lyapunov function theory, some sufficient conditions for global stability of the the disease-free equilibrium are obtained. The proposed mathematical model of the Chikungunya epidemic is used to investigate and understand the importance of some specific model parameters and to give some explanation and understanding about the real infected cases with Chikungunya virus in Colombia for data belonging to the year 2015. In this study, we were able to estimate the value of the basic reproduction number R 0 . We use bootstrapping and Markov chain Monte Carlo techniques in order to study parameters’ identifiability. Finally, important policies and insights are provided that could help government health institutions in reducing the number of cases of Chikungunya in Colombia.

Mathematical modeling to design public health policies for Chikungunya epidemic using optimal control

“…The proposed mathematical model has been used to explain the dynamics of the prevalence of infected people in Colombia 28 . Using the real data, the authors were able to find the values of the unknown epidemiological parameters of the model.…”

“…This mathematical model is defined in the following region, Ω={( s h ( t ), e h ( t ), i h ( t ), c h ( t ), s v ( t ), e v ( t ), i v ( t ))∈[0,1] 8 }, and the solutions will be defined for all time t ≥0 and remain in this region Ω. For more details about the mathematical model, see Reference 28. Initial conditions are given by ( s h (0), e h (0), i h (0), c h (0), s v (0), e v (0), i v (0)).…”

“…The numerical values of the parameters are presented in Table 1, which corresponds approximately to the country of Colombia for years 2016‐2017. These numerical values are the same ones used in Reference 28 and with transmission values β 1 =0.361 and β 2 =0.012. These values were obtained by fitting the mathematical model to real data regarding prevalence of Chikungunya in the human population from Colombia in year 2016 28 .…”

“…These numerical values are the same ones used in Reference 28 and with transmission values β 1 =0.361 and β 2 =0.012. These values were obtained by fitting the mathematical model to real data regarding prevalence of Chikungunya in the human population from Colombia in year 2016 28 . We use a total human population N h of 19 471 223, since this is the number of inhabitants that live under 2200 m where the mosquitoes that transmit the Chikungunya virus live 28 …”

“…There are some mathematical models for the dynamics of Chikungunya virus spread at the population level 27 . Here, we use a particular model developed for the study of the dynamics of Chikungunya in Colombia 28 . This model is given by a system of nonlinear differential equations where the populations of hosts and mosquitoes are homogeneous, and the parameter values were estimated previously 28 …”