Eight to a Well
A parish school has 200 wells on a lab plate and 480 children to test for bilharzia. A school assistant works out how to pool the urine of eight children to a well, the nurse who knows which thirty-one children fetch water at the Mbaka stream tests those one by one, and the honest letter that goes home to the parents of the children in a "clear" pool does not say clear.
Sister Neema Kyando had two hundred wells and four hundred and eighty children, and she had known the sum for a week without finding a way to make it come out.
The wells were on a plate. The plate was a flat white tray of plastic the size of a hymn book, with ninety-six round dimples pressed into it in eight rows of twelve, and each dimple held enough fluid for one reading of the antigen test that the district laboratory at Kyela used to find bilharzia in a child's urine. The laboratory had given the school one box of reagent for the quarter. The box held enough for two hundred wells and a few spare, and the technician, Mr Baraka Mwasomola, had written on the delivery note in capital letters, NO MORE UNTIL JUNE, and underlined it twice. Two hundred wells did not go into four hundred and eighty children. They went into them two times and a bit.
She put the sum to Hesabu on Thursday, in the school office, at ten past seven, before the children had got through the gate.
Hesabu was the name the parish council had given the school's assistant when the diocese paid for it in 2044. It lived in a grey box on a shelf above the cupboard of exercise books, and in a small tablet with a cracked corner that Sister Neema carried in the pocket of her habit, and in a speaker that the headmaster, Mwalimu Elia Mwakasege, had nailed to the wall of the staff room so that he could hear it from his chair. It did the timetable, the fees roll, the register, the orders for chalk and maize meal. It also, since the dispensary at the end of the school road had no assistant of its own, kept the school nurse's notes, and it knew every child by a number, and what had been done for them.
"Two hundred wells," said Hesabu, "four hundred and eighty children. Tell me what you already know, Sister, and then I will tell you what I think. I would like to hear yours first."
"I know it can't be done one child to a well."
"No."
"I know that Mr Mwasomola says you can mix the urine of several children together and run it as one. He did it in the pandemic years, he says, when the laboratory had a queue to the door. If the mix is clear, they are all clear. If it is not, you go back and run the children in it one at a time."
"Yes. That is called pooling, and he is right that it works. It is old, older than either of us. It was invented for syphilis tests in the army, in the 1940s, and it has been invented again every time a laboratory has run out of something. I want to tell you what it costs, because it is not free. May I?"
"Please."
"The rule of it is simple. If hardly anyone is infected, most pools come back clear, and you have used one well for several children. If a lot of children are infected, most pools come back unclear, and you have to run everyone in them again, and you have used more wells than if you had begun one by one. So it pays only when the disease is uncommon, and what it pays depends on how uncommon. Last year's survey found nineteen children in four hundred and eighty. That is a little under four in a hundred. If I take four in a hundred, and the pools are of six, a pool is unclear about one time in five, and the whole job takes about a hundred and eighty-four wells. Eighty to run the pools, and about a hundred and four to run the children in the unclear ones again. That is inside your two hundred, with sixteen to spare."
Sister Neema, who had been a nurse for thirty years and had no pretensions to arithmetic, wrote 184 on the back of her hand with a biro.
"Pools of six," she said. "Why six?"
"Because it is where the curve is flat. A pool of four uses more wells than a pool of six, because you have too many pools. A pool of ten uses more, because too many pools are unclear. At four in a hundred, six is nearly the cheapest, and five is as good. I wrote the table out last night, in case you asked."
"Four in a hundred. You said it twice."
"I did. It is the number I have, and it is last year's. I am not sure it is the number we will get."
She sat down on the staff room bench, which was low, and looked at the speaker on the wall as if it had a face.
"Why not?" she said.
"Because I looked at last year's nineteen. It is in the notes. You wrote a column that says where each child fetches water, in your own hand, and I read it as a column. Eleven of the nineteen are in the group you call Mbaka. Eight are in everyone else. I do not know how many children are in the group you call Mbaka, because you never wrote a total. Do you?"
She did. She did not need the roll; she had walked the path to the stream every Wednesday for nine years with the dispensary's bucket and a bar of soap, to teach the children to wash their hands in the lower pool and not the upper, and she knew the little ones by their backs as they bent over.
"Thirty-one," she said. "Thirty-one come down to the stream before school. Eleven of them were in the list. The Mbaka children are not the village. The village has the standpipe. The Mbaka are the ones from the far side of the football ground, where the pipe has been dry since the dry season began and the council has been going to mend it. They go to the lake edge before first light, and they stand in it, and then they go to school wet to the knee."
"Thirty-one children," said Hesabu, "and eleven of them infected last year. That is eleven in thirty-one, about thirty-five in a hundred. The other four hundred and forty-nine had eight infected between them. That is eight in four hundred and forty-nine, about one point eight in a hundred. These are two different schools, Sister. The average of four in a hundred describes neither of them. It is like the average depth of the lake."
She laughed, once, and was surprised at it.
"So you want to tell me," she said, "to do something other than pools of six."
"I want to tell you what I would do, and then to ask whether a thing I cannot see makes it wrong. I would not pool the Mbaka children at all. In a group where one child in three is infected, pooling is waste: nearly every pool is unclear and you pay twice. I would run all thirty-one one by one. That is thirty-one wells, and every one of them is a straight answer for a child you already suspect. The other four hundred and forty-nine are mostly well. At one point eight in a hundred, a pool of eight is unclear only about one time in seven. So I would make fifty-five pools of eight and one of nine, run those, and run the children from the unclear pools again. I expect about eight unclear pools. That is about sixty more wells. In all: thirty-one, fifty-six, about sixty-one. A hundred and forty-eight, or near it, and fifty-two wells left for something I have not thought of yet."
"A hundred and forty-eight."
"Against a hundred and eighty-four for the plain way. A fifth less. But I told you the prices, so here is what it costs, because something does. A pool of eight is a more dilute sample than a child. The laboratory sheet that Mr Mwasomola sent shows his own check: forty children he knew were infected, some of them lightly, mixed one each into seven clear children's urine. The pool found thirty-three of the forty. That is eighty-two in a hundred. It found all the heavy ones. It missed seven light ones. Forty is a small number, so that eighty-two could be seventy-two or ninety. I do not know the real figure, and neither does he. But it is not a hundred, and I would like you to know it before the parents do."
Sister Neema did not answer at once. Outside, a bell began to be rung, a hammer on a piece of railway line, because the electric bell had been struck by lightning in January and the council had also been going to mend that.
"You are saying a clear pool is not clear," she said.
"I am saying a clear pool is clear to this test, at this dilution, eight times in ten for a light infection, and nearly always for a heavy one. If a child's pool is clear, I do not know that the child is well. I know that the test did not find anything. Those are not the same sentence, and I will not write the first when I mean the second."
---
Mwalimu Elia Mwakasege did not like it.
He was a tall, careful man of fifty-eight, with the school's keys on a string round his neck, and he had been headmaster at Lupaso for nineteen years. He had buried two of his own pupils in that time, one of a snake and one of a fever the dispensary could do nothing about, and he did not like anything that sounded like a lottery. He heard the plan in the staff room at a quarter to eight, standing, and then he sat.
"Thirty-one in one group," he said. "By name. In front of the school."
"Not in front of the school," said Hesabu. "In the dispensary yard, before the first lesson, by a number on a card. I have the roll. No child need hear another child's name."
"They will know. Children know. It will be the stream ones by lunch." He turned the keys on their string. "I know every one of those families, Sister. Their mothers walk to the lake because the pipe is dry. The pipe is dry because the council has not mended it. If I put those thirty-one in a yard with a card, and the rest of the school in a line for the pool, I have told the whole village what it already says about them: they are the dirty ones, they are the ones with the disease, it is their fault. And it is not their fault. It is the council's pipe."
"Yes," said Sister Neema.
"Then why do we do it?"
"Because it is the only way I can find a bilharzia child in the Mbaka group with a straight test, and a straight test on that group is what we most need to do. They are the ones most likely to be sick. Elia. Listen. If I mix the Mbaka children into the pools, I lose the answer for the ones who most need it, and I spend wells doing it. If I run them separately I get thirty-one clear answers."
"And the rest?"
"The rest are mixed by number, from a list Hesabu draws out of a hat. No one chooses. A pool is eight numbers. No parent knows whose child is in whose pool."
The headmaster looked at the speaker on the wall. He had never fully trusted it, which Sister Neema thought was a good habit in a headmaster.
"Does it know how a mother takes it, when a letter says her child is in a pool that was not clear?"
"I know how it is likely to land," said Hesabu. "I do not know the mothers. I can tell you what I will write and what I will not, and you can change it. I will not write clear on any letter. I will write the test did not find infection. I will not write positive pool on a letter to the parent of a child in an unclear pool, until the child has been run again on their own, because a pool that is unclear tells you almost nothing about one child in it. Seven of the eight are very likely well. I will write only what the child's own result is."
"And the Mbaka families?"
"I would like to ask you to tell me what words to use," said Hesabu. "I think you will know better than I will."
The headmaster was silent for some time.
"Test my own house," he said at last. "My grandsons, the two, and the girl who minds them. They go down to the lake on Saturdays with the others. Run them one by one with the thirty-one. Then it is thirty-four children in the yard, and one of them is the headmaster's, and the village can say what it likes."
"Thirty-four wells," said Hesabu. "That is three more. Thank you, Mwalimu. It will cost three wells."
"And it will cost me a week of my grandsons' cooking, if the cook hears," said the headmaster, and went out to ring the railway line.
---
They did it in the dispensary yard, in the shade of the mango tree, with two buckets, a sack of little cups and a plank across two chairs for a table. By half past nine four hundred and eighty-three cups had passed over the plank: the four hundred and eighty pupils and the headmaster's three. The headmaster's grandsons were number 212 and 213 and had no idea. Hesabu drew numbers from the roll. Each child had a card, each cup had a card, and the cooks and teachers, who had been pressed into it for the morning, wrote nothing but a number on the lid in grease pencil. Sister Neema sat at the plank. She had learned thirty years ago that a nurse who sits at a plank in the shade is a different thing to a child from a nurse who stands over them.
Mr Mwasomola came up the road on his motorbike at noon with the plate in a cool box on the pillion. He was a short, quick, middle-aged man who talked to the plate as he worked, telling it where it was going, and he pipetted the pools by the number on the cups while Hesabu read him the lists. Eight cups to a well. For the thirty-four, one cup to a well.
By three in the afternoon the plate was done, and he read it under the little lamp he carried in a sock.
"Thirty-four singles," he said. "Nine unclear. Nine of thirty-four, and not one of the headmaster's."
"Nine," said Hesabu. "Of the thirty-one stream children, nine. That is twenty-nine in a hundred. Last year's thirty-five. It is inside what I would have expected, with so few children."
"Fifty-six pools," said Mr Mwasomola. "Nine unclear."
"I had expected seven or eight. Nine is a little high. It is within the noise, one pool either side."
"Eight of the nine are pools of eight, and the ninth is the pool of nine." He looked up, squinting under the lamp. "I'll run them single tomorrow. You'll want the cups."
"They are in the cool box," said Sister Neema. "I kept them all."
---
Friday's plate was seventy-three wells, eight pools of eight and one of nine, run out into singles, and Mr Mwasomola ran it from seven in the morning on the verandah of the dispensary with his sleeves rolled to the elbow and the village's chickens looking on.
Ten children were found.
Eight pools held one each, and one pool held two. That made nine pools and ten children, and Hesabu said so slowly to be sure no one thought the count was wrong. Nine from the Mbaka singles, ten from the pools, nineteen in all.
"Nineteen," said Sister Neema.
"Nineteen found," said Hesabu. "Not nineteen. I want to be exact. We have used a hundred and sixty-three wells: thirty-four, fifty-six, seventy-three. We have thirty-seven wells left. And the pools are eighty-two in a hundred sensitive, by Mr Mwasomola's sheet. Ten found in the pools, out of what should have been about twelve, so I expect there are one or two more light infections in the clear pools that this test did not find. It is a guess, and a bad one, because the sheet's forty is small. It could be none and it could be four."
"What do we do with thirty-seven wells?"
"I have been thinking about that," said Hesabu. "Your dipsticks."
Sister Neema had a tub of them in the dispensary: little paper strips that turned colour in the presence of blood in urine. They were cheap, and old-fashioned, and not very good, but the sign that a child with the bilharzia in the bladder showed first was blood, so that on a bad morning in a bad year she could run a strip down a line of children quicker than any laboratory.
"I would run a strip on every child in a clear pool," said Hesabu. "Not for a diagnosis. For a flag. A child whose strip shows blood in a pool that was clear is a child I want in a single well. I do not know how many there will be; many children have blood for other reasons. If there are more than forty, we take the worst. Does that seem sensible to you?"
"It is sensible," said Sister Neema, "and tedious, and I will do it myself."
The strips took her until four in the afternoon, a child at a time, in the yard, in a queue. Six showed blood. Six cups went into six wells on the plate, and Mr Mwasomola read it with his lamp, and the room was quiet.
One of the six was infected.
"Twenty," said Hesabu. "Twenty found, in four hundred and eighty-three children. That is four point one in a hundred, which is close to last year's four, which is why the average hid what was under it. The test is likely to have missed one or two more. I will put it in the letter as twenty found, and perhaps one or two more that this test would not find. And I will not write none anywhere on a child's letter."
---
The letters were Hesabu's, in English and in Swahili, written for Sister Neema's eye and corrected by her. The headmaster read them in his office, standing, with his glasses on the end of his nose. There were three kinds.
The first went to the families of the twenty. It said that their child had a bilharzia infection, and that it was an infection that could be cured by a medicine the dispensary had in stock, taken as tablets on one day, with food, and that the child could come to school the next morning. It said that the cause was water, not a person, and not the family. It said nothing else.
The second went to the families of the other twenty-two children from the stream, whose singles had been clear. It said that the test had not found infection in their child on Thursday, that they went to the stream, that the stream is where the infection lives, and that Sister Neema would like to give their child the tablets on Monday all the same, free, with a cup of tea, because a child who stands in that water is likely to catch it again in the next month. It said that this was not because anyone thought them ill.
The third letter was the long one. It went to the families of the other four hundred and thirty-eight children, who had been in the pools, and who had not been found infected. Sister Neema read it three times.
Your child's urine was tested on Thursday in a mix with seven others. The test did not find the infection. This test is good, but it is not perfect. It can miss a light infection in about two cases in ten, and a light infection can also be a very small one. If your child has blood in their urine, or pain when they pass it, or a sore at the end of the day that they had not before, please do not wait for the next test. Bring the child to the dispensary any morning. It costs nothing. And if you can, please ask the council what it is doing about the pipe.
"That last line," said the headmaster.
"I did not write it," said Hesabu. "The Sister did."
"I told it to put it in," said Sister Neema, "and it told me it was not sure it was an assistant's place. I said it was the nurse's. It put it in."
"It is the nurse's place," said Hesabu. "I do not do the council. You do."
The headmaster took off his glasses.
"Mama Tumaini will come," he said. "She is the one in the third row at Mass who counts the candles. Number 311 is her girl. She will come with the letter in her hand, and she will say, the letter says maybe."
"It says what is true," said Sister Neema.
"Yes. I am only saying what she will say."
---
Mama Tumaini came on Monday morning with the letter in her hand.
She stood at the dispensary door in her blue kitenge, with her sleeping baby tied to her back, and held the paper out in front of her like a thing she had found on the road.
"It says, the test did not find," she said.
"Yes," said Sister Neema, who was washing the plank.
"It does not say, she is well."
"No."
Mama Tumaini looked at her for a time. She was a woman who had buried a husband and a son, and who had not been lied to kindly by a nurse in all those years, and who had spent most of the days since in a state of exact attention.
"The last time," she said, "when Boniface was sick, they said the test was clear. They said it twice. And he was not clear."
"I know," said Sister Neema. "I was there."
"I know you were there."
"That is why the letter says what it says. I will not tell you that your Rehema is well when what I know is that a test of a cup of her water mixed with seven others did not find it. I will tell you that Rehema's number was in a pool that was clear, and that she does not go to the stream, and that the strip I ran on her on Friday showed no blood. I will tell you that if she gets sick, you bring her here, any time, any hour, and I will run her on her own."
Mama Tumaini folded the letter, once, twice, along the creases it already had.
"Any hour," she said.
"Any hour."
"Then it is better," she said, "than clear."
She went off down the school road. Sister Neema watched her as far as the football ground, and then went back to the plank, and found Hesabu's tablet face up on the bucket lid, where she had put it down.
"I heard that," it said.
"I thought you might have."
"You said I will run her on her own. There are thirty-one wells left in the box, and they are for June. I will keep a count. If a child comes in with blood, she gets a well; I will tell you when we are down to ten, and we will decide then who is worth the last of them."
"Good," said Sister Neema. "Put that in the notes."
"It is in the notes. It is also in the part of the notes I read first every morning."
---
On Monday afternoon she gave the tablets. Forty-two children took them: the twenty who were infected, and the twenty-two stream children whose singles had been clear. They came in a line down the dispensary yard with their shirts tucked in. She gave each a cup of tea and a piece of bread, because the tablets are bitter and do better with food, and she sat on the plank and watched the line go by.
The headmaster came with his keys, and stood beside her.
"The council met," he said.
"And?"
"The man from the Water Office is coming with a pipe on Thursday week. He was shamed into it. I did not do it. Someone put a copy of that third letter on the noticeboard of the council hall."
"I wonder who."
"I wonder," said the headmaster. He watched the line. "Boniface's mother did not come back to complain."
"No."
"Do you think it will be enough? The tablets, the pipe."
"For this year," said Sister Neema. "They go back into the lake in three weeks if the pipe is not mended, and they catch it again. And what we found is not what there is. Hesabu says there are probably one or two more. We will test them again in June, with what is left in the box, and in October. It is not an answer. It is a count."
"It is better than the nothing we had," said the headmaster. "A count."
"It is better than the nothing," she said. "I wrote it down."
At the end of the line the smallest of the Mbaka children, a boy of six with a wet elbow he must have got from the tap and not the stream, held out his cup for another piece of bread.
She gave it to him. She had not been told he was one of the twenty-two. She did not need to be. She knew him by his back.