Impact of contamination factors on the COVID-19 evolution in Senegal
Vieux Medoune Ndiaye, Serigne Omar Sarr, Babacar Mbaye Ndiaye
IImpact of contamination factors on the COVID-19evolution in Senegal
Vieux Medoune Ndiaye, Serigne Omar Sarr and Babacar Mbaye Ndiaye
Abstract.
In this article, we perform an analysis of COVID-19 on one of the SouthSaharan countries (hot zone), the Senegal (West Africa). Many questions remainunanswered: why the African continent is not very contaminated compared to othercontinents. Factors of cross immunity, temperature, population density, youth, etc.are taken into account for an analysis of the contamination factors. Numerical sim-ulations are carried out for a prediction over the coming week.
Keywords. coronavirus, COVID-19, immunity, forecasting, contamination factors.
1. Introduction
The COVID-19 pandemic is the new planetary threat at the start of 2020. Since itsappearance in December 2019 in Wuhan in Hubei province in China, the pandemicnow affects all five continents. The impressive multiplication of confirmed cases betweenEurope and America has caused an oscillation of the focus between these two continentsnotwithstanding health systems (but renowned for their performance).At the beginning of the epidemic, health authorities and international institutions believethat the pandemic would inevitably be devastating for the African continent due to thefragile health systems and insufficient medical equipment.If certain African countries have to face many cases of contamination, like in Egypt andSouth Africa, for a large part of the other countries the wave is less important thanexpected with a globally different kinetics.In Senegal, the threshold of 4851 cases was crossed on June 12th, 2020 with 1839 infectedand 56 deaths. This assessment is certainly alarming but less important compared tocertain countries of Europe and America and far from gravitating around the forecastsof the WHO and certain experts. Obviously the low number of tests and the lack ofdata partially skew the balance sheet but behind these figures, there are probably factorsinfluencing the slow speed of spread of the virus.These factors are worth considering. It is in this context that this work is fixed as a goalof reflection on the various and varied factors that can explain this particular kinetics ofthe epidemic in Senegal.First, we collect the pandemic data from [12], from March 03, 2020 to June 12, 2020. Inthe second step, we propose some contamination factors and machine learning technicsfor a week forecasting.The article is organized as follows. In section 2, we present some data analysis followed a r X i v : . [ q - b i o . P E ] J un Ndiaye V.M., Sarr O.S. and Ndiaye B.M.by contamination factors in section 3. In section 4, we perform machine learning technicsfor forecasting for the following week. Finally, in the section 5, we present conclusionsand perspectives.
2. Data analysis
The simulations are carried out from data in [12], from March 02, 2020 to June 12,2020. The numerical tests were performed by using the Python with Panda library [10],and were executed on a computer with following characteristics: intel(R) Core-i7 CPU2.60GHz, 24.0Gb of RAM, under UNIX system.According to daily reports, we first analyze and make some data preprocessing beforesimulations. The cumulative numbers of confirmed, recovered and deaths cases are illus-trated in Figure 1a and Figure 1b illustrates Dakar zones (with higher confirmed cases(see section 3.6)). In Figure 1b, ”Dakar Ouest” = East of Dakar, ”Dakar Nord” = Northof Dakar, ”Dakar centre” = Dakar center and ”Dakar sud” = South of Dakar.We get various summary statistics (per day), by giving the mean, standard deviation,minimum and maximum values, and the quantiles of the data (see Tables 1 and 2). (a)
Senegal cases - confirmed, re-covered and deaths (b)
Dakar zones [8]
Figure 1.
Senegal: community and severe cases values tests cases contact imported community confirmed mean 577.44 47.09 41.06 0.96 5.07 1332.50std 507.77 43.48 39.97 1.92 5.93 1512.43min 1 0 0 0 0 125% 97.25 7.5 3.5 0 0 124.550% 474 31 28 0 3 44275% 1008.75 89 75.5 1 8 2512max 1820 177 169 11 30 4851
Table 1.
Senegal summary statistics (per day) until June 12th, 2020(tests, cases, contact, imported, community and confirmed).mpact of contamination factors on the COVID-19 evolution in Senegal 3 values recovered deaths evacuated severes infected ratios mean 650.84 14.44 0.69 4.93 667.22 0.14std 842.50 17.52 0.46 6.68 687.49 0.22min 0 0 0 0 1 025% 14.5 0 0 0 107.5 0.06242650% 253 6 1 0 183 0.08063875% 1024.5 27 1 9 1454.5 0.102737max 3100 56 1 25 1839 1
Table 2.
Senegal summary statistics (per day) until June 12th, 2020(recovered, deaths, evacuated, severe, infected and ratios).The number of performed tests par day is not a constant (see Figure 2a). The Figure2b shows that in Senegal, between March 02 and June 12, 2020, the ratio (confirmedcases/tests) is almost constant despite variations in the number of daily tests performedand considered to be unrepresentative. Despite official statements about the peak period,it seems difficult to say whether the peak of contamination has already been reached orwill even be reached shortly. In addition, we find that the ratio varies on average by 10%.Figures 2c and 2d show that the maximum number of severe and community cases areless than 10% of the number of confirmed cases.
3. The indicator factors
In this section, we describe some natural indicator factors which can limit the spread ofthe virus in Senegal.
Actually, The COVID-19 period coincides with the dry season. Senegal is one of thesunniest countries in the world: more than 3,000 hours of sunshine a year. There are twoseasons: • a rainy season, from June to October, with greater precipitation from south tonorth; • a dry season, from November to May, with temperatures between 22 ◦ C and 30 ◦ C,and significant variations between the coast and the interior.The evolution from North to South: • in Dakar, the average daytime maximum is 24 ◦ C from January to March and be-tween 25 and 27 ◦ C in April, May and December. From June to October, tempera-tures reach 30 ◦ C. • in southern Senegal, the coolest period is from December to mid-February, withdaytime averages of around 24 ◦ C.In October and November, and from mid-February to April, maximum temperatures arearound 26 ◦ C. From July to September, they reach 30 ◦ C.The amount of precipitation increases from north to south of the country. In the far north(Senegal river region), the average annual rainfall is 300 mm, while in the far south (lowerCasamance, Kolda region), it can exceed 1,500 mm.The cumulative rainfall values from North to South are given in Figure 3, and Figure in4 shows the mapping of COVID-19 in Senegal as of June 12, 2020. Ndiaye V.M., Sarr O.S. and Ndiaye B.M. (a) number of tests (b) ratios (c) severe cases (d) community cases
Figure 2.
Senegal: community and severe cases
Figure 3.
Cumulative rainfall by December 31, 2019 [13]The hypothesis seems to be corroborated by the fact that the regions most affected by thepandemic have a rather temperate climate and that most of the cases are concentratedmpact of contamination factors on the COVID-19 evolution in Senegal 5 (a)
Confirmed cases in all regions (b)
Zoom on confirmed cases in regions
Figure 4.
Senegal: visualization of confirmed cases from North to Southeither in the extreme west of the country or in the extreme south. This hypothesis is inline with the work in [21], where they predict a sharp decline in the disease from July inSenegal.
The population of Senegal is young and varied. We have 54% of the population who isunder the age of 20 [17], whose annual growth rate is 3.8%. Life expectancy at birth(year 2017) is 64. Young people play a lot of sport. The relative youth of the Senegalesepopulation with fewer elderly people can really explain the low mortality rate.
Cross immunity describes acquired immunity against an infectious agent that protectsagainst another agent (virus or bacteria). Cross immunity is linked to the phenomenonof cross reaction. In general, an antibody is specific for an antigen; but sometimes an-tibodies bind to close antigens (they are called cross-reactive), because these antigenshave common epitomes or are of similar structure. People who have already encounteredcertain influenza viruses in their life would be better protected than others against otherinfluenza viruses ([14, 15, 16]). In Senegal, the seasonal flu virus is known to mutate eachyear, but these variations are often minor. This explains why there may be a share ofcross immunity with viruses encountered in previous years.Nevertheless, this new type of coronavirus (COVID-19) is caused by a new type of coro-navirus first named 2019-nCoV, then renamed SARS-CoV-2, never seen before.The Senegalese have known certain diseases for a very long time. Malaria occurs through-out the year and across the country. Bilharziasis is especially present in Casamance (southof Senegal), allergies: dust, pollen throughout the year, intestinal parasites are also verycommon.However, vaccination campaigns are carried out (certain vaccines are optional) by theMinistry of Health [12]: yellow fever, hepatitis A, tetanus, polio, diphtheria, BCG, MMR(Measles, Mumps, Rubella), whooping cough, meningitis A and C, typhoid.
The poverty of many urban and rural families does not always allow themto prepare two meals a day and to diversify their diet. They are often satisfied with abowl of rice or millet, sometimes with a few vegetables, a little fish, a piece of meat to Ndiaye V.M., Sarr O.S. and Ndiaye B.M.share among the many members of the family. Senegal is a country where fish is widelyconsumed. Garlic, bay leaf, etc. are used for the taste of the kitchen. The Senegalese dietconsists mainly of cereals (staple food): rice, wheat, millet and fonio.In addition, some senegalese dishes like ”lakhou thiakhane”, ”gourbane”, senegalese soup,etc. are recommended foods for the flu and malaria.
The main fruits are mangoes, which are part of the landscape. There arealso grapefruits (roses are better), papayas, oranges (often not very juicy, but good -consume Senegalese - pressed between the teeth), melons, corrosols and guavas, with adelicate and exotic fragrance, mads (fruits containing large seeds surrounded by pulp (seeFigure 5), sold in the street mixed with sugar), bananas produced in small quantities andoften imported from Ivory Coast, like pineapple.
The best known drink is undoubtedly bissap juice (hibiscus sabdariffa L.)decoction of red flower calyxes with a tangy taste) but you can also taste tamarind juice(dakkar) and ginger juice (ginger) also very widespread, the latter having a pungent tastethat will not please everyone.Street vendors and restaurants also offer drinks that are more original but more difficultto find: guava juice (buyap), mango, ditakh, sump, black plum, etc. (see Figure 5).The pulp of the baobab fruit (bouye), called monkey bread (see Figure 5b), a tree withmultiple virtues, from leaves to seeds, is consumed as juice, an excellent rehydratingagent, and increasingly in the form of food supplements. Bouye is also used in the man-ufacture of cosmetics and diabetes medicines.Plant contents oligo elements as zinc and selenium can modulate immunity with antiox-idant properties. Polar extracts of many senegalese plants revealed potent antioxidantactivity ([1, 2, 3]). (a) bissap (hibis-cus sabdariffa L.) (b) bouye(Adansoniadigitata L.) (c) mad (Sabasenegalensis) (d) sump (Balan-ites aegyptiacus(L.) Delile) (e) leng (Vi-tex donianaSweet) (f) gerte tubaab(Terminalia cat-appa L.)
Figure 5.
List of some fruits in Senegal (also used for drink) [8]mpact of contamination factors on the COVID-19 evolution in Senegal 7
More than 90% of the Senegalese population is of Muslim faith. The islamization ofthe country dates from the 11th century, when the Almoradives (Berber warrior monks)conquered northern Senegal. The appearance of Christianity is much more recent. Oftenmixed with its two religions, animism, with its rites and beliefs, is still very present.Behind this low rate of contamination compared to the countries of Europe and theAmericas, the simple religious ritual gestures could be among the salutes of the Senegalesepeople against the spread of the dreaded disease.In New Castle (United Kingdom) a recent report published by Professor Richard Webber,an eminent academic, in collaboration with Trevor Philipps, a writer and former Laborpolitician, has come up with a very interesting observation: the ablutions of Muslimsmay have reduces the risk of contamination. The report comes as Public Health Englandlaunches an investigation into the reasons why non-whites seem to be the most affectedby the disease (intensive care reports show that 34.5% of critically ill patients are fromethnic minorities, although they only represent around 14% of the population [18].In fact, if one of the keys to stopping the transmission of the virus is hand washing, areligious community in which all the faithful wash themselves thoroughly every day, andfive times a day before performing the five daily prayers, by conforming to a very rigorouspurification ritual, would it have anything to teach us?Second, fasting is good for health and is said to boost our immunity (see [22, 23]),and fasting twice a week is very good for your health. In addition to Ramadan, mostSenegalese fast twice a week and on certain specific days of certain months of the Muslimcalendar (Al-Hijira (Muharam 1), Lailat al Miraj (Rajab 27), Laylat Al Baraat (Sha’ban15), Waqf Al Arafa - Hajj (Dhu’l-Hijjah 9).
High population densities can catalyze the spread of COVID-19. With its 3,137,196 in-habitants, or almost a quarter of the population of Senegal (23.2%), living on an arearepresenting 0.3% of the total area of the country, Dakar is the most populated region ofSenegal and its population density is also the highest with 5,846 people/km2.Keeping to more than 1-m distance between people coughing and sneezing, as recom-mended by the WHO [20] becomes more difficult with higher population densities like inDakar. Therefore, avoiding situations with higher population densities will be a necessaryrequirement to limit the spread of COVID-19 [19].The relationship between the basic reproduction number, R , and the daily reproductivenumber, β , can be described by: β = τ c = R i (3.1)where τ denotes transmissibility and c contact rate and where the infectious period i equals one over the recovery rate γ . This relationship holds for well-mixed populations,as assumed by standard compartmental models like SIR or SEIR which apply the law ofmass action [4, 5, 6, 7]. They are also valid for small-to-medium spatial scales.The contact rate is directly related to the total number of contacts, C ( t ), generated forany person over a time period t , such that C ( t ) = ctN , for a situation with N persons(3,137,196 for Dakar). This means that the effect of the time period of exposure and thecrowd size to C ( t ) are equivalent.Parcelles Assainies, Guediewaye, etc. are zones with high density. This also involves com-munity cases (see Figure 6a). The urbanization rate is 44%. By June 12th, the infectedcases in Dakar is 2727 (West (718), South (684), North (665) and Center (660)). This is Ndiaye V.M., Sarr O.S. and Ndiaye B.M.not surprising, because the inhabitants of Dakar representing 23.5% of Senegal popula-tion. (a) Dakar north (b)
Dakar west and Dakar center (c)
Dakar south (d) zoom of Dakar cases
Figure 6.
Dakar region cases
If we take the distribution of contamination cases, we seethat Dakar (with high density area) is more contaminated. The figure 6 illustrates thevisualization of high density areas (for the North, South, West and Center). Figure 7illustrates this phenomenon (the first 5 (Figure 7a and the first 10 (Figure 7b)).In addition, the cumulative repartition of the number of confirmed cases per zone is givenby Figure 8. (a) the first 5 zones (b) the first 10 zones
Figure 7.
Number of confirmed cases in zonesmpact of contamination factors on the COVID-19 evolution in Senegal 9
Figure 8.
Cumulative number of confirmed cases per region
We perform the same simulation as in the previous sec-tion (by area). We see that Touba (in Figure 4b), Parcelles Assainies, Guediewaye andPikine (with high density area) are more contaminated. Figure 9 illustrates this phenom-enon (the first 5 (Figure 9a) and the first 10 (Figure 9b)). Also, the cumulative repartitionof the number of confirmed cases per district is given by Figure 10. (a) the first 5 district (b) the first 10 district
Figure 9.
Number of confirmed cases in districts0 Ndiaye V.M., Sarr O.S. and Ndiaye B.M.
Figure 10.
Cumulative number of confirmed cases per district
4. Forecast (using Prophet) for the next 10 days
We perform one week ahead forecast with Prophet [9], with 95% prediction intervals.Here, no tweaking of seasonality-related parameters and additional regressors are per-formed. Prophet is a procedure for forecasting time series data based on an additivemodel where non-linear trends are fit with yearly, weekly, and daily seasonality, plus hol-iday effects. It works best with time series that have strong seasonal effects and severalseasons of historical data. Prophet is robust to missing data and shifts in the trend, andtypically handles outliers well.For the average method, the forecasts of all future values are equal to the average (ormean) of the historical data. If we let the historical data be denoted by y , ..., y T , thenwe can write the forecasts asˆ y T + h | T = ¯ y = ( y + y + ... + y T ) /T The notation ˆ y T + h | T is a short-hand for the estimate of y T + h based on the data y , ..., y T .A prediction interval gives an interval within which we expect y t to lie with a specifiedprobability. For example, assuming that the forecast errors are normally distributed, a95% prediction interval for the h -step forecast is ˆ y T + h | T ± .
96 ˆ σ h where σ h is an estimateof the standard deviation of the h -step forecast distribution.Most importantly, with the model and parameters in hand, we can carry out simulationsfor a longer time and forecast the potential trends of the COVID-19 pandemic. For Figure11, the predicted cumulative number of confirmed cases is plotted for a shorter period ofnext 10 days.mpact of contamination factors on the COVID-19 evolution in Senegal 11Date ˆ y ˆ y lower ˆ y upper Table 3.
Senegal: predicted cumulative confirmed cases ∼ June 22, 2020.
Figure 11.
Senegal (Confirmed cases) : forecasting for the next 10 days ∼ June 22, 2020.We can summarize our basic predictions (from North to South), for all regions. At ∼ June22, 2020 we may obtain >
5. Conclusion and perspectives
Faced with the difficulty of enforcing social distancing measures, the systematic wearingof barrier masks and the multiple observations of favorable clinical evolution of confirmedcases for SARS-CoV2, it was logical and consistent to analyze and explore other con-tamination factors which are of interest in our tropical context. This is how the mostprobable hypotheses arise: the youth of the population, the combined ambient temper-ature and humidity, acquired immunity (cross immunity induced by certain vaccines orsimilar previous infections, collective immunity, etc.). Taking these factors into accountshould better model the course of the disease and not be limited to classical mathemati-cal models for monitoring the course of epidemics. An interdisciplinary approach seeks tovalidate new models inspired by the African context. Based to our analysis, we can pro-pose in future work, the generalized SIR model [4, 5, 6, 7] taking into account to all thesefactors (cross immunity, youth, etc.) to analysis the coronavirus pandemic (COVID-19).2 Ndiaye V.M., Sarr O.S. and Ndiaye B.M.In addition, the authorities’ decisions (social distancing, curfew, auto-discipline of sene-galese people, etc.) may flat the curve (see Figure 12).
Figure 12.
The impact of infected cases with intervention
Acknowledgement
The authors thanks the Non Linear Analysis, Geometry and Applications (NLAGA)project for supporting this work.