The Opponents
Neither Paraguay nor the Allies were prepared for a long-term war.
At the beginning of the conflict Paraguay's Army could put into the battlefield 30,000 men plus an equal number of reservists and its equipment was as good as his opponents were. Until the end of the conflict, some 80.000 men fought under the Paraguayan Flag. Taking into account that Paraguay's population summed up to 800,000, we can figure the efforts of the country to sustain the hostilities.
The weakness of this force, however, rested in its lack of trained leadership, of an industrial base to replace weapons and other means to war and the immense disadvantage in terms of population when compared with the combined Allies.
The Allies, for their turn, faced their own problems.
Uruguay was prostrated after the two-years civil war and, worst of all, occupied by a foreign army. When hostilities began was able to put into the fight less than 2,000 troops. Uruguay's population counted up 200,000.
The Argentine Army was far from being a perfect force of combat. Argentina had hardly started its process of union. Many provinces were still resentful of Buenos Aires hegemony after the Battle of Pavón in 1861 and looked with suspect on Brazil's intervention over the Uruguay Therefore, Argentine Army could rely only on Buenos Aires forces. In fact,many uprisings took place in the country during the war. As a result, much of the means and efforts were deviated to repress these riots.
It's believed that Argentina Army lined a force of 30.000 men out of a population of 1,5 million until the end of the war. This number however is not entirely reliable due to Argentina's troubles in gathering men to serve at the army in the countryside. When war broke out the army  fielded only 6,000 troops.
The Imperial Army had a well-trained team of officers. Many of them were veterans of the battles against the Argentinean Dictator Juan Manuel Rosas in 1852. Its equipment if not abundant, were suitable for a shorter conflict. Besides, Brazil's Navy was far the most powerful of the Latin America. The fleet included ironclad steamships and many other vessels.
Nevertheless, Brazil had its weak points. First, in terms of size the army was far from appropriate for a country which area is comparable to the extent of Europe. It lined up less than 20,000 men, dispersed along the territory and with problems of logistic and training. To make things worst, when the war broke out, part of the army was fighting in Uruguay. The second problem had to do with the country social structure. Many of the inhabitants of the Empire were slaves: at least 2 millions out of a population of 8,5 millions. It meant that part of the army was necessary to deal with the potential revolts of the slaves. As the war progressed, it became clear that slavery was responsible for draining much of the war efforts.
However, until the end of the war Brazil mobilized some 150,000 land troops (125,000 in the Volunteers or National Guard Battalions, 25,000 in the regular army and some others in small  police units ).  The total amount of men who fought in the Navy is not known, but according to Brazilian Navy archives, a sum of 6,500 fought during the entire campaign aboard the ships. By the end of the first year of war, the Empire could field a force  60,000 strong and by mid-1868 71,000 men were at disposal for the war. During the campaign 61 batallions were formed of volunteers, while the first line of the army was constitued of 22 others. The Army  formed five cavalry regiments between 1865-1870, four of which fought  in Paraguay.
The National Guard had its own cavalry regiments and infantry battalions, but the numbers of troops involved and the organization of this branch of the land force are not well known. It is believed that 15,000 to 18,000 National Guard men served as logistic support troops during the war and were not sent to Paraguay. Nevertheless, some battalions were organized as a fighting force.
The conflict was marked by poor logistic and diseases. From a certain point, neither side was able to use cavalry. Horses and men were victims of famine and cholera. The Imperial Navy, for instance, lost 170 men in action, 107 by accidents and 1,470 by diseases!
Although the problems, soldiers of both sides fought with bravery and distinction in many occasions. The Paraguayans, paticularly, showed great tenacity and stiff resistance even when became clear that the war was hopeless for their country. The commom soldier courage and devotion often wasted under the poor leadership of the officers on both sides.
The number of people killed in wars is always a matter for discussions. So, the estimations vary widely in the conflict. However, the true source of so many differents figures lay on the way the casualties were calculated. The allies sources (from where many, but not all, of the figures here are taken), count the Paraguayan casualties almost always in the category of "deads" or "killeds". The allies casualties, on the other hand, are mentioned in three categories: "deads", "wounded" and "missing". In fact, due to the poor health and care conditions on the battlefield, many of the wounded and missing  faced death just after an engagement, but not always they were counted as "dead" or "killed".
The more conservatives estimates reckon on 150,000 dead, half of which Paraguayans. Others count 400,000 killed, while some reach the number of 600,000.
A more accurate estimate may be halfway of the more exaggerating and conservative ones .
Based in some recent studies we are going to assume that by the end of the conflict  15% to 20%  of Paraguay's population were killed  by bullets or diseases. It means a toll of 120,000 to 160,000  dead among soldiers and civilians.
The Allies also suffered a great toll of casualties.
Argentina lost a number estimated between 27,000 and 30,000 men ( 18,000 due to combat, including internal riots, and  12,000 by diseases). Among the dead a great toll of civilian casualties ocurred, mainly in the Province of Corrientes.
From Uruguay's 5,000 soldiers less than half came back home.
Brazil casualties mount up to 30,000 killed in the battlefield or by wounds and an equal number (if not more) killed by cholera and looseness. Civilians casualties performed a high percentage  of deaths in the province of Mato Grosso. Out of a population of 75,000, some 5,000 were killed by diseases.
These numbers, however, does not include the losses at Uruguay's campaign from October,1864 until February 1865.
First Stages