COVID 19

Modelagem Numérica da Disseminação de Doenças Altamente Transmissíveis

Utilizando o Método dos Autômatos Celulares

Grupo de pesquisa Geofluxo/CNPq

Universidade de Brasília

Chamada Prospectiva de Propostas de Projetos e Ações de Pesquisa, Inovação e Extensão para o combate à COVID-19

Decanato de Pesquisa e Inovação (DPI) e o Decanato de Extensão (DEX) - UnB

Atuação

Tratamento

Pesquisa médica

Simulações Computacionais

Distanciamento social

Higienização

Equacionamento

Fluxo de estados

Suscetível

→

Infectado

↗ ↘

Recuperado

Falecido

Equação de conservação

$d S d t + d I d t + d R d t + d D d t = 0$ ${\frac{dS}{dt} + \frac{dI}{dt} + \frac{dR}{dt} + \frac{dD}{dt} = 0}$

Função Iota-Delta

$ι δ m n = m o d [m o d [\dots m o d [m o d [x, p m], p m - 1], \dots, p j], n]$ $\iota \delta_n^m = mod[mod[\ldots mod[mod[x, p_m], p_{m-1}],\ldots,p_j],n]$

Onde

$t, S, I, R, D \in ℕ;$ $t, S, I, R, D \in \mathbb{N};$

$m \geq j;$ $m \geq j ;$

$m, n \in ℤ +;$ $m, n \in \mathbb{Z}_+;$

$x \in ℂ;$ $x \in \mathbb{C};$

$j = π [n] + 1;$ $j = \pi[n] + 1;$

Referência

Ozelim, L. C. de S. M., Cavalcante, A. L. B., & Borges, L. P. de F. (2013). On the iota-delta function: Universality in cellular automata’s representation. Complex Systems, 21(4), 269-282.

Playground

susceptible

infectious

recovered

dead

Number of neighbors

0

1

2

3

4

5

6

7

8 Accumulative n^o of total contacts and infected contacts

Health Condition

70 %

30 %

0 %

Cenários

Escola

Mercado

Ônibus

Hospital

Ônibus

susceptible

infectious

recovered

dead

Number of neighbors

0

1

2

3

4

5

6

7

8 Accumulative n^o of total contacts and infected contacts

Health Condition

90.9 %

9.1 %

0 %

10 susceptible | 1 infected | 5 days to recovery | 50% of infection probability | 5% of death probability

Escola

susceptible

infectious

recovered

dead

Number of neighbors

0

1

2

3

4

5

6

7

8 Accumulative n^o of total contacts and infected contacts

Health Condition

90.9 %

9.1 %

0 %

20 susceptible | 2 infected | 4 days to recovery | 50% of infection probability | 0.5% of death probability

Mercado

susceptible

infectious

recovered

dead

Number of neighbors

0

1

2

3

4

5

6

7

8 Accumulative n^o of total contacts and infected contacts

Health Condition

95.2 %

4.8 %

0 %

100 susceptible | 5 infected | 4 days to recovery | 50% of infection probability | 0.5% of death probability

Hospital

susceptible

infectious

recovered

dead

Number of neighbors

0

1

2

3

4

5

6

7

8 Accumulative n^o of total contacts and infected contacts

Health Condition

66.7 %

33.3 %

0 %

20 susceptible | 10 infected | 5 days to recovery | 50% of infection probability | 5.0% of death probability

COVID 19

Modelagem Numérica da Disseminação de Doenças Altamente Transmissíveis

Utilizando o Método dos Autômatos Celulares

Grupo de pesquisa Geofluxo/CNPq

Universidade de Brasília

Atuação

Equacionamento

Fluxo de estados

Equação de conservação

dSdt+dIdt+dRdt+dDdt=0 {\frac{dS}{dt} + \frac{dI}{dt} + \frac{dR}{dt} + \frac{dD}{dt} = 0}

Função Iota-Delta

ιδmn=mod[mod[…mod[mod[x,pm],pm−1],…,pj],n] \iota \delta_n^m = mod[mod[\ldots mod[mod[x, p_m], p_{m-1}],\ldots,p_j],n]

Onde

t,S,I,R,D∈ℕ; t, S, I, R, D \in \mathbb{N};

m≥j; m \geq j ;

m,n∈ℤ+; m, n \in \mathbb{Z}_+;

x∈ℂ; x \in \mathbb{C};

j=π[n]+1; j = \pi[n] + 1;

Playground

susceptible

infectious

recovered

dead

Number of neighbors

0

1

2

3

4

5

6

7

8

Accumulative no of total contacts and infected contacts

Health Condition

70 %

30 %

0 %

0 %

Cenários

Ônibus

susceptible

infectious

recovered

dead

Number of neighbors

0

1

2

3

4

5

6

7

8

Accumulative no of total contacts and infected contacts

Health Condition

90.9 %

9.1 %

0 %

0 %

10 susceptible | 1 infected | 5 days to recovery | 50% of infection probability | 5% of death probability

Escola

susceptible

infectious

recovered

dead

Number of neighbors

0

1

2

3

4

5

6

7

8

Accumulative no of total contacts and infected contacts

Health Condition

90.9 %

$d S d t + d I d t + d R d t + d D d t = 0$ ${\frac{dS}{dt} + \frac{dI}{dt} + \frac{dR}{dt} + \frac{dD}{dt} = 0}$

$ι δ m n = m o d [m o d [\dots m o d [m o d [x, p m], p m - 1], \dots, p j], n]$ $\iota \delta_n^m = mod[mod[\ldots mod[mod[x, p_m], p_{m-1}],\ldots,p_j],n]$

$t, S, I, R, D \in ℕ;$ $t, S, I, R, D \in \mathbb{N};$

$m \geq j;$ $m \geq j ;$

$m, n \in ℤ +;$ $m, n \in \mathbb{Z}_+;$

$x \in ℂ;$ $x \in \mathbb{C};$

$j = π [n] + 1;$ $j = \pi[n] + 1;$

Accumulative n^o of total contacts and infected contacts

Accumulative n^o of total contacts and infected contacts

Accumulative n^o of total contacts and infected contacts

Accumulative n^o of total contacts and infected contacts

Accumulative n^o of total contacts and infected contacts