TRANSACTIONS OF THE ROYAL SOCIETY OF TROPICALMEDICINE AND HYGIENE (1991) 85, 255-259 The dynamics of infection and disease in Bancroftian filariasis 255 A. Srividya’, S. P. Pani’, P. K. Rajagopalan’, D. A. P. Bundy* and B. T. Grenfel13 ‘Vector Control Research Centre, Medical Complex, Indira Nagar, Pondicheny 605 006, India; 2Parasite Epidemiology Research Group Department of Pure and Applied Biology, Imperial College, Prince Consort Road, London, SW7 2BB, UK; ‘Department of Zoology, University of Cambridge, Dozoning Street, Cambridge, CB2 3EJ, UK Abstract This study examines the relationship between the dvnamics of Wwhereria bancrofti infection and the d&elopment of chronic lymph&c disease. Data sets from Pondicherry, south India, and Calcutta are used to estimate the age-specific proportion of the endemic population which has converted from microfilaria positive to amicrofilaraemia, and is assumed to be at risk of disease. For men, but not women, the age-prevalence profile of the estimated population ‘at risk’ is shown to correspond closely to the observed age-prevalence of chronic lymphatic disease in the samecommunity. For both sexes,and independent of age, approximately 11% of the population at risk eventually develop lymphoedema. These observations suggest that filariasis endemic populations consist of those individuals who remain amicrofilaraemic and asymptomatic, and those who progress through the sequence: uninfected, microfilaraemic, amicrofilar- aemic, to develop irreversible obstructive lymphatic pathology. Introduction Although the major clinical manifestations of Ban- croftian filariasis have been extensively described, their relationship with the course of infection remains enigmatic (WHO, 1984). Most of the recent work in this area has sought correlates between disease and immunological status. It has been suggested (OTTESEN, 1980) that there is a spectrum of disease with different manifestations corresponding to clus- ters of patients with different immune responses: hyporesponsive asymptomatic microfilaraemic indi- viduals; hyper-responsive asymptomatic amicrofilar- aemic individuals (‘endemic normals’), and those predominantly amicrofilaraemic individuals with lym- phatic pathology whose immune responsivenessis at an intermediate level. A fourth category of individuals with occult filariasis is of considerable immunological interest! but is difficult to examine in the present epidemlological analysesas it involves less than 1% of patients (OTTESEN, 1984). The implication of this categorization is that individuals are predisposed, perhaps genetically (OTTESEN et al., 1981), to a particular level of immune responseto infection? and thus to a particular type of symptomatology. This is an essentially static view of the epidemiology of lymphatic filariasis. In this paper we explore a dynamic perception of the development of lymphatic disease, in which it is assumed that individuals orogress from one categorv to another during the devdopment of pathol<g$ Specifically, it is assumed that individuals progress from uninfected to asymptomatic microfilaraemic, and then become amicrofilaraemic as lymphatic pathology develops. This model predicts that the proportion of the population which develops lympha- tic disease should be the same as, or less than, the proportion which has converted from microfilaraemia to amicrofilaraemia. This relationship is explored using exceptionally detailed longitudinal data on Bancroftian iilariasis in Pondicherry, south India (VANAMAIL et al., 1989; PANI et al., 1989) and cross-sectionaldata from Calcutta, Bengal (GUBLER & BHATTACHARYA, 1974; DONDERO et al., 1976). Materials and Methods Conceptual framework In H pre;ious paper (VANAMAIL et al., 1989) we used a reversible catalvtic model (MUENCH. 1959: HAIRSTON & JACHOW~KI,1968) io describe the dynamics of filariasis transmission. In brief, the model used data from an age-stratified cohort studv (1981-1986) of 7525 peopc in Pondicherry, south India (RAIAGOPALAN et al.. 1989: SUBRAMANIAN et al., 19‘89)-to estimate the rates at’which individuals becamemicrofilaria positive or negative. These analy- ses showed that the rate of becoming microtiaria positive was age-dependent, rising to a maximum in the 16-20 year age-class and declining slightly in adulthood. In contrast, the rate of loss of microfilarial positivity was independent of age and the loss occurred in all age-classes after an average period of 5.4 years of microfilaraemia. The equilibrium dynamics of the microfilaria nega- tive (U) and microfilaria positive (I) portions of the human population were successfully described by the coupled differential equations dI/dt=-bI+aU . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (1) dU/dt=-aU+bI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (2) where a is the instantaneous rate of gain of microfilaria positivity, and b is the instantaneous rate of loss. Using a similar model, HAIRSTON & JACHOWSKI (1968) suggested that the cumulative proportion of people at time t who had ever been microfilaria positive (I’f) could be estimated from I’,=l-exp(-at) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (3) where the rate of gain of microfilarial positivity is assumed to be independent of age. The corresponding r$ationship+for age-specific values of a is given by $i;r~-~~-IJ1) exp[-a,] (t2-!I)] . . . . . . . . . . . . . . . . . . . . . . . . . . (4) 1s the proportlon who have ever been microfildfa positive at time t2, It,1 is the proportion at time tl, and a,] is the rate of gain of microfilarial positivity between tl and t2. Note that for the first age class I*tl is zero and the relationship collapses to equation (3). Thus, provided the age-specific infection para-