Mathematical model for the propagation of T. Gondii in relation to pregnant women in the city of Neiva

Abstract

Toxoplasma gondii is Toxoplasmosis cause, one of the most frequent parasitosis in the world. In Colombia, congenital Toxoplasmosis is an infection of very high prevalence, it is considered that half of Colombia’s population has been exposed to this parasite. Similarly, in the city of Neiva the prevalence of this disease is high (55.4% for IgG and 10.4% for IgM) compared to other cities in Colombia, although this is not considered as a public health problem, hence the reason for this study.

Some existing mathematical models on Toxoplasmosis have been reviewed and it was determined that the most suitable for the treatment related to cats and water transport, given that the statistical study was carried out on a par with the mathematical model, showed the cats that have (p = 0.003, OR = 9,100) and drinking tap water (p = 0.000; OR = 4,149) were the risk factors with the greatest relationship with the disease in the city of Neiva.

The mathematical model used had a system in partial differential equations that models the propagation of the parasite through water and cats. It is an adaptation of a classic epidemiological model type SIR to which it can add dispersion of T. gondii and, additionally, an advective term that represents the transport by water of the parasite. The numerical solution of equation (1) was used to present the results of the simulations.