You cite the example of a small pox outbreak in Japan in 735 – 737 AD, but there may have been smallpox epidemics there dating back to 585. The epidemic of 585-587 is believed to have come from Korea, and there was an epidemic in 552 which was probably either plague or measles. Both these epidemics were blamed by adherents of the Shinto religion on the recent introduction of Buddhism from Korea. The Buddhists, in turn, said the 585 epidemic was retribution for the destruction of Buddhists temples and monuments. Although there are no specifics on casualties,
Thousands of people were afflicted with the disease, their bodies
covered with sores, and many died. Even the emperor and the chief of
the clan leaders were infected....autumn of 585, the emperor ordered that the Buddhist temples be rebuilt but banned conversions. He died shortly thereafter, becoming perhaps Japanese royalty’s first smallpox victim. He was succeeded by his brother Yomei... He too was stricken by smallpox in 585 and died in the continuing epidemic two years later.
Source: George C. Kohn, Encyclopedia of Plague and Pestilence: From Ancient Times to the Present
In 994-5, there was what appears to have been an even more serious epidemic in Japan. The origin of this epidemic seems to be unknown but the severity of it suggests that it was affecting a virgin population:
Historical sources are agreed on the severity of this epidemic, which apparently killed many in the elite ruling class over a brief
two-to-three-month period.... Overall, it is estimated that more than half of Japan’s population died during this epidemic
Source: George C. Kohn
Then, in 998 and 1025, Japan was hit by measles epidemics which, according to a local chronicle, infected everyone (all ages and social classes). The origin of these epidemics is not stated, though, but China or Korea seem the most likely points of origin.
The Mongols: in one incident in the second half of the sixteenth century, some Mongol traders coming into contact with the Chinese died from smallpox, rare but not unknown in Mongolia. Thinking they had been poisoned, fighting broke out. Subsequently,
Chinese immigrants settled north of the Great Wall and ...
intermingled with the Mongols. These communities were particularly
vulnerable to high mortality from epidemic diseases. One Chinese
observer claimed that the border communities had grown to 100,000 by
the 1590s, but "luckily" a great epidemic had cut their numbers down
Source: The Cambridge World History of Human Disease
For reasons which are not fully understood, the plague which was so devastating in Europe in 1347-49 and which also affected northern and western India (no details on mortality rate given), had little effect on Bengal, southern India and Sri Lanka.
Mortality rates for the Philippines are also hard to come by. What follows is a summary from Linda A. Newson, Conquest and Pestilence in the Early Spanish Philippines
China had extensive trade links with the Philippines but low population density, the time it took to travel from island to island, and ‘the Filipino habit of frequent washing’ seem to have ‘discouraged the spread of some infections’ in the pre-colonial (Spanish) era. Leprosy almost certainly came from China but, although leprosy and yaws were common in the Philippines prior to the arrival of the Spanish, they were rarely fatal. In short, the circumstantial evidence suggests that fatal diseases did not become endemic in the Philippines prior to the arrival of the Spanish. However, this does not preclude local outbreaks with high mortality rates. The first recorded major epidemic seems to be the smallpox epidemic of 1591, but this came via a Spanish ship from Mexico. A Jesuit priest of the time described it as 'vicious' with one third of the population in Batangas bedridden.
This island was hit by a smallpox epidemic which killed around 2,000 people in 1817-18. It was apparently spread by Arab slave traders and came from the coast of East Africa. These Arab slave traders subsequently spread smallpox to Reunion and Mauritius.
In 1867, a malaria epidemic killed 31,920 people. It had been introduced in 1866 either by Indian or African labourers (but possibly by British soldiers). The final death toll was around 43,000 out of a population of 330,000. This Mauritian Ministry of Health document states:
This was the worst calamity that Mauritius has known and it had serious economic impact on the island. Many people moved from the capital Port Louis (a coastal town at that time) to the high plateau (Curepipe) in order to escape the disease. During the next 100 years malaria became endemic and caused recurrent epidemic with high mortality – malaria was the principal
cause of death in the post world war II period.