MySQL 8.0

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CREATE TABLE mytable(
   start_dt VARCHAR(20) NOT NULL 
  ,end_dt   VARCHAR(20)
);
INSERT INTO mytable(start_dt,end_dt) VALUES ('2019-10-15 20:41:38','2019-10-16 01:44:03');
INSERT INTO mytable(start_dt,end_dt) VALUES ('2019-10-15 20:43:52','2019-10-15 22:18:54');
INSERT INTO mytable(start_dt,end_dt) VALUES ('2019-10-16 20:21:38',NULL);
INSERT INTO mytable(start_dt,end_dt) VALUES ('2019-10-17 01:42:35',NULL);
INSERT INTO mytable(start_dt,end_dt) VALUES ('2019-10-17 03:15:57','2019-10-17 04:14:17');
INSERT INTO mytable(start_dt,end_dt) VALUES ('2019-10-17 03:16:44','2019-10-17 04:14:31');
INSERT INTO mytable(start_dt,end_dt) VALUES ('2019-10-17 04:15:23','2019-10-17 04:53:28');
INSERT INTO mytable(start_dt,end_dt) VALUES ('2019-10-17 04:15:23',NULL);
select 
    date(dt) day, 
    sum(sum(no_tasks)) over(order by date(dt)) no_tasks 
from (
    select start_dt dt, 1 no_tasks from mytable
    union all select end_dt, -1 from mytable where end_dt is not null
) t
group by date(dt)
order by date(dt)


day
no_tasks


2019-10-15
1

2019-10-16
1

2019-10-17
3


select 
    dt_day, 
    @no_tasks := @no_tasks + no_tasks no_tasks 
from (
    select date(dt) dt_day, sum(no_tasks) no_tasks
	from (
		select start_dt dt, 1 no_tasks from mytable
		union all select end_dt, -1 from mytable where end_dt is not null
	) t
	group by dt_day
	order by dt_day
) t
cross join (select @no_tasks := 0) x
order by dt_day


dt_day
no_tasks


2019-10-15
1

2019-10-16
1

2019-10-17
3