We present a compartmental mathematical model of (SITR) to investigate the effect of saturation treatment in the dynamical spread of diarrhea in the community. The mathematical analysis shows that the disease free and the endemic equilibrium points of the model exist. The disease-free equilibrium is locally and globally asymptotically stable when R 0 < 1 and unstable otherwise R 0 > 1. Numerical simulation results, show the effect of saturation treatment function on the spread of diarrhea. Efficacy of treatment shows a great impact in the total eradication of diarrhea epidemic.

Background. In recent years, social network analysis methods have been applied to study the relationships among farmers. However, most studies have not paid attention to the different types of relationships that can be found in these networks, particularly with regard to the interactions between farmers. Hence, in this study, a multiplex network approach was used Purpose. to examine the interdependencies between farmers' relationships and the distinct relationship layers built around them were analyzed. We used data collected from a rural farming Methodology. community in Ghana and analyze our data using multiplex network analysis. The re Findings. sults showed that each layer generated by each type of relationship had a distinct structure and that most relationships were independent. Relationships among farmers for higher yields can facilitate the development of policies and strategies that encourage knowledge exchange and collaboration, funding access, and joint ventures. Appropriate management of the relationships can help maximize benets to farmers. Our Originality. theory-building study has implications for enhancing the productivity and performance of farmers.

An individual’s productivity is strongly related to work- and non-work-related interactions. Thus, the literature on farmers’ productivity often explores single-layer networks that illustrate the single categories of social relationships. In this study, we investigated farmers’ productivity using a multiplex structure underlying social interaction networks. Relational data were obtained from farmers in four different categories of social relationships. The multiplex network was analysed by applying multiplex degree centrality and layer-by-layer comparison. Also, power and role were analysed through the use of external data by determining their intra-layer correlation. The findings show that diverse types of relationships exist together and they positively affect farmers’ productivity in multiple ways and enhance their innovation capacity. Only 6 out of the 73 farmers had high-degree centrality (&gt; 10), with 18–63$\%$ relevance for the six farmers in the two layers—farming advice (FA) and loans (LO) layers—that the farmers considered important to their productivity. These farmers were more likely to be productive and help improve the productivity of others linked to them. Further, 62$\%$ of the edges in the social gathering and personal advice layers were similar, whereas only 3$\%$ of those in the FA and LO layers were similar, confirming the significance of the latter layers. The influence of social structures on farmers’ productivity implies that social connections enhance farmers’ confidence. The external data further confirm that the formation of some links depends on trust and power, whereas others do not.