Transmission dynamics and control of Sporotrichosis in domestic felines

Sporotrichosis is a subcutaneous mycosis with a global distribution, also known as “rose gardener’s disease”. Brazil is experiencing a rapid spread of the zoonotic transmission of of Sporothrix brasiliensis, the main etiological agent of this disease in this country, affecting domestic felines. Cost-effective interventions need to be developed to control this emergent public health problem. To allow for the comparison of alternative control strategies, we propose in this paper, a mathematical model representing the transmission of S. brasiliensis among cats, stratified by age and sex. Analytical properties of the model are derived and simulations show possible strategies for reducing the endemic levels of the disease in the cat population, with a positive impact on human health. The scenarios included mass treatment of infected cats and mass implementation of contact reduction practices, such as neutering. The results indicate that mass treatment can reduce substantially the disease prevalence, and this effect is potentialized when combined with neutering or other contact-reduction interventions. On the other hand, contact-reduction methods alone are not sufficient to reduce prevalence. Author summary Sporotrichosis, as a neglected tropical mycosis, has in domestic cats a very important reservoir for Sporothrix sp., its pathogen. Infected cats can easily transmit the fungus to other cats and also to humans by means of scratching and biting. Here we propose a mathematical model incorporating all forms of transmission of Sporothrix within a cat population, taking into account age and sex-related behavioral differences which can affect the transmission dynamics. The model also includes a treated compartment, which facilitates the exploration of pharmacological interventions to reduce the prevalence of the disease. We derive the next-generation matrix for the model, which allows the calculation of the disease’s basic reproduction number under different scenarios. Using the model, we explore different control scenarios involving treatment of the disease, but also the contribution of neutering of cats to the reduction of transmission through changes induced by neutering, of the cat’s social interactions.

Sporotrichosis is a neglected subcutaneous mycosis caused by species of Sporothrix sp. 2 Infections are typically caused by S. brasiliensis, S. schenckii or S. globosa [1,2]. 3 Although initially considered as a human disease, sporotrichosis was later described as a 4 zoonotic disease [3,4]. Countries with moderate to high burden include Brazil, Colombia, 5 Peru and Mexico, in the Americas; South Africa, in Africa; and China, in Asia [5][6][7]. 6 In Brazil, until the 1990's, most reports of human sporotrichosis were in adults 7 working in activities like gardening and planting. There were also less frequent 8 outbreaks linked to feline sporotrichosis, mainly involving cat owners and veterinarians 9 [8]. Since then, feline sporotrichosis has emerged as an epidemic/endemic zoonotic 10 disease of public health concern, initially in Rio de Janeiro, but nowadays, also in other 11 states. According to Gremião and colleagues, from 1998 to 2015, approximately 5,000 12 human cases were reported by the national reference center for treatment of this disease 13 [9]. The household is the main place of transmission, and cases are concentrated among 14 mid-aged housewives, students and elderly individuals [10]. The disease is strongly 15 under-reported both in animals and in humans. 16 Many animals can be infected by the fungus, including mice, rats, squirrels, cats and 17 dogs [11], but infections in domestic and stray cats, have been increasingly 18 described [7,[12][13][14]. Infected cats are the main source of infection for Sporothrix sp. in 19 regions of zoonotic transmission. Behavioral aspects of the cat, such as fights involving 20 scratching and biting, facilitate the transmission of this fungus [15,16]. 21 The strategies available to control the transmission of this fungus in the cat 22 population and reduce risk of infection in humans, are of two types. One is focused in 23 the screening and the treatment of infected individuals. The most common therapy is 24 based on long-term administration of itraconazole as a monotherapy or in association 25 with potassium iodide [17]. The second type is focused on the reduction of contact 26 between susceptible and infected cats and the control of cat population size via 27 neutering campaigns of females and males. Modeling the cost-effectiveness of these 28 strategies is important to guide the development of a sporotrichosis control plan [18,19]. 29 In this paper, we present a mathematical description of the dynamics of 30 sporotrichosis transmission in a population of domestic cats stratified by age and sex.

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The construction of the model is based on the literature on the ongoing feline 32 sporotrichosis epidemics in Rio de Janeiro [12,13,17]. At the time of this writing, we 33 found no published mathematical models of feline sporotrichosis transmission.

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The model

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The model takes the form of a system of ordinary differential equations describing the 36 population dynamics of a cat population in a large city (Fig 1). The cat population 37 December 2, 2021 2/14 was stratified in two sexes (1 = male, 2 = female), and three age classes: kitten (K) as 38 individuals less than one year of age, young (Y ) as those with 1 to 5 years, and adult 39 (A) as those with more years of age. The natural history of the disease was described by 40 three states: susceptible (S), infected (I), and treated (T ). Once infected, cats develop 41 the disease and eventually die from the infection since there is no spontaneous cure.

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Recovery, however, can be attained when cats are treated, and once cured, they return 43 to the susceptible class. The demographic dynamics of the feline population is governed by a density 45 dependent birth rate and density independent death rates. The birth rate, b(t), is given 46 The parameter C represents the environment carrying capacity for the total 48 domestic cat population, and r is the per capita fertility rate, per month. Cats die by 49 natural causes at age-dependent death rates m k , m y , m a .

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The transmission of Sporothrix between cats occurs by contacts motivated by fights 51 between males or by sexual encounters between males and females or, less likely, by 52 close contact between adults and kittens. We further assume that the young cats 53 interact more frequently than the older ones. To represent these different age and 54 sex-specific modes of transmission, we defined three types of transmission rates β K , β F 55 and β X . Transmission to kittens is governed by the expression β K = c k p k where c k is 56 the rate of contact between kittens and other cats and p k is the probability of 57 transmission through this contact. The transmission rate to young males through 58 fighting is described by the expression β F = c f p f , where c f is the fighting rate of the 59 youngsters, and p f is the probability of transmission per fight. For adult males we 60 multiply this transmission rate by l, an attenuation factor reflecting a lower fighting 61 rate in adults. The transmission during sexual encounters is sex and age-specific.

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Transmission to young males and young females are described as β X1 = c x1 p x1 and 63 β X2 = c x2 p x2 , respectively, where c xi is the rate of encounters and p xi is the probability 64 of transmission per contact. The constraints c x1 > c x2 and p x2 > p x1 imply that males 65 have more sexual contacts than females, but the probability of acquiring infection is 66 assumed to be higher in females. We further assume that older animals have less sexual 67 contacts than the youngsters, which is represented by the attenuation factor k1 for 68 males and k2 for females.The description of the parameters and the values used in the 69 numerical analysis are given in table 1.

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Once the transmission rates are defined, the next step is to define the force of infection, which is the rate of new infections in each of the 6 sub-populations defined by the 3 age classes and 2 sex classes: The following equations describe the demographic and transmission dynamics in does not confer immunity. youngsters or with adult males, the latter with lower probability. They can also acquire 84 infection from sexual contacts with young and adult females, the former more frequently 85 than the latter. As with the kittens, young infected individuals can die from other 86 causes or from sporotrichosis, or be treated and move to the T Y classes. Treated 87 animals can abandon treatment and return to the I Y compartment or recover and move 88 to the S Y compartment.
Adult cats: The equations describing the dynamics of adult cats are similar to the 90 youngster's. Adults face the same modes of exposure but at lower rates, since adults are 91 considered less active.
The full model presented above, in the absence of the disease can be reduced to the 93 following 6 equations, describing the population dynamics of the cat population and its 94 sex and age structure.  [24][25][26]. For this work, we considered 2 litters per year with 5 kittens each.

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The remaining parameters such as treatment rate (τ ), treatment abandonment rate (α), 106 cure rate (ρ), and death rate from the disease (µ) were attributed values considered 107 reasonable for the scenarios explored, as no reliable values were available for them. The demographic dynamics described in model ( 7) is shown in figure 2 using values 120 from Table 1. The age structure of the cat population at this equilibrium is 9.52% 121 kittens, 21.01% young, and 19.45% adults for each sex. Sex ratio is assumed 1:1 at birth 122 and there are no sex differences in natural death rates. 123 We derived closed form expressions for the age-structure of the feline population at 124 steady-state (eqs. 7): where δ = N 2(a k ay+a k ma+ayma+mamy) .

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This equilibrium (given by 7) is stable, as the dominant eigenvalue of the system's 127 Jacobian matrix at this equilibrium is real and negative.

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When simulating the introduction of sporotrichosis in this population, the cat 129 population is assumed to be at this steady-state age-structure, being all individuals The basic reproduction number, R 0 , measures the rate of increase of incidence upon the 133 arrival of an infected individual in a completely susceptible population. Values above 134 one indicate disease spread, while values below one indicate disease extinction. Deriving 135 an expression for R 0 is important since we can assess which parameters contribute the 136 most to transmission. One method to derive the R 0 is by computing the spectral radius 137 of the next-generation matrix of the model. Following the methodology proposed by where O k = a k + m k + µ k + τ , O y = a y + m y + µ y + τ , and O a = m a + µ a + τ , 142 being the output flow from infected compartments at each age class.

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The full matrix M was omitted due to its size. A simplified version is presented 144 instead, obtained by turning-off the treatment dynamics (τ = 0 and α = 0) and setting 145 the aging rates to zero. The justification is that aging is a slower process compared to 146 disease invasion and for the purposes of studying the instant of disease invasion, it could 147 be ignored. The simplified matrix M r (eq. 10) is: Due to the structure of M , it was not possible to derive a closed form expression for 149 R 0 , its spectral radius. But it is possible to calculate specific R 0 numerical values, by  Figure 3 shows the epidemic curve of sporotrichosis after the arrival of one infected cat 163 in the population with steady-state age structure, and R 0 = 1.227. No treatment or 164 other intervention is implemented. As the disease-free equilibrium is unstable, the 165 infected population increases towards the endemic prevalence equilibrium, of 166 approximately 70%, reached in a few years. The epidemic curve shape is typical of SIS 167 models, that is, models of diseases without cure or immunity acquisition. Since all 168 infected animals remain so until death, the observed prevalence results from the balance 169 between infection and loss to natural and disease-induced mortality. In the absence of 170 treatment, disease prevalence is greater among young cats, and among them, in males. 171 This results from the higher exposure of this group to different modes of transmission. 172 In the absence of treatment, figure 3 shows that the endemic equilibrium with 70% 173 of prevalence can be reached within a few years. The mechanisms of transmission   Table 2 shows the effect of control strategies on the prevalence of infection in 5 and 10 179 years. Important conclusions can be derived from this exercise. First, without 180 treatment, prevalence will increase to the same equilibrium despite the implementation 181 of contact reduction practices. Such practices affect the time to reach this equilibrium 182 but not its magnitude. Treatment of 50% of the infected animals can reduce the 183 prevalence to 11% (figure 4) while 70% treatment coverage can reduce to 5% in 5 years 184 without the need for further interventions. Disease elimination can be achieved by   Pharmacological treatment of cats with sporotrichosis, however, faces many 203 challenges. It is expensive and requires a long period (median=4 months) of daily 204 administration of oral antifungal drugs. This could be difficult to implement effectively 205 at large scale and specially in low-income regions [18]. We show that simpler 206 interventions such as mass neutering of male and female cats can synergistically increase 207 0.5β f 0 71% 71% C50 † β x [1,2] 0.5β f 0.5 8% 9% C50 † β x [1,2] 0.5β f 0.7 0% 0.5% C50 * , † 0.5β x [1,2] 0.5β f 0 70% 70% C50 * , † 0.5β x [1,2] 0.5β f 0.5 0% 0% C50 * , † 0.5β x [1,2] 0.5β f 0.7 0% 0%