Transmission Dynamics Of Rabies Research Articles

Dynamics of Rabies Transmission Model in Human and Dog Populations with Time Delay

Rabies is a fatal zoonotic disease caused by a virus through bites or saliva of an infected animal. Dogs are the main reservoir of Rabies and are responsible for most Human cases worldwide. In this research, a delay differential equations model for assessing the effects of controls and time delay as an incubation period on the transmission dynamics of Rabies in human and dog populations is formulated and analyzed. Basic properties of the model as par theories of delay differential equations are established, and the model is well-posed mathematically and biologically. Analysis of the model shows that there is a locally and globally asymptotically stable rabies-free equilibrium whenever the epidemiological threshold (the control reproduction number,) is less than unity. Furthermore, the model has a unique endemic equilibrium point when the control reproduction number, exceeds unity. Time delay is found to have an influence on the endemicity of rabies. Treatment and Vaccination of humans and dogs, coupled with an annual crop of puppies, are imposed to curtail the spread of Rabies in the populations. Numerical experiments are conducted to illustrate the theoretical results and control strategies. Delay differential equations, Effective reproduction number, Equilibria, Rabies, Stability

Stability analysis of a solution for the fractional‐order model on rabies transmission dynamics using a fixed‐point approach

Understanding the complex phenomena of rabies transmission dynamics requires effective tools. This research leverages the capabilities of the fixed‐point approach and employs the theoretical results to solve the model and extract meaningful insights from the results. So, a nonlinear ratio‐dependent incidence rate and a non‐integer Caputo‐Fabrizio derivative have been used to develop the rabies transmission dynamic model. The study investigated the results for the existence and uniqueness of the solution of the model (i.e., unique disease‐free equilibrium point) using Geraghty‐type contraction in b‐complete b‐dislocated quasi metric space. Additionally, determine the stability conditions for the disease‐free equilibrium point that the fixed point theorem provides by examining the range of the parameters. For this, we have established definitions, lemmas, and theorems that provide the conditions for the equilibrium point and its stability conditions for the model that contribute to a deeper understanding of the spread of infection. This research underscores the essential role played by the model and fixed‐point approach in advancing knowledge concerning rabies transmission dynamics.

Molecular Characterization of Lyssaviruses Originating from Domestic and Wild Cats Provides an Insight on the Diversity of Lyssaviruses and a Risk of Rabies Transmission to Other Susceptible Mammals and Humans in South Africa.

Rabies is one of the most significant public and veterinary health problems, causing approximately 59,000 human deaths annually in the developing countries of Asia and Africa. The aetiologic agent, a viral species of the Lyssavirus genus, is highly neurotropic and has a wide host range, including terrestrial mammals and several Chiropteran species. The Lyssavirus mokola (MOKV) was first isolated in the late 1960s from organ pools of shrews (Crocidura flavescens manni) in the Mokola forest (Nigeria). To date, at least 30 MOKV isolations have been confirmed, all exclusively from Africa, with 73% from southern Africa. There is limited knowledge about the epidemiology of MOKV, and the reservoir host species is unknown. Here, we report on the molecular characterization of rabies viruses originating from both domestic and African wild cats. A partial region of the lyssavirus genome, encoding the nucleoprotein, was amplified and sequenced. Nucleotide sequence analysis demonstrated that 98% of cats were infected with both the canid and mongoose rabies virus variants, as well as a rare lyssavirus, Lyssavirus mokola, from a domestic cat from Eswatini. Furthermore, the nucleotide sequence divergence between the recently identified MOKV isolate and the historical Lyssavirus mokola isolates ranged from 6.8% to 8.3%. This study further highlights the association between the potential host species of Lyssavirus mokola and the domestic cat as an incidental host, and the important role cats may play in rabies transmission dynamics in the country. Therefore, continuous vaccination of domestic cats against rabies is crucial, even after the elimination of dog-mediated rabies, as spillover related to sylvatic rabies cycles is likely to occur.

A next-generation matrix approach using Routh–Hurwitz criterion and quadratic Lyapunov function for modeling animal rabies with infective immigrants

Rabies remains a major public health concern in many regions of the world, particularly in poorer nations. This study proposes a mathematical model for the animal rabies transmission dynamics, considering infective immigrants and vaccination as potential control measures to address this issue. The effective reproduction number (Re) was calculated by using the next-generation matrix approach. By using Routh–Hurwitz Criterion, a disease-free equilibrium point (DFE) was obtained and proved to be locally asymptotically stable if Re<1 and unstable otherwise, and also, by using the quadratic Lyapunov function DFE was determined to be globally asymptotically stable. Moreover, sensitivity analysis of the model parameters on the (Re) was performed using the normalized forward sensitivity index method. For simulation analysis, the numerical analysis was performed with the help of the MATLAB software. The simulated data results revealed that the increase in vaccination rate and decreasing infective immigrants will reduce the spread of the decrease, which was depicted graphically.

Mathematical Analysis of Rabies Transmission Dynamics and Control

Rabies is a dangerous disease that kills many people than any other communicable disease and yet it is underrated. This results from the little knowledge on the myriad ways of transmission of the virus. A deterministic model is proposed to study the spread of the rabies virus in both domestic dogs (Canis familiaries) and humans (Homo sapiens). We elaborately studied the spread of the rabies virus from dogs to-dogs, dogs-to-humans and for the first time, humans-to-humans. Sensitivity analysis is performed to determine the influence of various parameters on the transmission of rabies the most. The rabies-free equilibrium and the endemic equilibrium points were determined and the conditions under which the equilibria are stable were also obtained. The stability conditions provide the conditions under which the disease will persist or get to be eradicated. Numerical solutions of the model were obtained using the ode45 routine in MATLAB. The study demonstrated that for rabies to be eradicated, the rate at which dogs are recruited must be decreased, culling of exposed and infected dogs should be increased and mass vaccination of the dog population should be targeted.

Rabies transmission in the Arctic: An agent-based model reveals the effects of broad-scale movement strategies on contact risk between Arctic foxes

Arctic rabies is an ongoing threat to human populations and domestic animals inpolar regions, where Arctic foxes (Vulpes lagopus) are the main reservoir hosts. Human-driven changes in resource availability are shifting the distribution of Arctic foxes and these changes may affect the risk of rabies transmission and spread. Our understanding of the effects of broad-scale movement strategies in Arctic foxes and spatial distribution of resources on contact patterns among Arctic foxes, and their consequences on the dynamics of rabies epidemiology remains limited, in part, due to the difficulty of obtaining contact data from such remote and expansive regions. In this perspective, we built a spatially explicit agent-based model coupled with hidden Markov models to explore how Arctic fox movement behavior, combined with Arctic fox population density, resource availability and rabies transmission dynamics, affects the risk of infectious contact between Arctic foxes across heterogeneous landscapes. The model was parameterized using a combination of unique field data collected in the Canadian High Arctic and published studies from other Arctic regions. A sensitivity analysis was performed to assess the effects of multiple model input parameters on contact rates among Arctic foxes. Our results showed that cumulative contact rates per fox were driven by predictors related to rabies transmission dynamics and fox carrying capacity, while unique contact rates per fox and unique infectious contact rates per rabid fox were best predicted by parameters associated with rabies transmission dynamics, fox movement behavior, and fox carrying capacity. Ultimately, our study provides new insights into the ecological drivers of rabies transmission and may inspire further research on modelling cost-effective rabies prevention strategies in the Arctic.

Understanding Rabies Transmission Dynamics and Control in the Three Administrative Districts of Davao City Using a Modified SEIV Model

Despite the control programs of the City Veterinarian’s Office (CVO), rabies is still geographically widespread across Davao City. Hence, a modified SEIV model incorporating different control strategies and adding population compartments focusing on reported rabies cases was formulated to understand dog rabies transmission dynamics. The model was fitted to the datasets of CVO from 2006–2020, such as the cumulative monthly positive rabies cases and the number of examined positive rabies samples in Talomo, Buhangin, and Poblacion districts. Results showed that the Talomo district had the highest rabies transmission rate but the lowest castration rate. On the other hand, the Poblacion district had the highest impounding rate and castration rate but the lowest birth and vaccination rate. Finally, the Buhangin district had the highest birth rate and vaccination rate but the lowest impounding rate and transmission rate. Sensitivity analysis (SA) was performed on over 10,000 samples of parameter space by the LHS method to obtain PRCC values. Results of the SA revealed that dog vaccination had a significantly strong influence among many interventions in mitigating rabies transmission – consistently in Talomo, Poblacion, and Buhangin districts. The results obtained in this study support the CVO’s ongoing mass canine rabies vaccination campaign in the city as a method of rabies control. Despite this, dog population control strategies (i.e. castration and impounding) must still be implemented in addition to intensifying vaccination strategy, as the birth rate also strongly contributes to increasing rabies transmission. Through the model and data fitting approaches, this study has provided information on the level of control measures implemented in three districts and can also be utilized to develop future rabies epidemiological models in Davao City and other locations.

The effects of geographical distributions of buildings and roads on the spatiotemporal spread of canine rabies: An individual-based modeling study.

Rabies is a fatal disease that has been a serious health concern, especially in developing countries. Although rabies is preventable by vaccination, the spread still occurs sporadically in many countries, including Thailand. Geographical structures, habitats, and behaviors of host populations are essential factors that may result in an enormous impact on the mechanism of propagation and persistence of the disease. To investigate the role of geographical structures on the transmission dynamics of canine rabies, we developed a stochastic individual-based model that integrates the exact configuration of buildings and roads. In our model, the spatial distribution of dogs was estimated based on the distribution of buildings, with roads considered to facilitate dog movement. Two contrasting areas with high- and low-risk of rabies transmission in Thailand, namely, Hatyai and Tepha districts, were chosen as study sites. Our modeling results indicated that the distinct geographical structures of buildings and roads in Hatyai and Tepha could contribute to the difference in the rabies transmission dynamics in these two areas. The high density of buildings and roads in Hatyai could facilitate more rabies transmission. We also investigated the impacts of rabies intervention, including reducing the dog population, restricting owned dog movement, and dog vaccination on the spread of canine rabies in these two areas. We found that reducing the dog population alone might not be sufficient for preventing rabies transmission in the high-risk area. Owned dog confinement could reduce more the likelihood of rabies transmission. Finally, a higher vaccination coverage may be required for controlling rabies transmission in the high-risk area compared to the low-risk area.

Roles of traditional medicine and traditional healers for rabies prevention and potential impacts on post-exposure prophylaxis: A literature review.

IntroductionGlobally, traditional medicine is widely used to treat a variety of injuries and illnesses, including dog bites, and exposures that are risky for rabies. However, efficacy of most traditional remedies used for rabies prevention or treatment has not been demonstrated in controlled trials or proven in community-based surveys.MethodsSix databases were searched including the terms rabies, traditional treatment, traditional remedy, traditional therapy, traditional medicine, and medicinal treatment to review traditional remedies used in the prevention and treatment of rabies. In addition, published literature of rabies transmission dynamics was used to estimate statistical likelihood of dog bite victims developing rabies to provide clarity as to why traditional healers have a high apparent success rate when preventing death from rabies in victims bitten by suspected rabid dogs.ResultsLiterature review yielded 50 articles, including three controlled experiments, that described use of traditional remedies for rabies prevention and treatment. Traditional remedies for rabies ranged from plant- or animal-based products to spiritual rituals; however, only a few controlled mice trials were conducted, and none of these trials demonstrated efficacy in preventing or treating rabies. Risk of dying from rabies after a bite from a dog with unknown rabies status is low, 1.90% (0.05%-29.60%). Therefore, traditional healers had a 98.10% (70.40%-99.95%) apparent success rate in preventing death from suspected rabid dog bites despite inefficaciousness of herbal remedies.ConclusionThere was no universal plant species or route of administration that was consistently used for rabies prevention or treatment across countries. No traditional remedy was efficacious in the prevention or treatment of rabies in randomized controlled experiments. Understanding the cultural context under which traditional remedies are used may facilitate collaboration of traditional healers with the modern medical system to ensure timely and appropriate use of proven therapies for prevention and clinical management of rabies.

Reservoir dynamics of rabies in south-east Tanzania and the roles of cross-species transmission and domestic dog vaccination.

Understanding the role of different species in the transmission of multi-host pathogens, such as rabies virus, is vital for effective control strategies. Across most of sub-Saharan Africa domestic dogs Canis familiaris are considered the reservoir for rabies, but the role of wildlife has been long debated. Here we explore the multi-host transmission dynamics of rabies across south-east Tanzania.Between January 2011 and July 2019, data on probable rabies cases were collected in the regions of Lindi and Mtwara. Hospital records of animal-bite patients presenting to healthcare facilities were used as sentinels for animal contact tracing. The timing, location and species of probable rabid animals were used to reconstruct transmission trees to infer who infected whom and the relative frequencies of within- and between-species transmission.During the study, 688 probable human rabies exposures were identified, resulting in 47 deaths. Of these exposures, 389 were from domestic dogs (56.5%) and 262 from jackals (38.1%). Over the same period, 549 probable animal rabies cases were traced: 303 in domestic dogs (55.2%) and 221 in jackals (40.3%), with the remainder in domestic cats and other wildlife species.Although dog-to-dog transmission was most commonly inferred (40.5% of transmission events), a third of inferred events involved wildlife-to-wildlife transmission (32.6%), and evidence suggested some sustained transmission chains within jackal populations.A steady decline in probable rabies cases in both humans and animals coincided with the implementation of widespread domestic dog vaccination during the first 6 years of the study. Following the lapse of this program, dog rabies cases began to increase in one of the northernmost districts. Synthesis and applications. In south-east Tanzania, despite a relatively high incidence of rabies in wildlife and evidence of wildlife-to-wildlife transmission, domestic dogs remain essential to the reservoir of infection. Continued dog vaccination alongside improved surveillance would allow a fuller understanding of the role of wildlife in maintaining transmission in this area. Nonetheless, dog vaccination clearly suppressed rabies in both domestic dog and wildlife populations, reducing both public health and conservation risks and, if sustained, has potential to eliminate rabies from this region.

Ecology of Arctic rabies: 60 years of disease surveillance in the warming climate of northern Canada.

Rabies occurs throughout the Arctic, representing an ongoing public health concern for residents of northern communities. The Arctic fox (Vulpes lagopus) is the main reservoir of the Arctic rabies virus variant, yet little is known about the epidemiology of Arctic rabies, such as the ecological mechanisms driving where and when epizootics in fox populations occur. In this study, we provide the first portrait of the spatio-temporal spread of rabies across northern Canada. We also explore the impact of seasonal and multiannual dynamics in Arctic fox populations and climatic factors on rabies transmission dynamics. We analysed data on rabies cases collected through passive surveillance systems in the Yukon, Northwest Territories, Nunavut, Nunavik and Labrador from 1953 to 2014. In addition, we analysed a large and unique database of trapped foxes tested for rabies in the Northwest Territories and Nunavut from 1974 to 1984 as part of active surveillance studies. Rabies cases occurred in all Arctic regions of Canada and were relatively synchronous among foxes and dogs (Canis familiaris). This study highlights the spread of Arctic rabies virus variant across northern Canada, with contrasting rabies dynamics between different yet connected areas. Population fluctuations of Arctic fox populations could drive rabies transmission dynamics in a complex way across northern Canada. Furthermore, this study suggests different impacts of climate and sea ice cover on the onset of rabies epizootics in northern Canada. These results lay the groundwork for the development of epidemiological models to better predict the spatio-temporal dynamics of rabies occurrence in both wild and domestic carnivores, leading to better estimates of human exposure and transmission risk.

Temporal and spatial distributions of animal and human rabies cases during 2012 and 2018, in Tunisia.

Rabies is one of the most important zoonosis in Tunisia. In the last 6 years, a dramatic increase in the number of cases in animals had raised concern about the transmission dynamics of rabies and the effectiveness of established control measures. For a better understanding of the epidemiological features of rabies in Tunisia, data on animal and human rabies cases and post‐exposure prophylaxis (PEP) protocol, for the period from 2012 to 2018, were analysed to describe the spatial and the temporal distributions of the disease and to guide targeted rabies control measures. Thus, the analysed data have shown that 2,642 animal and 25 human rabies cases were recorded between 2012 and 2018; only few case numbers were reported in wildlife. Time‐related distribution showed that the incidence of dog rabies increases over the period of study, from 24,8/100,000 dog population in 2012 to 35,2/100,000 dog population in 2018. Dog seems to be the main reservoir of rabies as it accounted for more than 59% of the animal confirmed cases and the source for more than 80% of the human confirmed cases. Geographical distribution of animal rabies cases revealed the presence of clusters in the North and the Center of Tunisia; only a little number of animal cases were reported in the South. In contrast, the overall human rabies incidence was 0.03 per 100,000 population, during the period of the study. We have found that the incidence of human rabies increases by 13.6% from 2012 to 2015 and drops steadily by 23.41% over the second period (2015 to 2018). A high number of PEP was recorded during the 7‐year period, with an average of 360 PEP per 100,000 inhabitants per year. Spatial analysis revealed the presence of clusters of PEP in the Northern and Central governorates. The present study pointed out the need to review the control strategy of rabies in Tunisia and conduct further studies on dog population to provide the basis for a new and efficacious policy of interventions and control program for rabies.

Analysis of time delayed Rabies model in human and dog populations with controls

Rabies is a fatal zoonotic disease caused by a virus through bites or saliva of an infected animal. Dogs are the main reservoir of rabies and responsible for most cases in humans worldwide. In this article, a delay differential equations model for assessing the effects of controls and time delay as incubation period on the transmission dynamics of rabies in human and dog populations is formulated and analyzed. Analysis from the model show that there is a locally and globally asymptotic stable disease-free equilibrium whenever a certain epidemiological threshold, the control reproduction number mathcal {R}_v, is less than unity. Furthermore, the model has a unique endemic equilibrium when mathcal {R}_v exceed unity which is also locally and globally asymptotically stable for all delays. Time delay is found to have influence on the endemicity of rabies. Vaccination of humans and dogs coupled with annual crop of puppies are imposed to curtail the spread of rabies in the populations. Sensitivity analysis on the number of infected humans and dogs revealed that increasing dog vaccination rate and decreasing annual birth of puppies are more effective in human populations. However in dog populations, the vaccination and birth control of puppies, have equal effective measures for rabies control. Numerical experiments are conducted to illustrate the theoretical results and control strategies.

Modeling transmission dynamics of rabies in Nepal.

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 () as well as intraspecies basic reproduction numbers of dogs () and jackals () 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 (, ) if isolated, the rabies epidemic may still occur () 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.

Model Simulation for the Spread of Rabies in Sarawak, Malaysia

There is a growing concern over the ongoing rabies epidemic in Sarawak that has remain unresolved ever since the outbreak began in July 2017. As of today, there has been 18 positive human rabies cases reported, which includes 17 fatalities, and one survivor who is now on life support after a severe neurological complications. Subsequently, the death rate now stands at approximately 94%. This paper is a preliminary report on the simulation of rabies transmission dynamics in Sarawak. At present, research is still lacking on the disease dynamics of rabies in Malaysia particularly in the state of Sarawak. We propose here a deterministic, compartmental model with SEIRS framework to fit actual data on the number of human infected rabies cases in Sarawak from June 2017 to January 2019. The simulation predicts that rabies in Sarawak will persist even with the current outbreak management and control efforts. Further, sensitivity analysis showed that dog vaccination rate is the most influential parameter and the basic reproduction number is estimated to be higher than 1. Henceforth, there is a need to increase the access to dog vaccines especially in remote rural areas with lack of health facilities. Our findings also suggest that controlling dog births could prevent the spread of rabies from perpetuating in the state. Neutering or using other fertility control methods would reduce the input of new susceptible domestic dogs into the population while Trap-Neuter-Vaccinate-Release (TNVR) method can be implemented to control new births of free-roaming strays. In summary, increasing the coverage of dog vaccination and reducing the number newborn dogs would be the more effective strategies to manage the current rabies outbreak in Sarawak.

Modeling the Transmission Dynamics of Rabies for Dog, Chinese Ferret Badger and Human Interactions in Zhejiang Province, China.

Human rabies is one of the major public health problems in China with an average of 1977 cases per year. It is estimated that 95% of these human rabies cases are due to dog bites. In recent years, the number of wildlife-associated human rabies cases has increased, particularly in the southeast and northeast regions of mainland China. Chinese ferret badgers (CFBs) are one of the most popular wildlife animals which are distributed mostly in the southeast region of China. Human cases caused by rabid CFB were first recorded in Huzhou, Zhejiang Province, in 1994. From 1996 to 2004, more than 30 human cases were caused by CFB bites in Zhejiang Province. In this paper, based on the reported data of the human rabies caused by both dogs and CFB in Zhejiang Province, we propose a multi-host zoonotic model for the dog-CFB-human transmission of rabies. We first evaluate the basic reproduction number [Formula: see text] discuss the stability of the disease-free equilibrium, and study persistence of the disease. Then we use our model to fit the reported data in Zhejiang Province from 2004 to 2017 and forecast the trend of human or livestock rabies. Finally by carrying out sensitivity analysis of the basic reproduction number in terms of parameters, we find that the transmission between dogs and CFB, the quantity of dogs, and the vaccination rate of dogs play important roles in the transmission of rabies. Our study suggests that rabies control and prevention strategies should include enhancing public education and awareness about rabies, increasing dog vaccination rate, reducing the dog and CFB interactions, and avoiding CFB bites or contact.

Rabies epidemic model with uncertainty in parameters: crisp and fuzzy approaches

A deterministic mathematical model is formulated to investigate the transmission dynamics of rabies. In particular, we investigate the effects of vaccination, carrying capacity and the transmission rate on the rabies epidemics and allow for uncertainty in the parameters. We perform crisp and fuzzy approaches. We find that, in the case of crisp parameters, rabies epidemics may be interrupted when the carrying capacity and the transmission rate are not high. Our findings suggest that limiting the growth of dog population and reducing the potential contact between susceptible and infectious dogs may aid in interrupting rabies epidemics. We extend the work by considering a fuzzy carrying capacity and allow for low, medium, and high level of carrying capacity. The result confirms the results obtained by using crisp carrying capacity, that is, when the carrying capacity is not too high, the vaccination could confine the disease effectively.

Spatiotemporal epidemic models for rabies among animals.

Rabies is a serious concern to public health and wildlife management worldwide. Over the last three decades, various mathematical models have been proposed to study the transmission dynamics of rabies. In this paper we provide a mini-review on some reaction-diffusion models describing the spatial spread of rabies among animals. More specifically, we introduce the susceptible-exposed-infectious models for the spatial transmission of rabies among foxes (Murray et al., 1986), the spatiotemporal epidemic model for rabies among raccoons (Neilan and Lenhart, 2011), the diffusive rabies model for skunk and bat interactions (Bonchering et al., 2012), and the reaction-diffusion model for rabies among dogs (Zhang et al., 2012). Numerical simulations on the spatiotemporal dynamics of these models from these papers are presented.

On the Spread of Rabies in Humans and Dogs

Rabies is a fatal disease in dogs as well as in humans. In this work we present a simple model representing rabies transmission dynamics in human and dog populations. Mathematical analysis based on the basic reproduction number, $\mathcal{R}_0$, which is the average number of new infective individuals produced by one infective individual introduced into a completely susceptible population, is presented. It is observed that the disease-free equilibrium is globally asymptotically stable if $\mathcal{R}_0 1$. A nonstandard finite difference scheme that replicates the dynamics of the continuous model is proposed. Numerical tests to support the theoretical analysis are provided.

Analysis and dynamically consistent nonstandard discretization for a rabies model in humans and dogs

Rabies is a fatal disease in dogs as well as in humans. A possible model to represent rabies transmission dynamics in human and dog populations is presented. The next generation matrix operator is used to determine the threshold parameter \(\mathcal {R}_0\), that is the average number of new infective individuals produced by one infective individual introduced into a completely susceptible population. If \(\mathcal {R}_0 1\). A nonstandard finite difference scheme that replicates the dynamics of the continuous model is proposed. Numerical tests to support the theoretical analysis are provided.