When infected with malaria, how many parasites are within a human host?
The uninucleate sporozoites are injected by the mosquito into a human host. They mature in the liver parenchymal cells in schizonts. Each schizont releases into the blood flow 2,000 to 40,000 uninucleate merozoites. Each of them can infect a red blood cell. Here, a merozoite can release other 10 to 36 merozoites [1].

The numer of injected sporozites depends on the bite and the number of bites [2]. And it seems that a parasitemia greater than 5000/microliters which is usually achieved by 10 infective bites during a 28-day period triggers the signs and symptoms [3].

I couldn't find any data on the mosquito parasitemia. It has been found that the infected mosquito and the parasite mutually benefit each other and thereby promote transmission of the infection. The Plasmodium-infected mosquitoes have a better survival and show an increased rate of blood-feeding, particularly from an infected host [4].

References:


James M. Crutcher and Stephen L. Hoffman. Medical Microbiology. 4th edition. 1996, The University of Texas Medical Branch at Galveston.
Garrett-Jones C, Shidrawi GR. Malaria vectorial capacity of a population of Anopheles gambiae: an exercise in epidemiological entomology. Bull. World Health Organ. 1969 Apr;40(4):531-45. PubMed PMID: 5306719. 
McElroy PD, Beier JC, Oster CN, Beadle C, Sherwood JA, Oloo AJ, Hoffman SL. Predicting outcome in malaria: correlation between rate of exposure to infected mosquitoes and level of Plasmodium falciparum parasitemia. Am. J. Trop. Med. Hyg. 1994 Nov;51(5):523-32. PubMed PMID: 7985743. 
Dr. B.S. Kakkilaya's Malaria Web Site. Life Cycle of Malaria.