No abstract

Anthrax is a rapidly fatal, infectious disease which occurs in many animal species, particularly herbivore mammals, and is one of the main causes of population decline in several national parks worldwide. As the infected animals face inevitable death and each infected carcass contributes spores to the surrounding environment, infected carcasses and the infected animals are the main sources of new infections. Thus any control measure should focus on vaccinating susceptible animals and the proper disposal of infected carcasses. In this paper, a system of ordinary differential equations modeling an anthrax epizootic in a wildlife reserve is formulated. Two controls representing vaccination of the susceptible animals and disposal of the infected carcasses are investigated in order to minimize the number of infected animals, the number of infected carcasses and the cost of vaccination and carcass disposal. Model parameters are estimated by using outbreak data from Malilangwe Wildlife Reserve, Zimbabwe, and some numerical results for the optimal control problem are presented.

Despite the global efforts to mitigate the ongoing COVID-19 pandemic, the disease transmission and the effective controls still remain uncertain as the outcome of the epidemic varies from place to place. In this regard, the province-wise data from Nepal provides a unique opportunity to study the effective control strategies. This is because (a) some provinces of Nepal share an open-border with India, resulting in a significantly high inflow of COVID-19 cases from India; (b) despite the inflow of a considerable number of cases, the local spread was quite controlled until mid-June of 2020, presumably due to control policies implemented; and (c) the relaxation of policies caused a rapid surge of the COVID-19 cases, providing a multi-phasic trend of disease dynamics. In this study, we used this unique data set to explore the inter-provincial disparities of the important indicators, such as epidemic trend, epidemic growth rate, and reproduction numbers. Furthermore, we extended our analysis to identify prevention and control policies that are effective in altering these indicators. Our analysis identified a noticeable inter-province variation in the epidemic trend (3 per day to 104 per day linear increase during third surge period), the median daily growth rate (1 to 4% per day exponential growth), the basic reproduction number (0.71 to 1.21), and the effective reproduction number (maximum values ranging from 1.20 to 2.86). Importantly, results from our modeling show that the type and number of control strategies that are effective in altering the indicators vary among provinces, underscoring the need for province-focused strategies along with the national-level strategy in order to ensure the control of a local spread.

Public perceptions and sentiments play a crucial role in the success of vaccine uptake in the community. While vaccines have proven to be the best preventive method to combat the flu, the attitude and knowledge about vaccines are a major hindrance to higher uptake in most of the countries. The yearly coverage, especially in the vulnerable groups in the population, often remains below the herd immunity level despite the Flu Awareness Campaign organized by WHO every year worldwide. This brings immense challenges to the nation's public health protection agency for strategic decision-making in controlling the flu outbreak every year. To understand the impact of public perceptions and vaccination decisions while designing optimal immunization policy, we model the individual decision-making as a two-strategy pairwise contest game, where pay-off is considered as a function of public health effort for the campaign. We use Pontryagin's maximum principle to identify the best possible strategy for public health to implement vaccination and reduce infection at a minimum cost. Our optimal analysis shows that the cost of public health initiatives is qualitatively and quantitatively different under different public perceptions and attitudes towards vaccinations. When individual risk perception evolves with vaccine uptake or disease induced death, our model demonstrates a feed-forward mechanism in the dynamics of vaccination and exhibits an increase in vaccine uptake. Using numerical simulation, we also observe that the optimal cost can be minimized by putting the effort in the beginning and later part of the outbreak rather than during the peak. It confers that public health efforts towards disseminating disease severity or actual vaccination risk might accelerate the vaccination coverage and mitigate the infection faster.

Even though vaccines against rabies are available, rabies still remains a burden killing a significant number of humans as well as domestic and wild animals in many parts of the world, including Nepal. In this study, we develop a mathematical model to describe transmission dynamics of rabies in Nepal. In particular, an indirect interspecies transmission from jackals to humans through dogs, which is relevant to the context of Nepal, is one of the novel features of our model. Our model utilizes annual dog-bite data collected from Nepal for a decade long period, allowing us to reasonably estimate parameters related to rabies transmission in Nepal. Using our model, we calculated the basic reproduction number ( 1.16 ) as well as intraspecies basic reproduction numbers of dogs ( 1.14 ) and jackals ( 0.07 ) for Nepal, and identified that the dog-related parameters are primary contributors to . Our results show that, along with dogs, jackals may also play an important role, albeit lesser extent, in the persistence of rabies in Nepal. Our model also suggests that control strategies may help reduce the prevalence significantly but the jackal vaccination may not be as effective as dog-related preventive strategies. To get deeper insight into the role of intraspecies and interspecies transmission between dog and jackal populations in the persistence of rabies, we also extended our model analysis into a wider parameter range. Interestingly, for some feasible parameters, even though rabies is theoretically controlled in each dog and jackal populations ( 1 , 1 ) if isolated, the rabies epidemic may still occur ( 1 ) due to interspecies transmission. These results may be useful to design effective prevention and control strategies for mitigating rabies burden in Nepal and other parts of the world.