* Spread of coronavirus: tmsnrt.rs/3aIRuz7 * Discount for cash over 3-month copper highest since Jan. * Discount for cash over 3-month aluminium near 5-year high LONDON, April 14 (Reuters) - Copper prices hit a four-week high on Tuesday, boosted by coronavirus-linked supply disruptions and expectations of stronger demand, although worry that optimism was premature capped gains. Benchmark copper on the London Metal Exchange was up 2.7% at $5,154 a tonne at 1056 GMT. Prices of the metal used by investors as gauge of economic health touched $5,200 earlier, the highest since March 17. "Some people are convinced things are improving and are positioning accordingly, but a "V" shaped recovery could turn out to be an illusion," said Peter Fertig, analyst at Quantitative Commodity Research. "China is starting up, but we are far from normalisation, price gains could be getting ahead of economic reality." DEMAND: China is the world's largest consumer of copper and other industrial metals. Markets were cheered last week by a survey of purchasing managers showing factory activity expanding in March after plunging in February. But analysts say the survey does not quantify the strength of the bounce and that industrial production - highly correlated with metals demand - is unlikely to return soon to levels seen before the coronavirus outbreak. POLL: That idea is reflected in a Reuters survey showing China's economy is expected to grow only 2.5% this year, the slowest annual pace in nearly half a century and a sharp drop from 6.1% last year. DISRUPTIONS: Peru's Antamina copper mine, controlled by BHP and Glencore, said it would halt all operations for at least two weeks, while miner Freeport-McMoRan said it was conducting limited operations at the Cerro Verde copper mine, also in Peru. "As Peruvian copper mines joined the rest of the world to suspend production, the supply risks have strengthened," said analyst Helen Lau of Argonaut Securities in a note, adding around a third of China's feedstock for smelting activities is imported. IMPORTS: China's unwrought copper imports in March rose 13% from a year ago as dwindling scrap supply increased demand for other forms of the metal and factories restarted. SPREADS: However, expectations of nearby surpluses can be seen in the discount for cash over the three-month copper MCU0-3 at three-month highs of $29 a tonne from levels near $3 a tonne on March 24. Expectations of large surpluses also pushed the discount for the cash over the three-month aluminium contract to $40 a tonne last week, the highest since June 2015. Three-month aluminium was up 0.8% at $1,491 a tonne. OTHER METALS: Zinc gained 0.9% to $1,919, lead slipped 0.8% to $1,708, tin added 2.4% to $15,320 and nickel climbed 1.3% to $11,825 a tonne.