The London School of Hygiene and Tropical Medicine and its projections of the African Covid19 epidemic
18 May 2020
INTRODUCTION
Founded in 1899 with a donation from an Indian philanthropist, the London School of Hygiene and Tropical Medicine is the United Kingdom’s leading institution in the fields of public health and infectious diseases. It has turned its attention to modelling the COVID 19 epidemic in Africa, and South Africa in particular. This brief will outline the structure and assumptions of the projection model and the following brief will set out its projections for South Africa of 5 May 2020.
THE STRUCTURE OF THE MODEL
The model is an SEIR model. The population is divided into four categories. Susceptible (S) people move to the exposed (E) category when they are infected. People move from the E to the I (infectious) category when they become infectious to others. The infectious are then moved to the R (removed) category when they are isolated, or they recover or die. The infected may be asymptomatic, in which case they move through the lower path, or they may become symptomatic, moving along the upper path. The asymptomatic are assumed to be half as infectious as the symptomatic throughout.
The model is stochastic. This means that its projections have a probability distribution rather than a precise outcome. This is so because the transition probabilities between states are not known precisely, but themselves have a probability distribution. The model works by drawing a sample set of transition probabilities, advancing six hours at a time for a year. This produces a set of outcomes. The process is repeated 500 times and the set of outcomes shapes their distribution. The model is stratified by age in five year age groups up to the age of 75, with the top group being 75+.
Outcomes are then sorted by magnitude and the outcomes at the 2.5^{th}, 25^{th}, 75^{th} and 97.5^{th} percentile of the distribution are reported. The distance between the 25^{th} and 75^{th} percentiles is the interquartile range and the distance between 2.5^{th} percentile and the 97.5^{th} percentile is the 95% confidence interval.
Africa has the advantage of a young population relative to other continents. However, in lowincome countries, an average person’s vulnerability may correspond to that of an individual with greater age in a highincome setting due to malnutrition, infections and often unmanaged noncommunicable diseases. In the model, agespecific severity risks (probability of becoming a severe case and critical case) derived from highincome countries are shifted towards younger ages by ten years.
CALIBRATION OF THE MODEL
The model is calibrated by the use of a variety of studies round the world[1]. Some of the salient model parameters are:
Average period between infection and becoming infectious 
4 days 
Average period of preclinical infectiousness 
1.5 days 
Average period of clinical infectiousness 
3.5 days 
Average period of subclinical infectiousness 
5 days 
R_{0} 
2.6 
Average delay from symptom onset to becoming a severe case 
7 days 
Risk of becoming a severe case 
From 0.76% for children under 10 to 61.76% for people age 70 and over 
Average duration of severe, noncritical disease 
8 days 
Proportion of severe cases which become critical 
30% 
Average duration of severe, critical cases 
10 days 
Case fatality ratio in critical cases 
75% 
Average period between symptom onset and death 
22 days 
INTERVENTIONS
The purpose of the model is not only to project the spread of the epidemic in the absence of mitigation. It is also to assess the impact of mitigation strategies. Three strategies are considered:
Selfisolation of symptomatic individuals.
Populationwide physical distancing, whereby all individuals reduce their contacts outside the household to a certain degree. The scenarios considered are 20% distancing and 50% distancing. Lockdown is assumed to be 80% distancing. The distancing percentage refers to the drop in contacts where infection is a possibility.
Shielding of high risk individuals by, for example placing them in physical isolation within their homes, or rehousing them. A shielding regime is specified by a coverage fraction and a reduction fraction, so 80/80 shielding is 80% coverage of 80% contact reduction. 40/80 and 80/80 scenarios are considered.
Finally two combinations are considered 80/80 shielding plus 20% distancing and 80/80 shielding plus 50% distancing.
THE PROBLEM OF DATES
Day zero for the model is when there were 50 infections. To convert model days into dates, one needs an estimate of the date of day zero. This the model does not provide because actual infections cannot be directly determined from reported cases. Certainly day zero must have been before 17 March, when 85 cases were reported. Since the first reported case was on 5 March, a reasonable estimate of day zero would be 10 March. The annexure provides a day to date conversion table on this assumption.
THE PROJECTIONS[2]
The table indicates the peak timing and values for the main outcomes. The top figure in each cell represents the timing of the peak in days from the beginning of the model and the bottom figure indicates daily new symptomatic cases and deaths and the demand for hospital beds at the peak.
To keep the table as readable as possible, only the midpoint of the interquartile range is reported. This has the disadvantage of suppressing the degree of uncertainty in these estimates, which is large. The interquartile range for the days is never less than 30 and it rises to 100 or above for later dates.
The 95% confidence intervals are wider still. This means, for instance, there is only a 50% chance that the peak date for incidence of symptomatic cases in the 20% distancing scenario lies between 120 and 180 days and for a 95% chance, the interval will widen from 100 days to 370 days. Uncertainty is also great in projections of demand for hospital beds. For instance, the critical care demand in the 80/80 shielding scenario has a 50% confidence interval from 57,000 to 110,000 and a 95% confidence interval from 11,000 to 140,000. The uncertainty should decline over time and more precise input assumptions become possible.
Table 1: Peak conditions
Outcome 
Unmitigated 
20% distancing 
50% distancing 
40/80 shielding 
80/80 shielding 
80/80 shielding 20% distancing 
80/80 shielding 50% distancing 
Incidence of symptomatic cases 
115 705,000 
150 390,000 
220 125,000 
130 570,000 
135 505,000 
150 345,000 
215 99,500 
All hospital demand 
130 450,000 
160 250,000 
220 78,000 
145 285,000 
145 230,000 
160 165,000 
240 45,500 
General hospital demand 
130 305,000 
165 165,000 
220 53,000 
145 185,000 
150 155,000 
160 105,000 
240 30,650 
Critical care demand 
130 160,000 
165 88,000 
230 28,500 
145 97,000 
150 83,500 
160 55,500 
245 16,500 
Incidence of deaths 
135 9,700 
175 5,200 
235 1,730 
155 6,000 
155 5,000 
175 3,400 
250 1,060 
Twelve month cumulative outcomes are also reported and they are displayed in Table 2. The first column refers to unmitigated outcomes. The remaining columns refer to the reduction in outcomes relative to the unmitigated case associated with each intervention.
Table 2: Twelve month cumulative outcomes
Outcome 
Unmitigated 
20% distancing 
50% distancing 
40/80 shielding 
80/80 shielding 
80/80 shielding 20% distancing 
80/80 shielding 50% distancing 

TOTAL 
REDUCTION 

Symptomatic cases 
20,500,000 
4,000,000 
11,100,000 
2,500,000 
3,000,000 
5,200,000 
12,100,000 
Hospital persondays 
15,000,000 
3,350,000 
7,950,000 
3,900,000 
5,450,000 
7,200,000 
10,700,000 
General hospital persondays 
9,750,000 
2,150,000 
5,150,000 
2,550,000 
3,900,000 
4,700,000 
6,750,000 
Critical hospital persondays 
5,100,000 
1,175,000 
2,750,000 
1,350,000 
2,050,000 
2,500,000 
3,600,000 
Deaths 
310,000 
70,500 
170,000 
83,000 
125,000 
150,000 
215,000 
CONCLUSION
Despite the uncertainties, the following conclusions can be drawn from the table:
Interventions can push out the expected timing of the peak can be pushed out by up to a 100 days. An unmitigated peak incidence could have been expected at the beginning of July. This date can be pushed out to as late as early October.
50% distancing radically reduces expected daily infections at the peak. If it is accompanied by 80/80 shielding, the incidence drops further. Of course, the cost of flattening the curve is that the epidemic is spread out over a longer period of time, extending the time for which shielding and distancing will be needed. The least risky strategy for those in need of shielding is to remain shielded until a vaccine is found, assuming one is.
The heaviest demand for hospital beds will come from the 60+ age group. For them, rigorous shielding for a long time will be essential. Even so, providing hospital care for the reckless and unlucky is likely to stretch capabilities to the limit and beyond.
It is clear how close to the beginning of the epidemic we still are. The model’s median projection indicates that it will get much, much worse. But it should be borne in mind that projected outcomes are highly uncertain and subject to revision in the light of new data.
Charles Simkins, Head of Research, Helen Suzman Foundation.
ANNEXURE: DAY TO DATE CONVERSION TABLE
Day 
Date 
0 
10Mar 
80 
29May 
90 
8Jun 
100 
18Jun 
110 
28Jun 
120 
8Jul 
130 
18Jul 
140 
28Jul 
150 
7Aug 
160 
17Aug 
170 
27Aug 
180 
6Sep 
190 
16Sep 
200 
26Sep 
210 
6Oct 
220 
16Oct 
230 
26Oct 
240 
5Nov 
250 
15Nov 
[1] A full list of the estimates of parameters is contained in tables S1 and S2 in Kevin van Zandvoort et al, Response strategies for COVID19 epidemics in African settings: a mathematical modelling study, 3 May 2020, available at https://cmmid.github.io/topics/covid19/covidresponsestrategiesafrica.html
[2] See LSHTM CMMID COVID19 Working Group, Modelling projections for COVID19 epidemic in South Africa, 5 May 2020, available at https://ln2.sync.com/dl/b3fc9ebc0?sync_id=1394099302#36ipcgk35mghvhh4vi29b9yy8e688twu