Thanks a lot for this important question.

There is an important analysis reflected in the WHO Essential Nutrition Action Publication (2012) that suggests the following:

"When assessed in successful programmes, it appears that the initial improvement in underweight prevalence in participants is quite rapid, reducing by up to 10 ppt in the first year or so. At the same time, severe malnutrition also falls rapidly to low levels (e.g. 10% to 2%). This pattern was seen in, for example, Bangladesh (early BNIP), Ethiopia, Senegal, Tanzania (Iringa), Thailand and other places. The reasons for this initial response are not known, and are likely to be in part from treatment of diseases and immunization.
The sustained rate, over a number of years, is what presumably makes a long-term difference. An expected dose-response is seen roughly in the sustained rate (Figure II-1), measuring the resources as CHNWs/1000 households (or children). The results suggest that a level of around 30 CHNWs/1000 (1 CHNW:33 children, estimated as part time, 0.1 FTEs) is needed for an improvement rate of 1 ppt/year or higher in underweight.
The most important implication is that community-based nutrition programmes can be effective, and that adequate resources – for example, enough CHNWs, trained and supported – must
be put into these, and sustained over years, for them to provide a substantial impact on child nutrition. For example, a with-programme improvement rate of 1.5 ppt/year is typical; current subregional child underweight prevalences are 13%–23% in Africa, with change rates of 0.1 to -0.2 ppt/year; in Asia these figures are 18%–33%, with change rates of -0.3 to -1.0 ppt/year. A rate of 1.5 ppt/year over 10 years reduces these prevalences by 15 ppt, i.e. to 0%–7% in Africa and 3%–18% in Asia (57). Thus, sustaining these activities at the required intensity for 10 years or so
would substantially reduce child malnutrition, as has been seen in several countries with national programmes (e.g. Thailand, Vietnam)."

Recommended ratios are usually 1:200 households max for full-time workers, enabling a visit to each HH every 2 months or so. This varies based on context particularly population density and available transportation. See discussion at linked article, page 1064:

https://www.ncbi.nlm.nih.gov/books/NBK11726/pdf/Bookshelf_NBK11726.pdf