Mathematical model of the life cycle of taenia-cysticercosis: transmission dynamics and chemotherapy (Part 1).

Background: Taenia solium is the aetiological agent of human taeniasis, pig cysticercosis and human neurocysticercosis, which are serious public health problems, especially in developing countries.
Methods: A mathematical model of the transmission dynamics of taeniasis-cysticercosis is formulated. The model consists of a coupled system of differential equations, which are density-dependent equations for describing the flow of the parasite through the life cycle. The model is hybrid since it comprises deterministic equations with stochastic elements which describe changes in the mean parasite burden and incorporates the overall pattern of the parasites' distribution.
Results: Sensitivity and bifurcation analyses were carried out to determine the range of values of the model. The model can reproduce the observed epidemiological patterns of human taeniasis, pig and human cysticercosis. For example, for a wide range of parameter values, the mean intensity of adult worms tends to rapidly stabilize in one parasite per individual host. From this model, we also derived a Susceptible-Infected model to describe the prevalence of infection in humans and pigs. Chemotherapeutic interventions against pig cysticercosis or human taeniasis may reduce rapidly and effectively the mean intensity of human taeniasis, pig cysticercosis and human cysticercosis. This effect can be achieved even if the protective efficacy of the drug is of the order of 90% and the coverage rate is 90%. This means that health in humans infected either with adult worms or cysticerci may be achieved by the application of anthelmintic drugs against pig cysticercosis. However, treatment against human cysticercosis alone, does not influence neither human teniasis nor pig cysticercosis. This is because human cysticercosis infection does not influence the value of the basic reproductive number (Ro).
Conclusions: Even coverage of 100% in the administration of anthelmintics did not eliminate the infection. Then elimination of the infection in all hosts does not seem a feasible goal to achieve by administering only chemotherapeutic interventions. Throughout the manuscript a discussion of our model in the context of other models of taeniasis-cysticercosis is presented.