An Age-Structured Model for Tilapia Lake Virus Transmission in Freshwater with Vertical and Horizontal Transmission

Global analysis of an age-structured tuberculosis model with an application to Jiangsu, China

Diagnostic delay for TB infected individuals and the lack of TB vaccines for adults are the main challenges to achieve the goals of WHO by 2050. In order to evaluate the impacts of diagnostic delay and vaccination for adults on prevalence of TB, we propose an age-structured model with latent age and infection age, and we incorporate Mycobacterium TB in the environment and vaccination into the model. Diagnostic delay is indicated by the age of infection before receiving treatment. The threshold dynamics are established in terms of the basic reproduction number R 0 . WhenR 0 < 1 , the disease-free equilibrium is globally asymptotically stable, which means that TB epidemic will die out; WhenR 0 = 1 , the disease-free equilibrium is globally attractive; there exists a unique endemic equilibrium and the endemic equilibrium is globally attractive whenR 0 > 1 . We estimate that the basic reproduction numberR 0 = 0.5320 (95% CI (0.3060, 0.7556)) in Jiangsu Province, which means that TB epidemic will die out. However, we find that the annual number of new TB cases by 2050 is 1,151 (95%CI: (138, 8,014)), which means that it is challenging to achieve the goal of WHO by 2050. To this end, we evaluate the possibility of achieving the goals of WHO if we start vaccinating adults and reduce diagnostic delay in 2025. Our results demonstrate that when the diagnostic delay is reduced from longer than four months to four months, or 20% adults are vaccinated, the goal of WHO in 2050 can be achieved, and 73,137 (95%CI: (23,906, 234,086)) and 54,828 (95%CI: (15,811, 206,468)) individuals will be prevented from being infected from 2025 to 2050, respectively. The modeling approaches and simulation results used in this work can help policymakers design control measures to reduce the prevalence of TB.

A Model for Brucellosis Disease Incorporating Age of Infection and Waning Immunity

This paper proposes a model for brucellosis transmission. The model takes into account the age of infection and waning immunity, that is, the progressive loss of immunity after recovery. Three routes of transmissions are considered: vertical transmission, and both direct and indirect routes of horizontal transmission. According to the well-posedness results, we provide explicit formulas for the equilibria. Next, we derive the basic reproduction number R0 and prove some stability results depending on the basic reproductive number. Finally, we perform numerical simulations using model parameters estimated from biological data to confirm our theoretical results. The results of these simulations suggest that for certain values of parameters, there will be periodic outbreaks of epidemics, and the disease will not be eradicated from the population. Our results also highlight the fact that the birth rate of cattle significantly influences the dynamics of the disease. The proposed model can be of a good use in studying the effects of vaccination on the cattle population.