Background: The prevalence of HIV varies greatly between and within countries. We aimed to build a comprehensive mathematical modelling tool capable of exploring the reasons of this heterogeneity and test its applicability by simulating the Malawian HIV epidemic.

Methods: We developed a flexible individual-based mathematical model for HIV transmission that comprises a spatial representation and individual-level determinants. We tested this model by calibrating it to the HIV epidemic in Malawi and exploring whether the heterogeneity in HIV prevalence could be reproduced. We ran the model for 1975-2030 with five alternative realizations of the geographical structure and mobility: (I) no geographical structure; 28 administrative districts including (II) only permanent inter-district relocations, (III) inter-district permanent relocations and casual sexual relationships, or (IV) permanent relocations between districts and to/from abroad and inter-district casual sex; and (V) a grid of 10 × 10km²cells, with permanent relocations and between-cell casual relationships. We assumed HIV was present in 1975 in the districts with >10 % prevalence in 2010. We calibrated the models to national and district-level prevalence estimates.

Results: Reaching the national prevalence required all adults to have at least 22 casual sex acts/year until 1990. Models II, III and V reproduced the geographical heterogeneity in prevalence in 2010 to some extent if between-district relationships were excluded (Model II; 4.9 %-21.1 %). Long-distance casual partnership mixing mitigated the differences in prevalence substantially (range across districts 4.1%-18.9 % in 2010 in Model III; 4.0%-17.6 % in Model V); with international migration the differences disappeared (Model IV; range across districts 6.9%-13.3 % in 2010). National prevalence decreased to 5 % by 2030.

Conclusion: Earlier introduction of HIV into the Southern part of Malawi may cause some level of heterogeneity in HIV prevalence. Other factors such as sociobehavioural characteristics are likely to have a major impact and need investigation.