Human mobility plays a crucial role in the temporal and spatial spreading of infectious diseases. During the past few decades, researchers have been extensively investigating how human mobility affects the propagation of diseases. However, the mechanism of human mobility shaping the spread of epidemics is still elusive. Here we examined the impact of human mobility on the infectious disease spread by developing the individual-based SEIR model that incorporates a model of human mobility. We considered the spread of human influenza in two contrasting countries, namely, Belgium and Martinique, as case studies, to assess the specific roles of human mobility on infection propagation. We found that our model can provide a geo-temporal spreading pattern of the epidemics that cannot be captured by a traditional homogenous epidemic model. The disease has a tendency to jump to high populated urban areas before spreading to more rural areas and then subsequently spread to all neighboring locations. This heterogeneous spread of the infection can be captured by the time of the first arrival of the infection $$(T_{fi} )$$(Tfi), which relates to the landscape of the human mobility characterized by the relative attractiveness. These findings can provide insights to better understand and forecast the disease spreading.

Carbapenem-resistant Klebsiella pneumoniae (CRKP) has emerged as a major threat to global public health. Epidemiological and infection controls associated with CRKP are challenging because of several potential elements involved in a complicated cycle of transmission. Here, we proposed a comprehensive mathematical model to investigate the transmission dynamics of CRKP, determine factors affecting the prevalence, and evaluate the impact of interventions on transmission. The model includes the essential compartments, which are uncolonized, asymptomatic colonized, symptomatic colonized, and relapsed patients. Additionally, symptomatic colonized and relapsed patients were further classified into subpopulations according to their number of treatment failures or relapses. We found that the admission of colonized patients and use of antibiotics significantly impacted the endemic transmission in health care units. Thus, we introduced the treatment efficacy, defined by combining the treatment duration and probability of successful treatment, to characterize and describe the effects of antibiotic treatment on transmission. We showed that a high antibiotic treatment efficacy results in a significantly reduced likelihood of patient readmission in the health care unit. Additionally, our findings demonstrate that CRKP transmission with different epidemiological characteristics must be controlled using distinct interventions.

Resistance to antimalarial drugs is currently a growing public health problem, resulting in more cases with treatment failure. Although previous studies suggested that a concentration gradient facilitates the antibiotic resistance evolution in bacteria, no attempt has been made to investigate the roles of a concentration gradient in malaria drug resistance. Unlike the person-to-person mode of transmission of bacteria, the malaria parasites need to switch back and forth between the human and mosquito hosts to complete the life cycle and to spread the resistant alleles. Here we developed a stochastic combined within- and between-hosts evolutionary dynamics model specific to malaria parasites in order to investigate the influence of an antimalarial concentration gradient on the evolutionary dynamics of malaria drug resistance. Every stage of malaria development in both human and mosquito hosts are individually modelled using the tau-leaping algorithm. We found that the concentration gradient can accelerate antimalarial resistance evolution. The gain in resistance evolution was improved by the increase in the parasite mutation rate and the mosquito biting rate. In addition, even though the rate of resistance evolution is not sensitive to the changes in parasite reduction ratios (PRRs) of antimalarial drugs, the probability of finding the antimalarial drug resistant parasites decreases when the PRR increases.