The children's mother is still alive, although she too has been infected with the HIV virus. It's now clear how the family contacted the virus, which is transmitted through certain bodily fluids.
Although the father and his two children are the first AIDS victims registered with the Afghan Health Ministry, they might not have been the first people to die of the disease in Afghanistan.
Naqibullah Safi, the head of the ministry's HIV/AIDS department, says he believes there have been other AIDS deaths that have not been officially registered.
"The virus existed in Afghanistan even before and it has spread. The low level of knowledge of our people [about HIV/AIDS] means it will be transmitted [across the country] very fast," said Safi.
Afghan officials estimate that about 200 to 300 Afghans are infected with HIV/AIDS. The real number could be higher, however, because the social stigma associated with the disease keeps many sufferers from seeking help.
Intravenous drug use, shared needles, and contaminated blood transfusions are believed to be the primary modes of transmission in Afghanistan.
The country is the world's top producer of opium. The United Nations says drug abuse is becoming a serious problem in many parts of the country.
The World Health Organization (WHO) warned last year that high levels of intravenous drug use and unsafe blood transfusions could lead to a rapid spread of the HIV virus in Afghanistan.
Other factors are adding to the risk factor, such as the high numbers of refugees and displaced people, and high levels of illiteracy.
Since the fall of the Taliban, more than 2 million Afghan refugees have returned to their country mainly from Pakistan and Iran, where the spread of HIV has been mainly among drug users.
It is believed that some HIV-positive Afghans contacted the virus from returning refugees.
There is little knowledge about the disease in the war-shattered country, where most of the population is illiterate.
According to the World Bank, only 47 percent of men and 15 percent of women in Afghanistan can read. Illiteracy presents a major barrier to HIV/AIDS awareness and prevention.
A barber in Kabul said he recently learned about AIDS and now uses disposable razors, a measure he believes will help prevent any of his clients from contracting HIV: "We use a new [razor] for every [customer], because they say the 'vex' disease has come. Even for a million, I would not work on a client who has the disease. The doctors talk about it, people talk about it, it's on TV, on the radio, they say it's the vex disease and it has no cure."
Lack of access to basic health care and poor medical facilities are other factors that may contribute to the spread of HIV in Afghanistan. Many of the country's existing facilities are not adequately equipped to handle HIV and AIDS patients. Hospital staff are not prepared to take adequate precautions to prevent themselves or their patients from infections.
Naqibullah Safi from the Afghan Health Ministry said: "The medical equipment used by doctors is not clean. Dentists, surgeons and people who work in laboratories do not properly sterilize the equipment."
Suman Mehta is the Asia Pacific and Middle East director for the United Nation's HIV/AIDS program, UNAIDS. She told RFE/RL that because of the many risk factors Afghanistan is very vulnerable to an HIV/AIDS epidemic: "The environment is very fertile for the epidemic to start raging. The numbers could raise at a very fast speed."
Mehta said Afghan women are especially vulnerable to AIDS because of their low socioeconomic status. There are many reports of war widows turning to prostitution in order to survive.
The UNAIDS official says that in order to stop the spread of HIV, Afghanistan's health system needs to be rebuilt and an action plan developed based on analysis of the country on a region-by-region basis.
There is also a serious need for education and raising awareness among the population and regional policymakers: "[It is important to build] the political environment which is right to address the issue, because right now there is much denial [about HIV/AIDS], so that needs to be taken care of. That has to be coupled with general awareness of what HIV/AIDS is, what it can do, and also spreading the good news that it is possible to prevent. And how to prevent it and how to remain free of AIDS is the message that needs to go out through multimedia sources to everybody in the country."
(RFE/RL's Afghan Service contributed to this report.)