%0 Journal Article
%T Maximum Equilibrium Prevalence of Mosquito-Borne Microparasite Infections in Humans
%A Marcos Amaku
%A Marcelo Nascimento Burattini
%A Francisco Antonio Bezerra Coutinho
%A Luis Fernandez Lopez
%A Eduardo Massad
%J Computational and Mathematical Methods in Medicine
%D 2013
%I Hindawi Publishing Corporation
%R 10.1155/2013/659038
%X To determine the maximum equilibrium prevalence of mosquito-borne microparasitic infections, this paper proposes a general model for vector-borne infections which is flexible enough to comprise the dynamics of a great number of the known diseases transmitted by arthropods. From equilibrium analysis, we determined the number of infected vectors as an explicit function of the model¡¯s parameters and the prevalence of infection in the hosts. From the analysis, it is also possible to derive the basic reproduction number and the equilibrium force of infection as a function of those parameters and variables. From the force of infection, we were able to conclude that, depending on the disease¡¯s structure and the model¡¯s parameters, there is a maximum value of equilibrium prevalence for each of the mosquito-borne microparasitic infections. The analysis is exemplified by the cases of malaria and dengue fever. With the values of the parameters chosen to illustrate those calculations, the maximum equilibrium prevalence found was 31% and 0.02% for malaria and dengue, respectively. The equilibrium analysis demonstrated that there is a maximum prevalence for the mosquito-borne microparasitic infections. 1. Introduction Vector-borne diseases such as malaria, dengue, yellow fever, plague, trypanosomiasis, and leishmaniasis have been major causes of morbidity and mortality through human history [1]. Currently, half of the world¡¯s population is infected with at least one type of vector-borne pathogens [2, 3]. Only one mosquito-borne infection, dengue fever, affects the lives of 3.6 billion people worldwide [4, 5]. In the 17th through early 20th centuries, human morbidity and mortality due to vector-borne diseases outstripped all other causes combined [6]. By the 1960s the majority of vector-borne infections have been effectively controlled or targeted for intensive programmes. However, such programmes were discontinued in the 1970s because vector-borne infections were no longer considered major public health problems [7¨C10]. As a consequence, in the 1980s, the world observed a resurgence of old vector-borne diseases and the emergence of new ones [11]. The historical paradigm of mosquito-borne infections, malaria, accounts for the most deaths than any other human vector-borne diseases, with approximately 300 million people infected and up to one million deaths every year [12, 13]. Explosive epidemics have also marked the resurgence of dengue and yellow fever [1], and a great number of the most important vector-borne human diseases have exhibited dramatic changes in
%U http://www.hindawi.com/journals/cmmm/2013/659038/