I got your model running using a shape file instead of a spatialite db.

Can you try a shape file first, to see if it's work. Then perhaps it would be easier, to identify any Spatialite problems. I also added my model code, so you can check against your model. I got another Python error than you using Spatialite:
Algorithm testModel starting... Prepare algorithm: QGISSELECTBYATTRIBUTE_1 Running Select by attribute [1/2] Parameters: INPUT =dbname='D:/Dropbox/qgis/Spatialite/spatialite_join_test/myDB.sqlite' table="jackdiane" (geometry) sql=, FIELD =Name, OPERATOR =0, VALUE =Jack String field "Name" = 'Jack' Converting outputs OK. Execution took 0.046 ms (1 outputs). Prepare algorithm: QGISSELECTBYATTRIBUTE_2 Running Select by attribute [2/2] Parameters: INPUT =dbname='D:/Dropbox/qgis/Spatialite/spatialite_join_test/myDB.sqlite' table="jackdiane" (geometry) sql=, FIELD =Age, OPERATOR =0, VALUE =3 Failed Error executing algorithm Select by attribute Unsupported field type "INTEGER"
Model:
{ "values": { "inputs": { "STRING_NAME": { "values": { "pos": { "values": { "y": 93.0, "x": 191.0 }, "class": "point" }, "param": { "values": { "isAdvanced": false, "name": "STRING_NAME", "default": "", "value": null, "multiline": false, "hidden": false, "optional": false, "description": "Name" }, "class": "processing.core.parameters.ParameterString" } }, "class": "processing.modeler.ModelerAlgorithm.ModelerParameter" }, "VECTORLAYER_LAYER": { "values": { "pos": { "values": { "y": 93.0, "x": 430.0 }, "class": "point" }, "param": { "values": { "isAdvanced": false, "name": "VECTORLAYER_LAYER", "shapetype": [ -1 ], "value": null, "exported": null, "hidden": false, "optional": false, "description": "Layer" }, "class": "processing.core.parameters.ParameterVector" } }, "class": "processing.modeler.ModelerAlgorithm.ModelerParameter" }, "STRING_AGE": { "values": { "pos": { "values": { "y": 191.0, "x": 484.0 }, "class": "point" }, "param": { "values": { "isAdvanced": false, "name": "STRING_AGE", "default": "", "value": null, "multiline": false, "hidden": false, "optional": false, "description": "Age" }, "class": "processing.core.parameters.ParameterString" } }, "class": "processing.modeler.ModelerAlgorithm.ModelerParameter" } }, "group": "testGroup", "name": "testModel", "algs": { "QGISSELECTBYATTRIBUTE_2": { "values": { "name": "QGISSELECTBYATTRIBUTE_2", "paramsFolded": true, "outputs": {}, "pos": { "values": { "y": 313.0, "x": 353.0 }, "class": "point" }, "outputsFolded": true, "dependencies": [], "params": { "OPERATOR": 0, "INPUT": { "values": { "alg": "QGISSELECTBYATTRIBUTE_1", "output": "OUTPUT" }, "class": "processing.modeler.ModelerAlgorithm.ValueFromOutput" }, "VALUE": { "values": { "name": "STRING_AGE" }, "class": "processing.modeler.ModelerAlgorithm.ValueFromInput" }, "FIELD": "Age" }, "active": true, "consoleName": "qgis:selectbyattribute", "description": "Select by attribute" }, "class": "processing.modeler.ModelerAlgorithm.Algorithm" }, "QGISSELECTBYATTRIBUTE_1": { "values": { "name": "QGISSELECTBYATTRIBUTE_1", "paramsFolded": true, "outputs": {}, "pos": { "values": { "y": 192.0, "x": 243.0 }, "class": "point" }, "outputsFolded": true, "dependencies": [], "params": { "OPERATOR": 0, "INPUT": { "values": { "name": "VECTORLAYER_LAYER" }, "class": "processing.modeler.ModelerAlgorithm.ValueFromInput" }, "VALUE": { "values": { "name": "STRING_NAME" }, "class": "processing.modeler.ModelerAlgorithm.ValueFromInput" }, "FIELD": "Name" }, "active": true, "consoleName": "qgis:selectbyattribute", "description": "Select by attribute" }, "class": "processing.modeler.ModelerAlgorithm.Algorithm" } } }, "class": "processing.modeler.ModelerAlgorithm.ModelerAlgorithm" }
Hope this can help you get going with the modeler.