Games like Epidemic
Games like Epidemic include 7 Days to Die, ARK: Survival Ascended, Project Zomboid, Once Human, and ARK: Survival Evolved. We matched them by the tags players give Epidemic on Steam (Base Building, Zombies, Open World, Inventory Management, and Building): closest matches first, and among equally close ones the better-known games.

7 Days to Die
Shared: Zombies · Open World · Base Building

ARK: Survival Ascended
Shared: Open World · Base Building · Survival

Project Zomboid
Shared: Zombies · Open World · Survival

Once Human
Shared: Open World · Survival · Building

ARK: Survival Evolved
Shared: Open World · Survival · Base Building

Rust
Shared: Open World · Survival · Building

Terraria
Shared: Survival · Pixel Graphics · Building

Core Keeper
Shared: Open World · Survival · Pixel Graphics

Raft
Shared: Survival · Open World · Base Building

Sons Of The Forest
Shared: Open World · Base Building · Survival

Scrap Mechanic
Shared: Building · Open World · Survival

Valheim
Shared: Open World · Survival · Base Building

Satisfactory
Shared: Base Building · Open World · Building

The Forest
Shared: Open World · Survival · Building

Palworld
Shared: Open World · Survival · Base Building

DayZ
Shared: Zombies · Open World · Survival

Enshrouded
Shared: Base Building · Open World · Survival

Space Engineers
Shared: Building · Base Building · Survival

Kenshi
Shared: Open World · Survival · Base Building

Factorio
Shared: Base Building · Open World · Survival

DYSMANTLE
Shared: Open World · Zombies · Base Building

Mist Survival
Shared: Zombies · Open World · Base Building

Night of the Dead
Shared: Zombies · Open World · Tower Defense

Necesse
Shared: Open World · Pixel Graphics · Survival