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Malaria transmission model for different levels of acquired immunity and temperature-dependent parameters (vector)
1Departamento de Matemática Aplicada do Instituto de Matemática, Estatística e Ciência da Computação, Universidade Estadual de Campinas. Campinas, SP, Brasil. hyunyang@ime.unicamp.br
Objective:
Describe the overall transmission of malaria through a compartmental model, considering the human host and mosquito vector.
Methods:
A mathematical model was developed based on the following parameters: human host immunity, assuming the existence of acquired immunity and immunological memory, which boosts the protective response upon reinfection; mosquito vector, taking into account that the average period of development from egg to adult mosquito and the extrinsic incubation period of parasites (transformation of infected but non-infectious mosquitoes into infectious mosquitoes) are dependent on the ambient temperature.
Results:
The steady state equilibrium values obtained with the model allowed the calculation of the basic reproduction ratio in terms of the model's parameters.
Conclusions:
The model allowed the calculation of the basic reproduction ratio, one of the most important epidemiological variables.