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- Journal of Theoretical Biology
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- National Science Foundation
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In this paper, we compare the performance between systems of ordinary and (Caputo) fractional differential equations depicting the susceptible-exposed-infectious-recovered (SEIR) models of diseases. In order to understand the origins of both approaches as mean-field approximations of integer and fractional stochastic processes, we introduce the fractional differential equations (FDEs) as approximations of some type of fractional nonlinear birth and death processes. Then, we examine validity of the two approaches against empirical courses of epidemics; we fit both of them to case counts of three measles epidemics that occurred during the pre-vaccination era in three different locations. While ordinary differential equations (ODEs) are commonly used to model epidemics, FDEs are more flexible in fitting empirical data and theoretically offer improved model predictions. The question arises whether, in practice, the benefits of using FDEs over ODEs outweigh the added computational complexities. While important differences in transient dynamics were observed, the FDE only outperformed the ODE in one of out three data sets. In general, FDE modeling approaches may be worth it in situations with large refined data sets and good numerical algorithms.more » « less
Abstract Background Measles is among the most highly infectious human diseases. By virtue of increasingly effective childhood vaccination, together with targeted supplemental immunization activities (SIAs), health authorities in the People’s Republic of China have reduced measles’ reproduction number from about 18 to 2.3. Despite substantial residual susceptibility among young adults, more in some locales than others, sustained routine childhood immunization likely would eliminate measles eventually. To support global eradication efforts, as well as expedite morbidity and mortality reductions in China, we evaluated alternative SIAs via mechanistic mathematical modelling. Methods Our model Chinese population is stratified by immune status (susceptible to measles infection; infected, but not yet infectious; infectious; and recovered or immunized), age (0, 1–4, 5–9, …, 65+ years) and location (31 provinces). Contacts between sub-populations are either empirical or a mixture of preferential and proportionate with respect to age and decline exponentially with distance between locations at age-dependent rates. We estimated initial conditions and most parameters from recent cross-sectional serological surveys, disease surveillance and demographic observations. Then we calculated the reproduction numbers and gradient of the effective number with respect to age- and location-specific immunization rates. We corroborated these analytical results by simulating adolescent and young adult SIAs using a version of our model in which the age-specific contact rates vary seasonally. Results Whereas the gradient indicates that vaccinating young adults generally is the optimal strategy, simulations indicate that a catch-up campaign among susceptible adolescent schoolchildren would accelerate elimination, with timing dependent on uptake. Conclusions These results are largely due to indirect effects (i.e. fewer infections than immunized people might otherwise cause), which meta-population models with realistic mixing are uniquely capable of reproducing accurately.more » « less
Measles is one of the highly contagious human viral diseases. Despite the availability of vaccines, measles outbreak frequently occurs in many places, including Nepal, partly due to the lack of compliance with vaccination. In this study, we develop a novel transmission dynamics model to evaluate the effects of monitored vaccination programs to control and eliminate measles. We use our model, parameterized with the data from the measles outbreak in Nepal, to calculate the vaccinated reproduction number, $ R_v $, of measles in Nepal. We perform model analyses to establish the global asymptotic stability of the disease-free equilibrium point for $ R_v < 1 $ and the uniform persistence of the disease for $ R_v > 1 $. Moreover, we perform model simulations to identify monitored vaccination strategies for the successful control of measles in Nepal. Our model predicts that the monitored vaccination programs can help control the potential resurgence of the disease.
Measles and rubella vaccinations are highly effective at reducing disease prevalence; however, logistic issues related to subcutaneous administration and vaccine wastage limit the extent of vaccination coverage. Microneedle (MN) patches can increase coverage by easing logistics through simplified administration and improved stability. This study demonstrates the thermostability of a bivalent measles and rubella vaccine MN patch. The data show that rubella vaccine stability requires pH buffering during drying; potassium phosphate buffer at neutral pH is optimal for both vaccines. Screening 43 excipients for their ability to retain potency during drying and storage yields sucrose‐threonine‐potassium phosphate buffer formulation at pH 7.5 as an optimal formulation. MN patches made with this formulation have no significant loss of vaccine titer after 1 month and remain within a one log10titer loss cutoff after 3–4 months at 5, 25, and 40 °C. Finally, these patches are shown to be immunogenic in juvenile rhesus macaques. This work demonstrates the potential for MN patches for measles and rubella vaccination to be removed from the cold chain, which is expected to decrease vaccine cost and wastage, and increase vaccination coverage.