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.
Highlights
The Chikungunya virus is a type of arbovirus, so it is only transmitted by hematopoietic arthropods that become infected after biting some vertebrates
In order to better understand the dynamics of how the Chikungunya virus is transmitted, we propose and analyze a mathematical model given by a system of nonlinear differential equations where the populations of hosts and mosquitoes are homogeneous
We present a mathematical model of the spread of the Chikungunya disease at the population level that incorporates the transmission vector by including cross-transmission between the human and vector populations
Summary
The Chikungunya virus is a type of arbovirus, so it is only transmitted by hematopoietic arthropods that become infected after biting some vertebrates. In [15], the authors presented results regarding the risk of Zika and Chikungunya virus transmission in human population centers of the eastern United States In this way, in order to better understand the dynamics of how the Chikungunya virus is transmitted, we propose and analyze a mathematical model given by a system of nonlinear differential equations where the populations of hosts and mosquitoes are homogeneous. The authors demonstrated the influence of humans on the infection of the latency period They remarked about the necessity of fitting the model to real data so that it will be useful in controlling the spread of the virus. Another interesting work was presented in [26], where the authors proposed a mathematical model of three age-structured transmissions of Chikungunya virus.
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