Optimal Control of Epidemic Models Involving Rabies and West Nile Viruses

This research considers the application of Optimal Control theory to minimize the spread of viral infections in disease models. The population models under consideration are systems of ordinary differential equations and represent epidemics arising due to either rabies or West Nile virus. Optimal control strategies are analyzed using Pontryagin’s Maximum Principle and illustrated based upon computer simulations. The first model describes a population of raccoons and its interaction with the rabies virus, thus dividing the animals into four classes: susceptible, exposed, immune, and recovered (SEIR). The model includes a birth pulse during the spring of the year and an equation reflecting the dynamics of a potential vaccine. The vaccine equation contains a linear control variable representing the rate at which the vaccine is distributed. The goal is to minimize the number of infected raccoons and the cost of vaccine distributed. Due to linearity in the control, there is the possibility of a singular control and the generalized Legendre-Clebsch condition will be satisfied to obtain new necessary conditions for the singular case. A scenario with a limited amount of vaccine is also investigated. The system is modified to include a density-dependent death rate for each of the S, E, I, R classes, and the results of this model are compared with those of the non-density dependent model to determine how the different death rates affect control strategies. The second disease model considered describes the dynamics of mosquito, bird and human populations exposed to the West Nile virus. The mosquito and bird categories will be divided into susceptible and infected classes. In addition to these two groups, humans will also have the potential of entering the exposed, hospitalized and recovered classes. In this model, birth and death rates are assumed to be density-dependent. Two controls are applied with one control representing pesticide efforts to decrease the number of mosquitos and a second control representing prevention and repellant methods. The basic reproduction number is considered to justify the need for control. Approximations of the optimal solutions of the models are obtained using an iterative method. The numerical algorithm, Runge-Kutta of order four, is programmed in Matlab. Graphical results show the appropriate amount of control for various situations

Transmission dynamics of rabies virus in Thailand: Implications for disease control

BACKGROUND: In Thailand, rabies remains a neglected disease with authorities continuing to rely on human death statistics while ignoring the financial burden resulting from an enormous increase in post-exposure prophylaxis. Past attempts to conduct a mass dog vaccination and sterilization program have been limited to Bangkok city and have not been successful. We have used molecular epidemiology to define geographic localization of rabies virus phylogroups and their pattern of spread in Thailand. METHODS: We analyzed 239 nucleoprotein gene sequences from animal and human brain samples collected from all over Thailand between 1998 and 2002. We then reconstructed a phylogenetic tree correlating these data with geographical information. RESULTS: All sequences formed a monophyletic tree of 2 distinct phylogroups, TH1 and TH2. Three subgroups were identified in the TH1 subgroup and were distributed in the middle region of the country. Eight subgroups of TH2 viruses were identified widely distributed throughout the country overlapping the TH1 territory. There was a correlation between human-dependent transportation routes and the distribution of virus. CONCLUSION: Inter-regional migration paths of the viruses might be correlated with translocation of dogs associated with humans. Interconnecting factors between human socioeconomic and population density might determine the transmission dynamics of virus in a rural-to-urban polarity. The presence of 2 or more rabies virus groups in a location might be indicative of a gene flow, reflecting a translocation of dogs within such region and adjacent areas. Different approaches may be required for rabies control based on the homo- or heterogeneity of the virus. Areas containing homogeneous virus populations should be targeted first. Control of dog movement associated with humans is essential

Molecular Evolution and Phylogeography of Co-circulating IHNV and VHSV in Italy

Infectious haematopoietic necrosis virus (IHNV) and viral haemorrhagic septicaemia virus (VHSV) are the most important viral pathogens impacting rainbow trout farming. These viruses are persistent in Italy, where they are responsible for severe disease outbreaks (epizootics) that affect the profitability of the trout industry. Despite the importance of IHNV and VHSV, little is known about their evolution at a local scale, although this is likely to be important for virus eradication and control. To address this issue we performed a detailed molecular evolutionary and epidemiological analysis of IHNV and VHSV in trout farms from northern Italy. Full-length glycoprotein gene sequences of a selection of VHSV (n=108) and IHNV (n=89) strains were obtained. This revealed that Italian VHSV strains belong to sublineages Ia1 and Ia2 of genotype Ia and are distributed into 7 genetic clusters. In contrast, all Italian IHNV isolates fell within genogroup E, for which only a single genetic cluster was identified. More striking was that IHNV has evolved more rapidly than VHSV (mean rates of 11 and 7.3 × 10-4 nucleotide substitutions per site, per year, respectively), indicating that these viruses exhibit fundamentally different evolutionary dynamics. The time to the most recent common ancestor of both IHNV and VHSV was consistent with the first reports of these pathogens in Italy. By combining sequence data with epidemiological information it was possible to identify different patterns of virus spread among trout farms, in which adjacent facilities can be infected by either genetically similar or different viruses, and farms located in different water catchments can be infected by identical strains. Overall, these findings highlight the importance of combining molecular and epidemiological information to identify the determinants of IHN and VHS spread, and to provide data that is central to future surveillance strategies and possibly control

Regional opening strategies with commuter testing and containment of new SARS-CoV-2 variants

Background Despite the accelerating vaccination process, a large majority of the population is still susceptible to SARS-CoV-2. In addition, we face the spread of novel variants. Until we overcome the pandemic, reasonable mitigation and opening strategies are crucial to balance public health and economic interests. Methods We model the spread of SARS-CoV-2 over the German counties by a graph-SIR-type model with particular focus on commuter testing. We account for political interventions by varying contact reduction values in private and public locations such as homes, schools, workplaces, and other. We consider different levels of lockdown strictness, commuter testing strategies, or the delay of intervention implementation. We conduct numerical simulations to assess the effectiveness of the different intervention strategies after one month. The virus dynamics in the counties are initialized randomly with incidences between 75-150 weekly new cases per 100,000 inhabitants (red zones) or below 10 (green zones) and consider 25 different initial scenarios of randomly distributed red zones (between 2 and 20 % of all counties). To account for uncertainty, we consider an ensemble set of 500 Monte Carlo runs for each scenario. Results We find that the strength of the lockdown in regions with out of control virus dynamics is most important to avoid the spread into neighboring regions. With very strict lockdowns in red zones, commuter testing rates of twice a week can substantially contribute to the safety of adjacent regions. In contrast, less strict lockdowns with the same commuter testing rate quickly and substantially lead to overall higher infection dynamics. A further key contributor is the potential delay of the intervention implementation. In order to keep the spread of the virus under control, strict regional lockdowns with minimum delay and commuter testing of at least twice a week are advisable

Elucidating the phylodynamics of endemic rabies virus in eastern Africa using whole-genome sequencing

Many of the pathogens perceived to pose the greatest risk to humans are viral zoonoses, responsible for a range of emerging and endemic infectious diseases. Phylogeography is a useful tool to understand the processes that give rise to spatial patterns and drive dynamics in virus populations. Increasingly, whole-genome information is being used to uncover these patterns, but the limits of phylogenetic resolution that can be achieved with this are unclear. Here, whole-genome variation was used to uncover fine-scale population structure in endemic canine rabies virus circulating in Tanzania. This is the first whole-genome population study of rabies virus and the first comprehensive phylogenetic analysis of rabies virus in East Africa, providing important insights into rabies transmission in an endemic system. In addition, sub-continental scale patterns of population structure were identified using partial gene data and used to determine population structure at larger spatial scales in Africa. While rabies virus has a defined spatial structure at large scales, increasingly frequent levels of admixture were observed at regional and local levels. Discrete phylogeographic analysis revealed long-distance dispersal within Tanzania, which could be attributed to human-mediated movement, and we found evidence of multiple persistent, co-circulating lineages at a very local scale in a single district, despite on-going mass dog vaccination campaigns. This may reflect the wider endemic circulation of these lineages over several decades alongside increased admixture due to human-mediated introductions. These data indicate that successful rabies control in Tanzania could be established at a national level, since most dispersal appears to be restricted within the confines of country borders but some coordination with neighbouring countries may be required to limit transboundary movements. Evidence of complex patterns of rabies circulation within Tanzania necessitates the use of whole-genome sequencing to delineate finer scale population structure that can that can guide interventions, such as the spatial scale and design of dog vaccination campaigns and dog movement controls to achieve and maintain freedom from disease