RESUME_TABLE:
WEEK    | TOTAL_NEW |   TOTAL_SOLVED
1       |   10      |   3
2       |   13      |   15
3       |   6       |   7

REPORT_TABLE:
WEEK    |   PREV_TOTAL  |   NEW_CASES   |   SOLVED_CASES    |   NEW_TOTAL
1       |   0           |   10          |   3               |   7
2       |   7           |   13          |   15              |   5
3       |   5           |   6           |   7               |   4

12:57:06 HR@vm_xe> l
  1  select week
  2         ,lag(total_cases_by_now - total_solved_by_now) over (order by week) prev_total
  3         ,total_new new_cases
  4         ,total_solved solved_cases
  5         ,total_cases_by_now - total_solved_by_now new_total
  6    from (
  7    select week
  8           ,total_new
  9           ,total_solved
 10           ,sum(total_new) over(order by week asc) as total_cases_by_now
 11           ,sum(total_solved) over (order by week asc) as total_solved_by_now
 12      from resume_table
 13* )
12:57:07 HR@vm_xe> /

      WEEK   PREV_TOTAL  NEW_CASES SOLVED_CASES  NEW_TOTAL
---------- ------------ ---------- ------------ ----------
         1                      10            3          7
         2            7         13           15          5
         3            5          6            7          4

3 rows selected.

Elapsed: 00:00:00.01

with resume_table as
(
    select 1 week, 10 total_new, 3 total_solved from dual union all
    select 2 week, 13 total_new, 15 total_solved from dual union all
    select 3 week, 6 total_new,  7 total_solved from dual
)
select week, prev_total, total_new, total_solved, new_total
from resume_table
model
    dimension by (week)
    measures (total_new, total_solved, 0 prev_total, 0 new_total)
    rules sequential order
    (
        new_total[any] order by week =
            nvl(new_total[cv(week)-1], 0) + total_new[cv()] - total_solved[cv()]
        ,prev_total[any] order by week = nvl(new_total[cv(week)-1], 0)
    )
order by week;

RESUME_LEFT
WEEK | LEFT
1    | 7
2    | -2
3    | -1

CREATE VIEW resume_left
  (SELECT week,total_new-total_solved "left" FROM resume_table)

PREV_TOTAL=(SELECT sum(left) FROM RESUME_LEFT WHERE week<REPORT_TABLE.week)

PREV_TOTAL=(SELECT sum(total_new)-sum(total_solved)
  FROM resume_table
  WHERE week<REPORT_TABLE.week)