key: cord-0889700-mzqjd5y1 authors: Djilali, Salih; Ghanbari, Behzad title: Coronavirus pandemic: A predictive analysis of the peak outbreak epidemic in South Africa, Turkey, and Brazil date: 2020-06-05 journal: Chaos Solitons Fractals DOI: 10.1016/j.chaos.2020.109971 sha: 9761a48349ea367f0330a4a365824fcc454f16db doc_id: 889700 cord_uid: mzqjd5y1 In this research, we are interested in predicting the epidemic peak outbreak of the Coronavirus in South Africa, Turkey, and Brazil. Until now, there is no known safe treatment, hence the immunity system of the individual has a crucial role in recovering from this contagious disease. In general, the aged individuals probably have the highest rate of mortality due to COVID-19. It is well known that this immunity system can be affected by the age of the individual, so it is wise to consider an age-structured SEIR system to model Coronavirus transmission. For the COVID-19 epidemic, the individuals in the incubation stage are capable of infecting the susceptible individuals. All the mentioned points are regarded in building the responsible predictive mathematical model. The investigated model allows us to predict the spread of COID-19 in South Africa, Turkey, and Brazil. The epidemic peak outbreak in these countries is considered, and the estimated time of the end of infection is regarded by the help of some numerical simulations. Further, the influence of the isolation of the infected persons on the spread of COVID-19 disease is investigated. Coronaviruses are a large group of viruses that can infect animals and humans and cause res-2 piratory distress; they may be as mild as a cold or as severe as pneumonia. In rare cases, animal [1, 27] . Another important and newer breed is the Coronavirus MERS virus, 6 which was discovered in 2012 in the Middle East. The virus was first transmitted from camels to of the disease is a virus, antibiotics do not affect the pathogen. In medical centers, without any specific treatment for the disease, they usually treat the symptoms and make the patient feel more 19 comfortable. 20 As it has been mentioned, the main method of transmission of the disease is the respiratory 21 droplets that a person secretes when coughing. The risk of COVID-19 disease is diminished by 22 someone asymptomatic. But many people with the disease have only slight symptoms. This is 23 especially true in the early stages of the disease. Therefore, COVID-19 can be infected by a person 24 who suffers from a mild cough and does not feel ill. WHO is assessing ongoing research on the 25 transmission period of COVID-19 and the method of isolation and other measures for controlling 26 the spread of 6, 8, 10, 11, 12, 13, 18, 20, 26, 28] . In [32], it is obtained that an infected 27 person that passes 60s has a 5.3% chance of dying due to COVID-19 disease. So we are interested 28 in studying the influence of the age structure of the studied countries on the spread of COVID-19, 29 where the percentage of the aged individuals next to the total size of populations in South Africa, 30 Turkey and Brazil are given in the following The responsible model for our predictions is expressed as: S(0, θ) = S 0 (θ) ∈ L 1 (0, +∞), E(0, θ) = E 0 (θ) ∈ L 1 (0, +∞), where 0 ≤ S(t, θ), E(t, θ), I(t, θ) ≤ 1 stand respectively for the categories of the susceptible 58 individuals, exposed individuals, infected individuals at the time t (measured in days) with the Tables 1, 2 +∞ 0 E(t, ω)dω) stands for the total fraction of the infected individuals (resp. due to COVID-19. The responsible mortality functional η(θ) can be expressed as: For the well possessiveness of our system, we assume that the initial conditions belong the space Now we are in a situation to calculate the basic reproduction number, which going to help prediction of the epidemic outbreak in the studied countries. For the model (1), we have I(t, a)da. We expect that i(t) (the 89 total proportion of infected individuals) has the following special form: Using the values of x 1 , x 2 , x 3 found in Table 2 , we can determine the value of the transmission rate ρ, which by taking a look at (3) it is difficult to deduce it. Hence, using the fact that 0 ≤ δ(0) ≤ δ * we can obtain that: where ρ 1 = x 2 +ν 2s(0) , ρ 2 = x 2 (x 2 +ν) s(0)(2x 2 −x 3 ) . Besides, the choice of the transmission rate ρ is highlighted in 91 Table 2 . For obtaining an approximative number of the individuals in the exposed class we can calculate 94 the number of the new infected individuals in five days, this gives us an approximation to the 95 number of persons in the exposed stage. On the other hand, using Fig. 3 Further, we can also mention that COVID-19 will disappear from the South African community by 101 the 100 days, starting from the date 15/04/2020. For obtaining an approximative number of the individuals in the exposed class we can calculate 104 the number of the new infected individuals in five days. In Turkey, the infection will reach to its 105 higher percentage after 52 days starting from 15/04/2020, with 0.899% of the total population, 106 which means that 7.3718 × 10 5 active infection cases, this means that Turkey is in advance stage for 107 the spread of the COVID-19 compering with South Africa, where a serious measure is needed before 108 the infection cases become higher. Further, we can also mention that COVID-19 will disappear from 109 the population in Turkey after 97 days, starting from the date 15/04/2020. functional η(t) has the following special form: where η 0 takes the values of η used in Table 2 also µ = 0.16 (see [15] ), next, we presume that the 128 time of restrictions is T = 40 starting from 15/04/2020. As it has been shown in Fig. 6 we can see where q represents the proportion of the revealed infected individuals and moved to the quarantine. Other parameters have the same interpretations as it has been mentioned in the introductions 145 section. The real value of the parameter q is not known, where the quantity of tests is responsible 146 for revealing the percentage of infected individuals that moved to the quarantine. So, we will use 147 several values of the parameter q and see how it can influence the spread of the COVID-19 disease. The obtained results are highlighted in Fig. 7 . To mention that q=0 refers to the case of the 149 absence of the quarantine. Hence the system (6) behaves in the same manner of (1). Indeed, for q = 0 (no isolation) the pandemic peak outbreak will e reached as it has been obtained To mention that the restriction has a bad influence on the economic system of the countries, but Thus, as a conclusion we can highlight that the quantity of tests for revealing the infected 185 persons is essential tool for fighting Coronavirus disease, and the full restriction has a bad influence 186 of the economic system of the studied countries. It can be avoided if the percentage of the isolated 187 infected individuals is more than 50% (q=0.5 in Fig. 7) , where for this case the number of the 188 declared infection cases will decrease immediately. 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