Model development
Development of compartmental model
A compartmental model (Fig. 1) was developed comprising two transmission pathways.
Compartmental transmission model with a treated (moxidectin/sarolaner) and not-treated pathway
In each transmission pathway, a proportion (defined by the host preference) of the Aedes aegypti mosquito population is expected to feed on dogs, of which a proportion is infected with D. immitis. When a mosquito feeds on a non-infected dog, the mosquito remains uninfected. When a mosquito feeds on an infected dog, the mosquito may become infected. In the non-treated pathway, there is no medical interference with the heartworm transmission cycle, and the mosquito will be able to complete its gonotrophic cycle. In the treated transmission pathway, all or a proportion of the dogs receive a combination of moxidectin and sarolaner. It is expected that sarolaner will be 100% effective against Ae. aegypti mosquitoes for at least 28 days and that mortality will occur within 72 h [14]. Since sarolaner has no mosquito-repellent properties, the mosquito will be able to take in a full blood meal and potentially infect the dog with heartworm. Moxidectin has 100% efficacy against larval heartworm stages and therefore can prevent the establishment of a new infection in treated dogs [2, 9, 12]. While data on fluralaner and prevention of egg laying [18] are available, no combination product with efficacy against heartworm is currently available. No data on prevention of mosquito egg prevention are available for other isoxazolines. Therefore, the model focussed on a combination of sarolaner and moxidectin (Simparica Trio®).
Heartworm has a 6–9-month pre-patent period in dogs, indicating that dogs may be infected but not yet able to transmit infection during that period of time (not infectious). In the current model, infected dogs are in the pre-patent period and infectious dogs are infected with patent infections. Nevertheless, it was assumed that all non-treated dogs acquiring an infection would become infectious, and the effect of the prophylactic treatment was evaluated based on a change in the proportion of infectious dogs. Similarly, after ingesting the infected blood meal, the mosquito becomes infected, but it takes another 6 days for the mosquito to become infectious. In both the dogs and mosquitoes, an infected and infectious compartment in the respective populations was considered in the model. Mosquitoes were divided into four different categories: non-infected, infected, infectious and treated mosquitoes (who will die within 72 h) and four different age classes, which all have a maximum lifespan of 24 days. The model also included five dog categories, i.e. non-infected dogs (treated and untreated), infected dogs (treated and untreated) and infectious dogs (untreated), able to transmit the infection to mosquitoes. Age differences were not accounted for in dogs, although it was considered that dogs must be at least 6 months to become infectious. Each model etended over 61 time steps, with each time step encompassing 6 days. While it is acknowledged that the introduction of infected mosquitoes into an environment cannot be avoided [20, 21], this model considered an isolated mosquito population. The same applies to dog migration; consequently, it is possible that the modelling scenarios will evolve to an end stage where all dogs end up either infectious or remaining uninfected. This must be considered when interpreting the modelling results.
Epidemiological parameters considered in the compartmental model
After the development of the compartmental model, a list of epidemiological parameters was defined. Parameter values were obtained through a literature review in PubMed and Google Scholar and through expert opinion. An overview of the parameters considered in the model is provided in Table 1, of which three were considered as a variable throughout the model assessment. The host preference (HP) is a parameter measuring the feeding preference of the mosquitoes to different hosts.
A higher HP in dogs leads to a higher disease transmission rate in an endemic environment. Several Ae. aegypti HP studies have been published [5, 22,23,24], and the HP to dogs is reported to vary from 2 to 50%. This parameter has a high uncertainty in the model. The second parameter was the D. immitis prevalence (DP) in dogs in the Mississippi Delta (Southern US states including Georgia, Alabama, Louisiana, Mississippi, Tennessee, Arkansas), which is reported to vary from 8% in veterinary clinics [1, 25] to 34% in animal shelters [26, 27]. Concerning treatment compliance (TC), 60% of the dog owners provided prophylactic treatment for their pets at the veterinary clinic but only 40% complied with a treatment schedule as recommended by the American Heartworm Society [27].
Model sensitivity analysis
The sensitivity of the model for HP and DP was analysed while maintaining TC at a constant rate of 40%. During this sensitivity analysis, the impact of 5% incremental changes of one parameter on the shape of the curves was assessed while maintaining the other parameter at the median value described in the literature. The HP was modelled from 5 to 40% while the DP parameter was set to 21%. The DP was also modelled from 5 to 40%, while the HP was set to 25%. After this sensitivity analysis with 5% increments, incremental steps of 2% were performed for certain intervals. Finally, the sensitivity of the model to a combination of parameters was assessed. The aim of this sensitivity analysis was to assess the impact of these model parameters on the modelling results.
Modelling the impact of treatment compliance in four different epidemiological scenarios
In this study, four epidemiological scenarios were considered (as outlined in Table 2) to assess the impact of treatment compliance on the disease dynamics in dogs and the potential impact on mosquito populations.
Each scenario had a unique combination of DP and mosquito HP, which were kept constant while varying the treatment compliance from 40 to 80% with 5% incremental steps. In the first three scenarios (Table 2), an 8% heartworm DP as observed in veterinary practices in the Mississippi Delta area [1, 25] was replicated. Across the range described in the literature, three HP values were included: 25% (scenario 1; mean of the combined literature data—see Table 1); 14% (scenario 2) and 2% (scenario 3) as the lowest HP value [28]. A fourth scenario was developed in which a 34% heartworm DP in shelters in the Mississippi Delta [26, 27] was replicated. As previously suggested [24], when the dog-human ratio is high, mosquito feeding on dogs increases. Therefore, a high value for HP was used in scenario 4. Maximum value for HP according to the literature was 50%, but when considering the high uncertainty for this parameter and the fact that increasing the HP above 25% only resulted in marginal changes of the modelling results, an HP of 25% was used in scenario 4.
As 100% compliance in a dog population is not readily achieved, the effects of different prophylactic treatment compliance ratios on the potential transmission of heartworm were evaluated in these four epidemiological scenarios by comparing the proportion of infectious dogs to the proportion of the not infected dogs. Ideally, the proportion of not infected dogs is maximised as opposed to the proportion of infectious dogs, i.e. a minimum number of dogs will be newly infected and maximum number of dogs remain uninfected. First, the impact of increasing the treatment compliance from 40 to 60% was evaluated. According to the literature, 60% of the dog owners purchase the prophylactic treatment but only 40% correctly and compliantly administer the treatment they purchase. The impact of further increasing the treatment compliance was evaluated in the different scenarios.
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