Irish police investigating the death of Ashling Murphy have renewed an appeal for information, saying “significant progress” has been made in the murder probe.
It comes as police released the description of a man they want to speak to in relation to the 23-year-old’s murder in Co Offaly.
Ms Murphy was found dead after going for a run on the banks of the Grand Canal in Tullamore.
The murder has caused widespread anger and shock in Ireland and beyond, with tens of thousands of people attending vigils in recent days.
Police have asked anyone who saw a man dressed in black tracksuit top with no hood, black tracksuit bottoms with a large white stripe or white writing on the side and black runners to come forward.
Officers have asked members of the public whether they saw this man walking in the Tullamore area, or if they gave the man a lift on the evening last Wednesday.
The public has also been asked if they noticed him loitering at any location or “involved in any activity which drew your attention”.
The investigation into the teacher’s murder continued on Monday as officers examined the scene at the canal bank at Cappincur.
Police said that “significant progress” is being made, but would not confirm any specific details.
It comes as they identified a new person of interest, who is believed to be in hospital in the Dublin region receiving treatment, and are waiting to speak to him.
As their investigation continues, gardai believe the development of DNA profiles will form an integral part of the search for Ms Murphy’s killer.
A complaint from another woman, who said she was followed on the same canal path hours before the murder, is still being investigated.
Gardai remained at the scene on Monday to carry out further investigations of the area.
Police appealed to anyone who has not made contact with the investigation team and who has any information to come forward.
Gardai said in a statement: “We are now asking for any member of the public who was on the Grand Canal Way on the morning or afternoon of the January 12 between Digby’s bridge and Ballycommon to contact the investigation team.
“Whether you think you saw anything or not please contact gardai in Tullamore.
“We continue to appeal for any information on a Falcon Storm mountain bike with straight handlebars and distinctive yellow/green front forks prior to 4pm on Wednesday and in the previous days and weeks.
“We are now asking for people in Tullamore to think about last Wednesday after 4pm and not to confine their thoughts to the Falcon Storm mountain bike.”
Gardai said they are concerned about people sharing information on social media, particularly private messaging apps.
Gardai have appealed for people to stop sharing these messages.
“Not only are they misinformed, inaccurate and dangerous, they are unhelpful to the criminal investigation,” they said in a statement.
“If you have information, which is relevant to this criminal investigation you should contact the investigation team at Tullamore Garda Station with this information.”
Earlier, campaigners demanded more to be done to tackle domestic, sexual, and gender-based violence in Ireland in the wake of Ms Murphy’s murder.
Mary McDermott, chief executive officer at Safe Ireland, which campaigns for women and children’s safety, said the country does not have a minister with full responsibility for gender-based and domestic violence, saying it is “scattered” across various Government departments.
She told RTE Morning Ireland: “Refuge and support services are under (the department of) children and the rest of the responsibility, which we know requires a whole of Government response, is scattered across the rest of Government departments.
“It needs a whole-level response but at the moment it is fragmented and scattered.
“The Tanaiste (Leo Varadkar) said there is a need for a lead minister.
“We hope it brings all the areas under one ministry to respond in a coherent and systematic and fully resourced way.
“Domestic violence in this country is a large-scale social problem.
“It is not a matter of poor personal choice.
“While we welcome all targeted actions that address the individual, if it is not systemically responded to we will fail.
“We think domestic violence is akin to climate change and call for a high-level unit to set out and consider this.”
Over the weekend, Minister for Justice Helen McEntee said a new Government strategy to tackle domestic, sexual and gender-based violence will be published by the start of March.
It would, she said, take a “zero-tolerance” approach to violence against women.
Members of the public continued to bring floral tributes and messages to the canal throughout the day, while a long line of mourners waited to pay their respects outside Ms Murphy’s family home in Blue Ball.
Ms Murphy’s funeral will take place on Tuesday at St Brigid’s Church, Mountbolus, in Co Offaly.
Unions including the Irish National Teachers’ Organisation, Association of Secondary Teachers in Ireland, and Teachers’ Union Ireland have urged schools and colleges across Ireland to observe a minute’s silence at 11am the same day.
They said in a joint statement: “We are encouraging schools to fall silent to remember a beloved primary school teacher, taken far too soon, and show our solidarity with her friends, family, colleagues and pupils as Ashling is laid to rest.”
Meanwhile, MLAs gathered in front of Parliament Buildings at Stormont for a vigil.
Before the Northern Ireland Assembly resumed business following its recess, politicians from the main parties came together.
First Minister Paul Givan, deputy First Minister Michelle O’Neill, DUP leader Sir Jeffrey Donaldson, and SDLP leader Colum Eastwood gathered in front of a portrait of Ms Murphy and flowers.