The correct matching between the diseases and their causal organisms is as follows:
- Sleeping sickness (P) is caused by Trypanosoma brucei, a protozoan parasite transmitted by tsetse flies. Therefore, P matches with 2 (Trypanosoma brucei).
- Chagas disease (Q) is caused by Trypanosoma cruzi, a protozoan parasite transmitted by triatomine bugs. Therefore, Q matches with 1 (Trypanosoma cruzi).
- Elephantiasis (R) is caused by Wuchereria bancrofti, a parasitic roundworm transmitted by mosquitoes. Therefore, R matches with 4 (Wuchereria bancrofti).
- Lyme disease (S) is caused by Borrelia burgdorferi, a bacteria transmitted by ticks. Therefore, S matches with 3 (Borrelia burgdorferi).
Thus, the correct answer is option (D).