Mathematical model describing CoViD-19 in São Paulo State, Brazil – Evaluating isolation as control mechanism and forecasting epidemiological scenarios of release

Abstract

We formulated a mathematical model considering young (below 60 years old) and elder (above 60 years) subpopulations to describe the introduction and dissemination of new coronavirus epidemics in the São Paulo State, Brazil. From the data collected in São Paulo State, we estimated the model parameters and calculated the basic reproduction number as R 0 = 6.828. Considering isolation as a control mechanism, we varied the releasing proportions of young and elder persons to assess their epidemiological impacts. The best scenarios were release of young persons, but maintaining elder persons isolated. To avoid the collapse of the health care system, the isolation must be at least 80%.

̃Evaluating reduction in CoViD-19 cases by isolation and protective measures in São Paulo State, Brazil, and scenarios of release

“…This new trend can not be explained by an increased proportion in isolation (see Figure 4). To take into account this new tendency of data, in [32] we hypothesized that the using of face mask, constant hygiene (washing hands with alcohol and gel, and protection of mouth, nose and eyes, etc. ), social distancing and other protective measures may decrease the transmission of infection.…”

“…Depending on the epidemiological status, a higher number of persons harbouring the virus will be in close contact with elder persons, which constitute a group under higher risk of infection and death. As we have pointed out in [31] [32], the presence of infectious young persons increases greatly the risk of infection in elder persons.…”

“…In [31] and [32] we estimated the additional mortality rates based on the observed data and concluded that their values did not provide long-term reliable values. For instance, this estimation resulted in deaths of 30% up to 80% of severe CoViD-19 cases at the end of the first wave of epidemics.…”

“…Persons in class Q 2 j acquire immunity after period 1/ γ 3 j , where γ 3 j is the recovery rate of mild CoViD-19, and enter into immune class I . Another route of exit from class Q 2 j are being caught by a test at a rate η 2 j and enter into class I (assumption of adherence to isolation), or enter to class Q 3 y convinced by an education campaign at a rate ε 4 j , which is temporary, hence ξ j is the rate of abandonment of protective measures [32].…”

“…Mathematical models allow us to understand the progression of viral infections if the natural history of the disease is well documented. Based on this knowledge being improved as epidemics evolves, in [31] we considered continuous isolation and release rates in the modelling to describe new coronavirus epidemics, which was improved by considering intermittent pulses in isolation and release in [32]. In both models, asymptomatic and severe CoviD-19 persons are allowed to transmit virus.…”