The Australian and his American-born wife, who settled in Jerusalem in 1988, lost their 15-year-old daughter, Malki, in the Sbarro restaurant terror attack in 2001.

And before that their younger daughter, Haya, was rendered profoundly brain damaged as a result of Israeli "hospital mismanagement".

Yet the couple have emerged from their tragedies with a grim determination to make the world a better place.

Arnold, who will be touring the British Jewish community in March, told me: "Haya, who is now 18, became very ill at a year old as a result of terrible hospital mismanagement, about which I never speak.

"She was born well, but became profoundly brain damaged. We were dealt with in a very insensitive way by the health care system in Israel at the time that our child became so badly disabled."

Many in that situation, with six other children to care for, would have entrusted their severely handicapped daughter to an institution or would have engaged full-time carers' support.

But that is not the Roth way of dealing with tragedy.

Arnold told me that when bad things happen, "It may be that all you really want to do is throw yourself under the blanket and never come out again.

"Since that is not an option and you have responsibilities to the family around you, your mode of dealing is always modified by those needs."

Frimet, who had just qualified as a lawyer and had a job lined up, decided to become Haya's full-time carer, which she still is to this day, as Haya is blind and suffering from cerebral palsy.

Arnold said: "We realised that no-one cared for Haya as we did and that we would not allow anyone else to take from us the privilege of caring for her.

"Haya lives with us at home. Frimet believes firmly in the value of having a special needs child close, that parents can do a better job than anybody else."

Malki, who was nine when Haya was born, followed in her mother's footsteps.

Arnold said: "Malki showed a remarkable degree of understanding and responsibility, stemming from a feeling of connectedness and love. It was clear to her that her sister had very serious problems and needed a great deal of intervention by people round her.

"She stepped up and said, 'OK, I'm here to do these things'. She showed considerable maturity and insight."

Malki began accompanying her mother on long and difficult stays in the hospital.

When she was 14, Malki searched her Jerusalem neighbourhood to find another special needs child to help during her summer break.

She became a mother's help for a child with the Jewish genetic disease of Canavan.

Arnold recalled: "She would come home with these marvellous stories about the little boy and what she was doing for him.

"These were not easy things to do. But all she talked about was how much fun it was. It was really extraordinary. Malki was a presence in our lives that was like pure sunshine.

"She didn't just do it with us, looking after the daily challenges of a child who had enormous, endless needs. But she was also able to take this and convey it to her school friends. She became something of an agent of change in her own social circle."

An active member of the Ezra religious youth movement, Malki became a leader in a group in Ma'ale Adumim, where she would spend every second Shabbat and every Tuesday afternoon.

It was only after her death in the terror attack the following year that her family discovered the work Malki had done with new young immigrants from the former Soviet Union, who were confronted with social challenges.

Arnold said: "Malki was really deeply involved in helping some of these girls figure out life's challenges.

"She took responsibility for them as only an adult would. This is a child whose life we memorialise, not because we are parents and we have nothing else to do. Her life was really extraordinary. She radiated positive values and really influenced people."

During the shiva week for Malki, her family decided to set up Keren Malki in her memory.

Arnold explained: "The Keren Malki Foundation was set up by the family, based on a decision we took during the shiva. We decided we were going to do something that reflected Malki's spirit.

"It was not hard for us to work out a broad brush strategy to empower families who have a child with special needs whom they want to care for at home."

Keren Malki, which has helped thousands of Israeli families with special needs children, provides them with medical equipment and therapies not provided by the Israeli healthcare system.

But Arnold does not just tour the world on fundraising missions, he also wants to change people's perceptions of the victims of terror, both politically and socially.

He said: "The fact that Malki's life was so beautiful and snuffed out in such a hideous way has implications for all of us. I feel an obligation because the things she stood for are marvellous.

"It so hurts me to see terrorism discussed in statistical terms."

He was also deeply upset that his Israeli neighbours often walked away because they did not know how to deal with the family's tragedy.

He said: "Terror attacks were not meted out in an equitable way across the community.

"While everyone was threatened, only a relatively small number of people in Jerusalem, several thousand families, lost a child, sibling or loved one during those years of the Arafat war. That is a lot of people for a small community.

"Just in our street we had five or six families who lost a child during that awful period. It is an impact that is difficult to put into words. People don't talk about it. They don't say, 'I am so lucky that my child wasn't killed. You poor sucker, I am sorry for you'. Nobody says those things.

"Once you have a community that is impacted in every direction in this awful way, you see people's behaviour changing. They take steps to protect themselves from coming into contact with danger or - a much more serious issue - steps to avoid having to confront the loss of others. People most certainly kept away.

"There is a terrible tendency in Israeli society, for perfectly understandable reasons, to sweep away the broken glass and allow life to continue as quickly as possible in order not to give victory to the terrorist."

But Arnold said: "The terrorists have certainly won in the case of the families they have impacted upon and those who were subsequently terrified.

"The question now is what we are doing for our victims and the social, mental and emotional health of society."

Having subsequently met with victims of terror all over the world, he says that the same phenomenon affects families of all nationalities.

In fact, straight after his British tour, Arnold is to address a conference in Spain to mark the 10th anniversary of the Madrid bombings.

He said: "People don't have the emotional depth to deal with something that no one should have to deal with.

"I have heard it from people in the UK, Spain, Northern Ireland and Australia. It happens because there is so little preparation in our society for dealing with these inequitably distributed terrible occurrences."

In the Roth family, one of Malki's siblings suffered at her school because staff had no clue how to deal with the traumatised child.

After pulling the child out of the school, Frimet wrote to the Israeli Ministry of Education explaining the problem. The school wrote back in a manner which Arnold describes as "extremely defensive and offensive".

But Frimet was asked by the Ministry to address school counsellors which produced constructive results.

Arnold is also very active in opposing the release of Israeli terrorists in political exchanges.

He failed in his attempt to stop the Sbarro terrorist Ahlam Tamimi being exchanged for Gilad Shalit. She subsequently became a Jordanian media personality.

And Arnold is currently making little headway in his repeated calls to Israeli Prime Minister Benjamin Netanyahu and US Secretary of State John Kerry not to release terrorists in the current peace negotiations.

Arnold has addressed the UN on the subject of terror victims.

He said: "The Israeli government is acting as though the needs of the victims were of no consequence.

"They have released thousands of killers without giving the victims a chance to be heard. I am a lawyer.

"The penal code in almost every country in the civilised world gives victims a voice as of right. When the killer of a person's child is going to be released the voice of the victims is heard.

"But it has not happened at all here."

He warned: "If you ignore the commitment of a society to live according to the principles of justice, you are bringing your society to a very dangerous place. We wish the US and Israeli governments would understand that."

Arnold will speak on Tuesday, March 4, at Beth Hamidrash Hagadol Synagogue, Leeds, and the following day to the Liverpool Jewish Forum.

On Thursday, March 6, he is to address a Manchester business breakfast and Yeshurun Fly the Flag and StandWithUs UK. He will spend Shabbat in Glasgow, speaking at Giffnock Synagogue and at an interfaith dialogue.

On Sunday, March 9 he will speak at Edinburgh Synagogue.