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Healthy Math

Simple mathematical tools and statistics help prevent and control epidemics

“My work consists of translating epidemiological concepts into mathematical language, applying them in preparing scenarios of infectious diseases and providing information to help strategies for containing or eradicating infectious diseases”. This is how the researcher Hyun Mo Yang sums up his dedication to mathematical epidemiology, a field of applied research that has shown highly positive results in a short time. Linked  to the Mathematics, Statistics and Scientific Computing Institute (Imecc) of the Campinas State University (Unicamp), Yang has two projects in the field, both financed by FAPESP.

Born in 1959 in Teajon, South Korea, and living since 1968 in São Paulo, Yang specialized in mathematical and statistical instruments applied to Nuclear Physics. He graduated in 1983 from the Physics Institute of the University of São Paulo (USP), where he completed his master’s degree in 1985, and his doctorate in 1990, both in Nuclear Physics. In immersing himself in such a specialized subject, little by little, he began to feel the need to devote himself also to an area with more social scope and he set out in epidemiological studies.

Plagues and dengue
Between 1998 and 2000, Yang conducted the Study of the Transmission of Epidemics and Diseases Caused by Micro and Macro-parasites and Possible Containment Mechanisms. Before even completing it he moved on to develop another project in November 1999: The Study of the Biological, Social and Environmental Factors in the Transmission of Dengue in order to Establish Mechanisms for Containment and Prevention – Quantitative Epidemiological. Undertaken in partnership with the Control of Endemic Diseases Superintendency (Sucen in the Portuguese acronym), of the State Health Secretariat, the new project covers the study of mathematical models for the factors involved in the transmission of diseases by the mosquito Aedes aegypti.

Objectives and models
In the struggle against infectious diseases, attempts are made to contain and combat them in order to achieve results in the short-term. To do this, they are examined in two groups: those transmitted indirectly (depending on insects or other vectors, such as dengue, malaria and Chaga’s disease) and those transmitted directly (which do not depend on intermediaries to be transmitted, such as measles, mumps, and German measles). There are some crucial questions. For example: how to establish the priority areas for campaigns for combating transmitting insects? How to define priority age groups for a vaccination campaign? Or what is the most appropriate time for the campaign?

In summary, there are two main objectives: a mathematical description of the dissemination and an analysis of the containment or eradication mechanisms for the diseases. To carry this out, statistical models applied to non-infectious diseases are not enough. Dynamic mathematical models have to be developed taking into account factors such as temperature, socioeconomic conditions, propagation characteristics of the microorganisms and various other factors, including the interaction between three distinct groups of people: the infected, the recovered and the susceptible. “Doing the modeling just for the model’s sake may be very pretty but you have to do it so that it leads to a result”, says Yang.

Mathematical epidemiology can also help in understanding various environmental and socioeconomic factors related with public health. An example is the study Yang recently developed, in partnership with Marcelo Ferreira, of USP’s Biomedical Sciences Institute, intended to help understanding the effects of global warming and the social and economic conditions involved in malaria transmission . The work was published in the May 2000 issue of Public Health magazine (Assessing the Effects of Global Warming and Local Social and Economic Conditions on Malaria Transmission).

In other works, he had already handled mathematical models applied to infectious diseases in general, including the transmission of the HIV virus.

His studies have convinced him of the need to expand the base of professionals in mathematical epidemiology. “Besides doing the research as such, I should like to arouse the interest of students of the exact sciences in the immense field of the application of mathematics to medical and biological sciences”.

Mathematical epidemiology has old roots. The first steps had already been taken in 1760 with the work of the Swiss Daniel Bernoulli (1700-1782), Essai d’une Nouvelle Analyse de La Mortalité Causée par la Petite Vérole et des Advantages de l’inoculation pour la Prévenir (Essay on a New Analysis of Mortality Caused by Smallpox and the Advantages of Vaccination in Preventing It).

Open field
However, this pioneering effort was only to be taken up again in the early years of the 20th century by British scientists, in work done on various epidemic diseases. The field is still little explored. According to the epidemiologist Eduardo Massad, deputy-director of USP’s School of Medicine, even in developed countries public health programs have little contact with research using the dynamic models of mathematical epidemiology. Even the United States, that have the powerful Centers for Disease Control (CDCs) commanded from Atlanta, Georgia, realized, a short time ago, the importance of the field, where statistical probability applications generally predominate. According to Massad, the tradition of use of dynamic mathematical models only really exists in Britain. In Brazil, the country still has serious epidemic problems, particularly those associated with the so-called tropical diseases, so Yang has a broad field to work in.

Control of German Measles

The first significant experiment in applying mathematical epidemiological models to a control strategy for a directly transmitted infectious disease in Brazil took place on 1992 in the State of São Paulo. At the time, the Pan-American Health Organization (PAHO) had recommended vaccinating all children and teenagers  from 9 months to 15 years of age with the triple vaccine – against German measles, measles, and mumps. The expected cost of the campaign, that should have provided 12 million doses, was US$ 35 million.

Nonetheless, a study then in course sponsored by FAPESP – Methods of Assessing the Effect of Strategies for Immunizing against Directly Transmitted Diseases – gave the authorities the certainty of being able to reach the same immunizing potential with less work and with a significant reduction in the expected costs.

“Our work showed that it would be enough to vaccinate everyone between 1 and 10 years of age, which would require only 7 million vaccine doses”, states Eduardo Massad, coordinator of this study and the head of the Medical Information Technology Laboratory of the USP’s Faculty of Medicine. Using this strategy enabled the cost of vaccination to be lowered by US$ 15 million, a saving of  43%. Done between 1992 and 1995, the study was financed by  R$ 145,000.

The campaign gave FAPESP the opportunity of publicizing the highly significant results: effective control of congenital German measles syndrome, the cause of high levels of deafness, blindness, and metal retardation in children all over the country, was achieved. Besides this, serological studies carried out between 1992 and 1995 with blood samples from 3,000 children in schools and day care centers in public system in São Paulo showed strong indications that the German measles virus was no longer circulating in the State among children up to 10 years old, as reported by Notícias FAPESP in April 1996.

Regarding measles, the results achieved by the 1992 campaign would have enabled total immunization of the population for at least seven years, since routine vaccination, applied to children between 9 months and 15 years of age, would be able to prevent outbreaks of epidemics, according to Yang.

This routine vaccination, however, was not efficient, in Yang’s opinion, since there were failures in the vaccination itself and the vaccination stations ran out of supplies. “As a result, we saw a serious measles epidemic in 1997”, points out the researcher. He also points to a factor against which vaccination campaigns have little preventive power: the campaign and the routine vaccination were unable to prevent migratory tendencies and the variations in non-biological factors. Therefore, the inclusion of susceptible and infected individuals alters the scenario of a community that, otherwise, would have a much higher number of immune individuals after a mass vaccination campaign.

The Projects
1. Study of the Transmission of Epidemics and Diseases Caused by Micro and Macro-parasites and Possible Containment Mechanisms; Type Support for research project; Coordinator Hyun Mo Yang – Unicamp; Investment R$ 10,000.00 and US$ 22,189.73
2. The Study of the Biological, Social and Environmental Factors in the Transmission of Dengue in Establishing Mechanisms for Containment and Prevention – Quantitative Epidemiological (nº 98/14184-4); Type Public Policy Research Program; Coordinator Hyun Mo Yang – Unicamp; Investment R$ 11,820 (Phase I) and R$ 137,000 (Phase II – project being examined)