As opposed to multi-agency care. See discussion entry.

"Integrated care is when health and social care services work together to ensure individuals get the right treatment and care they need for their health concerns"

?

This is how it is known in North America.

It seems that the multi-agency approach (cf. Chris' reference comment) may take the form of either parallel or sequential care. 'Sequential care' seems to come closest to the description of 'ketenzorg' in your example. You might even consider expanding this to 'sequential multi-agency care' :-)
Another option seems to be 'continuum of care' as in the second and third example below (cf. also Tina's answer).

The current service configuration for dual diagnosis involves a multi-agency approach, with substance use and mental health services working either in parallel (providing care at the same time) or sequentially (one service provides care, then the other takes over).
http://visit.lincoln.ac.uk/C6/C12/.../DD Module 15.pdf

Many health care patients receive sequential care from a series of vertically-related providers, such as hospitals, physicians, nursing facilities, and home health agencies. Several strategies have emerged to address long-standing concerns about efficient coordination along this continuum of care.
http://www.business.unr.edu/faculty/parker/wp/ParkerWendel20...

The "Continuum of Care" for maternal, newborn and child health includes integrated service delivery for mothers and children from pregnancy to delivery, the immediate postnatal period, and childhood. Such care is provided by families and communities, through outpatient services, clinics and other health facilities.
http://www.who.int/.../continuum_of_care/.../index.html