models/Task.js

```javascript
const mongoose = require('mongoose');

const TaskSchema = new mongoose.Schema({
    title: {
        type: String,
        required: true
    },
    description: {
        type: String
    },
    department: {
        type: mongoose.Schema.Types.ObjectId,
        ref: 'Department',
        required: true
    },
    assignedTo: {
        type: mongoose.Schema.Types.ObjectId,
        ref: 'User',
        required: true
    },
    createdBy: {
        type: mongoose.Schema.Types.ObjectId,
        ref: 'User',
        required: true
    },
    dueDate: {
        type: Date,
        required: true
    },
    priority: {
        type: String,
        enum: ['low', 'medium', 'high'],
        default: 'medium'
    },
    status: {
        type: String,
        enum: ['pending', 'in-progress', 'completed', 'overdue'],
        default: 'pending'
    },
    createdAt: {
        type: Date,
        default: Date.now
    },
    startedDate: {
        type: Date
    },
    completedDate: {
        type: Date
    }
});

module.exports = mongoose.model('Task', TaskSchema);
```