A two-patch mathematical model of Dengue virus type 2 (DENV-2) that accounts for vectors’ vertical transmission and between patches human dispersal is introduced. Dispersal is modelled via a Lagrangian approach. A host-patch residence-times basic reproduction number is derived and conditions under which the disease dies out or persists are established. Analytical and numerical results highlight the role of hosts’ dispersal in mitigating or exacerbating disease dynamics. The framework is used to explore dengue dynamics using, as a starting point, the 2002 outbreak in the state of Colima, Mexico.

Background
The transmission dynamics of Tuberculosis (TB) involve complex epidemiological and socio-economical interactions between individuals living in highly distinct regional conditions. The level of exogenous reinfection and first time infection rates within high-incidence settings may influence the impact of control programs on TB prevalence. The impact that effective population size and the distribution of individuals’ residence times in different patches have on TB transmission and control are studied using selected scenarios where risk is defined by the estimated or perceive first time infection and/or exogenous re-infection rates.
Methods
This study aims at enhancing the understanding of TB dynamics, within simplified, two patch, risk-defined environments, in the presence of short term mobility and variations in reinfection and infection rates via a mathematical model. The modeling framework captures the role of individuals’ ‘daily’ dynamics within and between places of residency, work or business via the average proportion of time spent in residence and as visitors to TB-risk environments (patches). As a result, the effective population size of Patch i (home of i-residents) at time t must account for visitors and residents of Patch i, at time t.
Results
The study identifies critical social behaviors mechanisms that can facilitate or eliminate TB infection in vulnerable populations. The results suggest that short-term mobility between heterogeneous patches contributes to significant overall increases in TB prevalence when risk is considered only in terms of direct new infection transmission, compared to the effect of exogenous reinfection. Although, the role of exogenous reinfection increases the risk that come from large movement of individuals, due to catastrophes or conflict, to TB-free areas.
Conclusions
The study highlights that allowing infected individuals to move from high to low TB prevalence areas (for example via the sharing of treatment and isolation facilities) may lead to a reduction in the total TB prevalence in the overall population. The higher the population size heterogeneity between distinct risk patches, the larger the benefit (low overall prevalence) under the same “traveling” patterns. Policies need to account for population specific factors (such as risks that are inherent with high levels of migration, local and regional mobility patterns, and first time infection rates) in order to be long lasting, effective and results in low number of drug resistant cases.