Strategic divorces
We are at last in a position to simulate the effects of divorce and remarriage on the lifetime risk of HIV infection in rural Malawi. We focus in this paper on the southern region where marriage is earliest, divorce is most common, and remarriage is swiftest. This is also the area where because of the activities of the journal keepers we have the best insights into sexual activity outside marriage although, even so, the relevant behavioural input parameters for the model are admittedly speculative.
We first construct two baseline models incorporating the first-marriage patterns of the southern region. We hold constant the parameters governing the sexual activity of unmarried people and the affairs and sexual encounters of married people so that the observed differences stem entirely from divorce and remarriage, mediated, of course, by the extent of sexual activity with non-marital partners. The models differ in that the first does not allow for any divorce or remarriage — marriages are permitted to end only through the death of a spouse, and the survivor does not remarry — whereas the second incorporates the southern region’s patterns of divorce and remarriage.
The models produce a lifetime probability of HIV of 25 per cent in the absence of divorce and remarriage, and of 34 per cent when divorce and remarriage occur according to the regional patterns. However, that divorce and remarriage according to the patterns observed in the south have the net effect of adding nine percentage points to the probability of lifetime HIV infection does not greatly advance our understanding of the mechanisms by which the effect is produced. Most critically, divorce is generated in the second model merely by reference to the regional divorce schedule: we pick a random probability, and where it falls on the probability distribution of the time to divorce dictates whether, and when, a divorce occurs. Thus, divorce is simulated to occur independently of spouses’ sexual activity with other people, a grossly unrealistic assumption given that, as we documented earlier, people may take steps to separate themselves from a risky spouse. What we need to do instead is simulate divorce as a function of such extramarital sexual behaviour.
We define two such strategies. The first is to divorce a spouse once he or she has developed AIDS. Most Malawians do not know their HIV status because testing for HIV is uncommon, especially in rural areas, but people do recognize the symptoms of AIDS and it is likely that at this point some married AIDS sufferers are abandoned by their spouses. The model activates divorce according to a user-defined probability at the point at which either a husband or a wife is simulated to progress to full-blown AIDS.
The second strategy is to divorce a spouse on the basis not of disease status but of behaviour. To operationalize this, we input a threshold number of months for which people in the simulation will tolerate spousal infidelity, and set up a counter for each spouse with a minimum value of zero. If a person has extramarital sex in a particular month, the counter is incremented by a value of one, but if a month goes by without extramarital sex, the counter is reduced by one (although it is not permitted to fall below zero which would imply that people could bank their virtuous months and draw on the accrued credits at a later date). When the counter reaches a threshold number of months and if the individual has had extramarital sex in the current month, there is a possibility (operationalized by a user-defined probability) that a divorce will occur. If it does, it occurs promptly, just like the actual strategic divorces described in the journals. The rule targets repeat offenders but, given that the counter goes backwards in months when a spouse does not misbehave, it also gives people a chance to redeem themselves in the eyes of their spouse by remaining faithful after an affair has been discovered. The present simulations incorporate a threshold for wives’ tolerance of their husband’s infidelity of six months, and a lower threshold of husbands’ tolerance of their wife’s infidelity of four months.
To demonstrate the contrasts most clearly, in simulations in which the HIV-avoidance strategies were activated the probabilities of divorcing an AIDS sufferer or an unfaithful spouse, which are defined by the user, were set to one.
Simulations of each of these strategies were varied further according to whether there was no underlying divorce, meaning that all divorces were the result of strategies to avoid HIV, or whether there was a low level of background divorce. This latter is the more realistic option since, as described earlier, divorces are caused by many factors other than fear of infection. We do not use the observed regional pattern of divorce because it is likely that many of the divorces in the real population were produced by real-life strategies to avoid infection, and application of our simulated HIV-avoidance strategies to that baseline would lead to excessively high divorce rates. On the basis of no empirical evidence whatsoever but a hunch that the risk of divorce for reasons other than the fear of infection would decline rather rapidly with duration we posited an annual probability of divorce of 0.03 in the first year of marriage, 0.02 in the second, and 0.01 in each subsequent year; this implies that five per cent will divorce within two years of marriage, seven per cent within ten years, and nine per cent within 20 years.
Finally, the simulations were distinguished according to whether remarriage is permitted. Simulations which do not allow for remarriage provide a useful basis of comparison for ones in which it does occur. In addition, apprehension, if not fear, of the surviving spouses of AIDS victims is widespread, so the no-remarriage assumption given an AIDS death or AIDS-related divorce is not entirely unrealistic although the strategy may better be viewed as pertaining to a potential new spouse rather than to the divorcing individual.
Simulated lifetime probabilities of HIV infection pertain to simulations with no underlying divorce, column a not permitting remarriage and permitting remarriage at the observed level for the southern region. We incorporate divorce at our hypothetical low background level. The numbered rows distinguish the strategies adopted, with the first row showing the results of baseline simulations which did not incorporate any HIV-avoidance strategies. In the absence of divorce, people remarrying are the widows and widowers of people who died either of AIDS or of some other cause. With low background divorce, people remarrying in model 1d are ones who divorced according to the input level — we call these non-strategic divorce — as well as people whose spouses have died. What happens when additional divorce occurs if a spouse develops AIDS, shows what happens when additional divorce occurs if a spouse has been designated unfaithful shows the effect of people’s using either rule to precipitate divorce. The additional divorces occurring we call strategic divorces.
We try to reveal that the strategy of divorcing a spouse who develops the signs of AIDS is ineffective in reducing the lifetime probability of HIV infection. In a bid for realism the model assumes that sexual activity ceases once when an individual progresses to AIDS, but we had anticipated that this divorce strategy might actually increase lifetime HIV infection because the divorcing spouse would re-enter the marriage market a little sooner if marriage ended through AIDS-related divorce rather than an AIDS death. In addition, the divorcing partner might already be infected.
In contrast, the strategy of divorcing a spouse who has been caught having sex with other people is effective. In the absence of remarriage, lifetime HIV infection falls by between six and eight percentage points, depending on the level of background divorce . The gains are smaller — between two and three percentage points — when remarriage is allowed to occur.
Thus, remarriage is risky. The extent of the risk can be gauged by comparing runs that differ only according to whether remarriage may occur. With no non-strategic divorce, remarriage adds four percentage points to lifetime risk if there is either no divorce at all, or divorce only when a spouse develops AIDS (which has no effect on lifetime infection), but it adds eight or nine percentage points to lifetime risk if divorce occurs in response to a partner’s unfaithfulness. This implies that when there is strategic divorce, about half the increase in lifetime risk caused by remarriage is attributable to remarriage per se, irrespective of whether the previous marriage ended through death from any cause, including AIDS, or through divorce because a spouse had AIDS. The other half of the increase in lifetime risk is attributable to the re-entry into the marriage market of people who have experienced a strategic divorce on the grounds of spousal infidelity.
A similar conclusion can be drawn from a comparison of runs in the presence of non-strategic divorce, that is, with background divorce. Remarriage per se adds five percentage points to lifetime risk, but remarriage after additional divorce because of spousal infidelity adds ten or eleven percentage points. Thus divorce because of spousal infidelity is a reasonable strategy, but not remarrying thereafter is an even better one.
The risk remarriage poses to women is particularly noteworthy because each simulation incorporates a certain amount of sexual activity outside marriage. Even though, according to the specifications, 90 per cent of divorcees and widows have the propensity to have an affair with an annual probability of 0.30 (beyond age 17), it appears that women are overall at lesser risk of infection if none remarries than if some do. Although affairs expose women to a greater variety of sexual partners than does marriage, only slightly more than one-quarter of women (0.90 x 0.30) embark on an affair in any year, the rate of partner change is not excessive since affairs last on average for one year, and coital frequency within such affairs is only half that within marriage. In contrast, the coital frequency of the remarried female population is many times higher, and with that increase comes an elevated risk of HIV infection from new husbands.
No lifetime probability of HIV infection is as high as the 34 per cent (reported earlier in the text) that we obtained from an initial simulation with the regional pattern of divorce and remarriage, in which divorce occurred independently of spousal disease or activity, that is, all divorces were non-strategic. This might seem to suggest that divorcing according to any of the HIV-avoidance strategies we have defined is preferable to not so divorcing, even if remarriage is permitted thereafter. However, a factor contributing to the lower figures in the table than produced by the regional simulation is that the table’s simulations were produced with either no or low underlying divorce. This means not only that correspondingly fewer people in the table’s simulations divorced, but that, as a result, fewer remarried.
Naturally enough, the proportions divorced at each exact duration of marriage rise with the stringency of the divorce strategy but they also rise, slightly, if remarriage is permitted after a spouse has developed AIDS, although they do not rise if remarriage is permitted after divorce because of infidelity. Presumably remarriage after an AIDS-related divorce increases HIV infection among married women and hence increases divorce itself.
The shift in the divorce schedules from the top to the bottom of Table 16 is remarkable. Even without background divorce, when strategic divorces are precipitated by disease or infidelity, the proportions divorcing within ten years of marriage reach 30 per cent with no remarriage, and 34 per cent with remarriage. As expected, the highest proportions in the table are achieved by incorporating a low level of background divorce. It was not expected, however, that one of the simulated divorce schedules would strikingly resemble the actual regional schedule. This schedule was simulated with low background divorce, with additional divorce precipitated by either AIDS or infidelity, and with a possibility of remarriage after such strategic divorces.
The serendipitous correspondence between the actual divorce schedule and this simulated one does not mean that this particular simulation captures the “truth” either about sexual activity with non-spouses in southern rural Malawi or about spouses’ recourse to strategic divorce in a bid to forestall infection with HIV. On the contrary, other combinations of input could lead to
the same result. Rather, the correspondence suggests a degree of consistency between reality and the particular simulation: if women marry and remarry according to the observed pattern, and if women’s and men’s sexual behaviour corresponds to the model input, both inside and outside marriage, and if couple’s divorce according to the strategies we have devised, then women’s divorce patterns will look very like the ones actually observed in this population, and their lifetime probability of HIV infection will be 27 per cent.
Moreover, identifying this particular run gives us an appropriate point of comparison with the initial regional model. Divorce and remarriage occur at the same rate in each population. In one, divorce occurs without reference to spouse’s behaviour, and women’s lifetime risk of HIV infection is 34 per cent. In the other, some divorces are triggered by a spouse’s developing AIDS or being unfaithful, and the lifetime risk is 27 per cent. The strategy represents a 20 per cent reduction in risk.
Finally, recalling our introductory remarks concerning other studies’ observations of the variation in HIV prevalence according to marital status we show for this simulation the proportion of women of each marital status and at each single year of age who are HIV positive. In line with those studies, married women are more likely to be infected than the never-married, especially at young ages, although comparison is difficult at the older ages because so few older women remain unmarried. Likewise, widows and divorcees, in turn, are more likely to be infected, age for age, than married women. That divorcees are more likely to be HIV positive than widows stems from the simulation’s high, but unfortunately realistic, level of background (pre-AIDS) mortality: widows are not necessarily AIDS widows. A simulation (not shown) identical in every way except that background mortality was set with female life expectancy of 60 years rather than 45 years, as in the present simulations, produced a higher prevalence of HIV among widows than divorcees at single years of age until the early thirties.
Faithful couples
Despite the emphasis in this paper on sexual infidelity, the notion that rural Malawian spouses might be faithful to one another is far from fanciful. The journals are replete with references to people who do not manage to “depend” only on their spouse, meaning that they have other sexual partners as well, but there are also many references to the opposite, to people who do manage to “depend” on their spouse, meaning that at least in terms of the “depending” partner, the relationship is a sexually exclusive one. One frequently mentioned motivation for such fidelity is fear of AIDS.
In order to examine the implications for women’s lifetime infection with HIV we next constructed some models in which all couples maintained a sexually exclusive relationship. In terms of model input parameters this means that the propensity for married women to have affairs, previously 0.25, and the propensities for married men to have affairs and visit bar girls, both previously 0.50 are now set to zero. The parameters guiding individuals’ sexual behaviour outside marriage (that is, before first marriage and between marriages) we leave untouched.
We show the lifetime risks of HIV infections derived from the resulting simulations, and the corresponding simulated divorce. In these variants, background divorce is set first to the low level and then to the actual regional level. Simulations incorporating one of the HIV-avoidance strategies already simulated, that people divorce a spouse who develops AIDS, are shown in the second row. The other strategy, of divorcing an unfaithful spouse, is inapplicable in these simulations because all couples are faithful.
The lifetime probability of HIV infection is non-zero (seven per cent) when all couples are faithful and remarriage does not occur. Some of this infection is acquired before the first marriage, and some after that marriage has ended: our couples may be faithful once they are married but they have the same patterns of sexual activity when they are not married as the people in our earlier simulations..
Some familiar patterns emerge, although — and this is the most striking feature of the table — at a lower level than before. As before, divorcing a spouse with AIDS has no effect on women’s lifetime risk of HIV acquisition. Likewise, remarriage is risky, the level of risk rising with the level of divorce and hence the numbers remarrying.
Unlike before, no simulation produces a divorce schedule resembling the actual one. Undoubtedly, an intermediate level of background divorce could be devised to do the job, but the essential point of the simulations is that, with remarriage, a population looking otherwise rather like that of rural southern Malawi, in which all couples are mutually faithful can expect to demonstrate a lifetime risk of HIV infection of somewhere between ten and seventeen per cent. The latter figure is probably too high because it is achieved with too much divorce. Moreover, it is questionable whether our simulated Darby-and-Joan couples could be expected to divorce at a rate as high as is observed in the actual population given the absence of spousal infidelity as a catalyst.
In conclusion, since the proportions of women ultimately infected with HIV are merely the endpoints of a process of HIV acquisition over the life course we next show graphically, for a selection of simulations, the evolution with age of the cumulative proportions of the original cohort of women who are HIV positive. The simulation that best fits the rural southern Malawian population is the second from the top. The effect of no remarriage, everything else being the same, is evident. The effect of spousal fidelity, even with remarriage is pronounced.
In each model the rate of HIV acquisition decelerates beyond a certain age, but this age comes earlier the more stringent the HIV-avoidance strategies that are imposed. Indeed, in terms of HIV infection, the faithful couples already look different from the others by the time they turn twenty.
