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The dengue vaccine, CYD-TDV (Dengvaxia), has been licensed in 20 countries in Latin America and Southeast Asia beginning in 2015. In April 2018, the World Health Organization (WHO) advised that CYD-TDV should only be administered to individuals with a history of previous dengue virus infection. Using literature-based parameters, a mathematical model of dengue transmission and vaccination was developed to determine the optimal vaccination strategy while considering the effect of antibody-dependent enhancement (ADE). We computed the optimal vaccination rates under various vaccination costs and serological profiles. We observe that the optimal dengue vaccination rates for seropositive individuals are highest at the initial phase of a vaccination program, requiring intense effort at the early phase of an epidemic. The model shows that even in the presence of ADE, vaccination could reduce dengue incidence and provide population benefits. Specifically, optimal vaccination rates increase with a higher proportion of monotypic seropositive individuals, resulting in a higher impact of vaccination. Even in the presence of ADE and with limited vaccine efficacy, our work provides a population-level perspective on the potential merits of dengue vaccination.

Optimal control strategies for controlling seasonal influenza transmission in the US are of high interest, because of the significant epidemiological and economic burden of influenza. To evaluate optimal strategies of vaccination and social distancing, we used an age-structured dynamic model of seasonal influenza. We applied optimal control theory to identify the best way of reducing morbidity and mortality at a minimal cost. In combination with the Pontryagins maximum principle, we calculated time-dependent optimal policies of vaccination and social distancing to minimize the epidemiological and economic burden associated with seasonal influenza. We computed optimal age-specific intervention strategies and analyze them under various costs of interventions and disease transmissibility. Our results show that combined strategies have a stronger impact on the reduction of the final epidemic size. Our results also suggest that the optimal vaccination can be achieved by allocating most vaccines to preschool-age children (age under five) followed by young adults (age 20-39) and school age children (age 6-19). We find that the optimal vaccination rates for all age groups are highest at the beginning of the outbreak, requiring intense effort at the early phase of an epidemic. On the other hand, optimal social distancing of clinical cases tends to last the entire duration of an outbreak, and its intensity is relatively equal for all age groups. Furthermore, with higher transmissibility of the influenza virus (i.e. higher R0), the optimal control strategy needs to include more efforts to increase vaccination rates rather than efforts to encourage social distancing. Taken together, public health agencies need to consider both the transmissibility of the virus and ways to encourage early vaccination as well as voluntary social distancing of symptomatic cases in order to determine optimal intervention strategies against seasonal influenza.

Individuals who carry the sickle cell trait ($S$-gene) have a greatly reduced risk of experiencing symptomatic malaria infections. However, previous studies suggestthat the sickle cell trait does not protect against acquiring asymptomatic malaria infections, although the proportion of symptomatic infections is up to $50\%$ in areas where malaria is endemic. To examine the differential impact of the sickle cell trait on symptomatic and asymptomatic malaria, we developed a mathematical model of malaria transmission that incorporates the evolutionary dynamics of $S$-gene frequency. Our model indicates that the fitness of sickle cell trait is likely to increase with the proportion of symptomatic malaria infections. Our model also shows that control efforts aimed at diminishing the burden of symptomatic malaria are not likely to eradicate malaria in endemic areas, due to the increase in the relative prevalence of asymptomatic infection, the reservoir of malaria. Furthermore, when the prevalence of symptomatic malaria is reduced, both the fitness and frequency of the $S$-gene may decrease. In turn, a decreased frequency of the $S$-gene may eventually increase the overall prevalence of both symptomatic and asymptomatic malaria. Therefore, the control of symptomatic malaria might result in evolutionary repercussions, despite short-term epidemiological benefits.

Limited production capacity and delays in vaccine development aremajor obstacles to vaccination programs that are designed tomitigate a pandemic influenza. In order to evaluate and compare theimpact of various vaccination strategies during a pandemic influenza, we developed an age/risk-structured model of influenzatransmission, and parameterized it with epidemiological data fromthe 2009 H1N1 influenza A pandemic. Our model predicts that theimpact of vaccination would be considerably diminished by delays invaccination and staggered vaccine supply. Nonetheless, prioritizing limited H1N1 vaccine toindividuals with a high risk of complications, followed byschool-age children, and then preschool-age children, would minimizean overall attack rate as well as hospitalizations anddeaths. This vaccination scheme would maximize the benefits ofvaccination by protecting the high-risk people directly, andgenerating indirect protection by vaccinating children who are mostlikely to transmit the disease.

Rubella is a highly contagious childhood disease that causesrelatively mild symptoms. However, rubella can result in severecongenital defects, known as congenital rubella syndrome (CRS), iftransmitted from a mother to a fetus. Consequently, women havehigher incentive to vaccinate against rubella than men do. Withinthe population vaccination reduces transmission but also increasesthe average age of infection and possibly the risk of CRS amongunvaccinated females. To evaluate how the balance among thesefactors results in optimal coverage of vaccination, we developed agame theoretic age-structured epidemiological model of rubellatransmission and vaccination. We found that high levels ofvaccination for both genders are most effective in maximizingaverage utility across the population by decreasing the risk of CRSand reducing transmission of rubella. By contrast, the demands forvaccines driven by self-interest among males and females are $0\%$and $100\%$ acceptance, respectively, if the cost of vaccination isrelatively low. Our results suggest that the rubella vaccination bymales that is likely to be achieved on voluntary basis withoutadditional incentives would have been far lower than the populationoptimum, if rubella vaccine were offered separately instead ofcombined with measles and mumps vaccination as the MMR vaccine.

The roles of immigration and vaccination on disease dynamics are explored in a simple setting that considers the possibility of conferred immunity. We focus on SIR and SIS models with a vaccinated class. Conditions for the existence of multiple endemic steady states and a fold bifurcation are discussed.