Maximum equilibrium prevalence of mosquito-borne microparasite infections in humans.
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.
School of Veterinary Medicine, University of São Paulo, Avenida Prof. Dr. Orlando Marques de Paiva 87, Cep 05508-270 São Paulo, SP, Brazil.
Marcos
M
Amaku
School of Medicine, University of Sao Paulo and LIM 01-HCFMUSP, Rua Teodoro Sampaio 115, Cep 05405-000 São Paulo, SP, Brazil.
Marcelo Nascimento
MN
Burattini
School of Medicine, University of Sao Paulo and LIM 01-HCFMUSP, Rua Teodoro Sampaio 115, Cep 05405-000 São Paulo, SP, Brazil.
Francisco Antonio Bezerra
FA
Coutinho
School of Medicine, University of Sao Paulo and LIM 01-HCFMUSP, Rua Teodoro Sampaio 115, Cep 05405-000 São Paulo, SP, Brazil ; CIARA, Florida International University, Miami, FL 33199, USA.
Luis Fernandez
LF
Lopez
School of Medicine, University of Sao Paulo and LIM 01-HCFMUSP, Rua Teodoro Sampaio 115, Cep 05405-000 São Paulo, SP, Brazil ; London School of Hygiene and Tropical Medicine, London University, London WC1E 7HT, UK.
Eduardo
E
Massad
D000465:Algorithms; D000818:Animals; D050936:Basic Reproduction Number; D003141:Communicable Diseases / Q000453:epidemiology* / Q000635:transmission; D009033:Culicidae; D003715:Dengue / Q000453:epidemiology* / Q000635:transmission; D004196:Disease Outbreaks; D006801:Humans; D007303:Insect Vectors; D008288:Malaria / Q000453:epidemiology* / Q000635:transmission; D008962:Models, Theoretical; D010272:Parasitic Diseases / Q000453:epidemiology* / Q000635:transmission; D015995:Prevalence; D013269:Stochastic Processes