Joan L. Aron

Mathematical modelling of immunity to malaria

Abstract A comparison of two epidemiological models of immunity to malaria shows that different characterizations of immunity boosted by exposure to infection generate qualitatively different results. Attempts to control disease by reducing transmission or increasing the recovery rate can produce an increase in prevalence in the compartmental model with discrete epidemiological states. However, the parasite density always decreases in response to disease control in the model with continuous epidemiological variables. Each model accounts for some epidemiological patterns. The increase in prevalence seen in the compartmental model is in accord with observed effects of variation in transmission. Parasite suppression in areas of antimalarial drug use is consistent with the effect of an increased recovery rate in the density model. Future work should combine the two approaches, perhaps by using the compartmental model over the low to moderate range of infection rates and switching to the density model at high infection rates. In any case, the validation of models needs to take account of the usage of antimalarial drugs as well as the intensity of transmission.

Acquired immunity dependent upon exposure in an SIRS epidemic model

Abstract The dynamics of immunity boosted by reexposure to infection are incorporated into an SIRS (Susceptible/Infected/Recovered (immune)/Susceptible) epidemic model. The basic reproductive rate, R 0 , is derived. If R 0 is less than unity, there exists a unique, stable equilibrium which is disease-free. If R 0 is greater than unity, the disease-free equilibrium is unstable and there exists a unique stable endemic equilibrium. The qualitative picture is unchanged if immune individuals also contribute to transmission, as long as the degree of infectivity of immune individuals does not exceed that of infected individuals who are ill. Analysis of this simple model illustrates how the phenomenon of boosted immunity complicates disease control. Partially effective disease control may be harmful because reduction of transmission may lead to increased prevalence of illness. Furthermore, predictions concerning the effect of control are sensitive to uncertainty about the relative contributions of symptomatic infected individuals and asymptomatic immune carriers to the reservoir of infection.

Incidence estimates of late stages of trachoma among women in a hyperendemic area of central Tanzania

:The purpose of this study is to estimate 5‐year incidences of conjunctival scarring and trichiasis, and 10‐year incidence of corneal opacities due to trachoma, using prevalence data from a population sample of 6038 women living in a trachoma‐hyperendemic area of central Tanzania. Previous surveys have documented the age‐specific prevalence of scarring, trichiasis, and corneal opacities in women in hyperendemic areas. Using the age‐stratified prevalences of these different clinical signs, corresponding incidence rates were estimated. Transition rates from one sign to the next were also obtained by restricting the risk group to only women with a specific trachoma sign. Thus, the 5‐year incidence of trichiasis among women with conjunctival scarring, and the 10‐year incidence of corneal opacities among women with trichiasis were estimated. Incidences of all the signs markedly increased with age. For scarring, 5‐year incidence rates increased from 3.1% in the 15–19 age category to 14.3% for women between 55 and 59 years. The 5‐year incidence of trichiasis ranged from 0.3% in the 15–19 age category to 7.5% in the age group 55–59. Corneal opacities due to trachoma were highest in the age group 45–54; the 10‐year incidence increased to 2.8%. The 5‐year incidence of trichiasis among only women with scars increased from 3.2% in the 15–19 age group to 15.1% in women in the 55–59 age group. Once trichiasis is present, almost one‐third of the women below 35 and more than 40% of the women older than 45 will develop corneal opacities in a 10‐year interval. These estimates are important in understanding the dynamics of progression of trachoma from conjunctival scarring to the potentially blinding signs of trichiasis and corneal opacities. They provide important information for planning adequate services in areas where trachoma is endemic and surgery for trichiasis is a key factor to avoid blindness from trachoma. They also provide clues to the pathogenesis that may be useful in the development of new methods of control.

Multiple attractors in the response to a vaccination program.

Though it is well known that multiple attractors may co-exist in the SEIR (susceptible/exposed/infective/recovered) epidemic model with vital dynamics and seasonally forced oscillations in transmission, the epidemiological significance of multiple attractors has been a subject of debate. I show that the co-existence of attractors is relevant in using the model to study the dynamics of the introduction of a vaccination program into a stable epidemic cycle. Responses to the program may include more than one attractor. The exact timing of the introduction of the program relative to the original epidemic cycle is critical in determining which attractor appears in the response. Analysis of this simple model suggests that the role of multiple attractors in the response to vaccination should be examined in more realistic epidemiological models.

Note on the formulation of a stochastic model of superinfection

Abstract We incorporate a process of removal (e.g., death) directly into the basic stochastic model for superinfection and recovery in order to describe explicitly the dynamics of infection within an individual. Formulae are derived for the mean duration of infection and the probability of removal during a bout of infection. A common method of approximating this joint process with a differential equation results in overestimation of these two quantities.

Application of Models from Epidemiology to Metrics for Computer Virus Risk

One aspect of maintaining integrity in information systems is establishing an organizational environment that will prevent the damage caused by external agents. One particularly insidious such agent is the computer virus. It can alter data often without the owner or user of that data being aware. Establishing such an environment can often rely on the availability of metrics for organizational characteristics associated with harm to data integrity. This paper will focus on the development of organizational metrics for the threat of computer viruses. It is expected that many of these metrics will apply to other threats to data integrity although we have not pursued that line of research.

Assessment of the risk of HIV spread via non-steady heterosexual partners in the U.S. population

We evaluate the conditions for the initial spread of HIV infection via non-steady heterosexual partners in the U.S. population. The main source of data is a 1988 U.S. survey on sexual partners in the 12 months prior to the survey. The behavioral data are coupled with a multi-state life table constructed from 1985 U.S. rates of marriage, divorce and mortality. The life table allows for projections that take age, sex and marital status into account.

Mathematical modeling of immunity to malaria

Abstract A comparison of two epidemiological models of immunity to malaria shows that different characterizations of immunity boosted by exposure to infection generate qualitatively different results. Attempts to control disease by reducing transmission or increasing the recovery rate can produce an increase in prevalence in the compartmental model with discrete epidemiological states. However, the parasite density always decreases in response to disease control in the model with continuous epidemiological variables. Each model accounts for some epidemiological patterns. The increase in prevalence seen in the compartmental model is in accord with observed effects of variation in transmission. Parasite suppression in areas of antimalarial drug use is consistent with the effect of an increased recovery rate in the density model. Future work should combine the two approaches, perhaps by using the compartmental model over the low to moderate range of infection rates and switching to the density model at high infection rates. In any case, the validation of models needs to take account of the usage of antimalarial drugs as well as the intensity of transmission.