Interdisciplinary Perspectives on Infectious Diseases

Volume 2018, Article ID 4373981, 16 pages

https://doi.org/10.1155/2018/4373981

## Transmission Dynamics of Bovine Anaplasmosis in a Cattle Herd

^{1}Department of Molecular Biosciences, University of Kansas, Lawrence, KS, USA^{2}Department of Ecology and Evolutionary Biology, University of Kansas, Lawrence, KS, USA

Correspondence should be addressed to Folashade B. Agusto; moc.liamg@otsugabf

Received 18 October 2017; Revised 16 January 2018; Accepted 13 March 2018; Published 2 May 2018

Academic Editor: Subhada Prasad Pani

Copyright © 2018 Taylor A. Zabel and Folashade B. Agusto. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Bovine anaplasmosis is an infectious disease of cattle caused by the obligate intercellular bacterium,* Anaplasma marginale*, and it primarily occurs in tropical and subtropical regions of the world. In this study, an age-structured deterministic model for the transmission dynamics of bovine anaplasmosis was developed; the model incorporates symptomatic and asymptomatic cattle classes. Sensitivity analysis was carried out to determine the parameters with the highest impact on the reproduction number. The dominant parameters were the bovine natural and disease-induced death rates, disease progression rate in adult cattle, the mechanical devices transmission probability and contact rates, the pathogen contamination, and decay rates on the mechanical devices. The result of the sensitivity analysis suggests that control strategies to effectively prevent/control the spread of bovine anaplasmosis should focus on these parameters according to their positive or negative effect as seen from the sensitivity index. Following the results of the sensitivity analysis, three control strategies were investigated, namely, bovine-culling, safety-control, and universal. In addition to these strategies, three effectiveness levels (low, medium, and high) were considered for each control strategy using the cumulative number of newly infected cases in both juvenile and adult cattle as measure function. The universal strategy (comprising both cattle-culling and safety-control strategies) is only marginally better at reducing the number of infected cattle compare to the safety-control strategy. This result suggests that efforts should be aimed at improving and maintaining good hygiene practices; furthermore, the added benefit of culling infected cows is only minimal and not cost-efficient.

#### 1. Introduction

Bovine anaplasmosis is an infectious disease of cattle caused by the obligate intercellular bacterium,* Anaplasma marginale*, which is of the order Rickettsiales [1]. The disease primarily occurs in tropical and subtropical regions and can provide significant issues regarding beef and dairy production-potential if left untreated [2]. Bovine anaplasmosis has been reported in every state within the United States, and it has been endemic in Mexico, Central America, South America, and the Caribbean Islands [3].* Anaplasma marginale* is host-specific, with only a few reported cases found in sheep and goats. It has only been found to infect erythrocytic cells in cattle under natural conditions.

The tick is considered the primary vector for this disease, and it acquires* A. marginale* by feeding on infected erythrocytes in cattle. It then acts as a reservoir by replicating in several tissues, but primarily in the midgut and salivary glands, with the latter of greater importance for transmission back to cattle [4].* A. marginale* is capable of vertical transmission in tick species, so it is quite an effective reservoir of the disease. Ticks go through four life stages: egg, larvae, nymph (juvenile), and adult. All stages of the tick’s life cycle require feeding on blood, although the target of feeding usually changes at each stage. Ticks usually feed on cattle during the nymph and adult stages, which is when transmission of the disease between species occurs [5]. Vaccines have been created for* A. marginale* in cattle, but they only alleviate the symptoms and do not protect cattle from persistent infection as a carrier [6].* A. marginale* vaccine has also not yet been approved by the USDA [7].

The incubation period of the infection for cattle varies depending on the dose of the infective agent and ranges from 7 to 60 days, with an average of 28 days [2]. Signs and symptoms include fever, weight loss, abortion, and potentially death (for cattle older than 2 years), although juvenile cattle less than 9 months old are usually asymptomatic. Cattle who survive exposure to* Anaplasma* become immune to the disease; however, they carry the disease for life, which is a concern for nave portions of the population [7].

Before the early 1900s, anaplasmosis was commonly confused with another disease, babesiosis, which is of the genus* Babesia* in protozoa [8]. Epidemiologically, they share similar transmission paths and appear to affect cattle at a greater symptomatic intensity as they age. Ticks, biting flies, and stable flies are the most common vectors for anaplasmosis, but mechanical transmission can also occur through fomites or surgical equipment if they are not properly sterilized [2]. Mechanical transmission is likely the only agent to spread bovine anaplasmosis in regions where the aforementioned vectors are absent.

Bovine anaplasmosis is significant enough to study using a mathematical model due to its economic impact on farmers and ranchers. When* Anaplasma* infects a previously uninfected herd, the producer can expect a 3.6% reduction in successful calving, 30% increase in the cull rate, and 30% mortality in adults showing signs [14, 15]. These rates are a significant detriment to cattlemen, and preventative strategies for the disease could be better incorporated using a target reproduction number which includes accurate geographical data and disease progression. Currently, only one known mathematical model exists to determine the spread of* A. marginale*, and it was a Bayesian Space-Time model used to determine the probability of the disease based on climate [1].

The aim of this study is to develop a more general transmission compartmental model which incorporates the juvenile and adult classes of cattle, the nymph (juvenile) and adult classes of ticks, and an environmental portion to account for mechanical transmission of the disease. Also the incorporation of an asymptomatic infectious class for the adult cattle as a complement to the symptomatic infectious class which usually contains older adult cattle is noteworthy. To the best of our knowledge, this is the first compartmental model developed to study the disease transmission. Using this model, we aim to understand the basic properties of the model, such as the model stability at the disease-free equilibrium. We will also use the model to investigate the impact of different control measures on disease spread within a cattle herd following the results obtained from sensitivity analysis.

#### 2. Material and Methods

##### 2.1. Formulation of the Model

This model was created as follows by incorporating three subgroups: cattle, tick, and mechanical modes of transmission such as syringe needles used in the administration of antibiotics (denoted here as the environment). The cattle population is divided into juvenile (cattle less than 9 months old) and adult subpopulations, and it is further divided into susceptible (), asymptomatic infectious (), symptomatic infectious (), and carrier () compartments, where for juvenile and adult subpopulations, respectively. As previously mentioned, juvenile cattle do not experience symptoms of the disease, so they do not have asymptomatic infectious subpopulation. Therefore, the total cattle population is given as The tick population was sequestered into nymph and larvae classes, each containing a susceptible class () and an infectious class (), where for nymph and larvae classes, respectively. Thus, the total tick population can be defined as Individuals move between compartments according to their disease status. The susceptible () juvenile cattle population increases via recruitment through either birth or grafting into the herd at the rate (). It is assumed that vertical transmission of the disease does not occur because it has only been shown experimentally (through third-trimester exposure) and has not been shown to occur naturally [16]. Thus, for simplicity, it is assumed that any juvenile cattle coming into the herd are too young to have been exposed to the disease. Thus, there is no inflow into the asymptomatic infectious () or carrier () juvenile cattle classes. The juvenile population is reduced through maturation at the rate () or through the natural death at the rate (). The force of infection in the juvenile cattle (i.e., the rate at which the juvenile cattle are infected) is given as where the parameters and are the probabilities that infection will occur if a juvenile cow is bitten by an infectious tick or poked by a mechanical device carrying the pathogen. The parameters and denote the tick biting rate and contact rate of the juvenile cow with a mechanical device, respectively. This assumes that each tick bite or mechanical device contact occurs at a constant rate and that this is shared among all the juvenile cattle hosts within the population. The susceptible juvenile cattle move out of the susceptible compartment at the rate () to the asymptomatic class. Thus, the equation for the susceptible juvenile cattle population is given as follows: It is assumed that juvenile cattle are not symptomatically infectious because they rarely exhibit acute symptoms [11]. As a result, death related to the disease is not incorporated into the model formulation. The population of asymptomatic infectious juvenile cattle decreases at the rate () to the carrier class. This class also maturate at the rate () and experience natural death at the rate (). Thus, the asymptomatic infectious compartment is given as The carrier class for juvenile cattle receives members of the asymptomatic infectious juvenile class and is depleted through maturation at the rate () and natural death at the rate (). It is assumed that juvenile cattle within this class remain carriers for the rest of their time as a juvenile and hold their carrier status into adulthood [7]. There is no anaplasmosis related death in this compartment due to carriers’ immunity to the pathogen. Therefore, the equation is given as The corresponding compartments for susceptible, asymptomatic infectious, and carrier for the adult cattle classes are similarly given, and the rate at which adult cattle acquire the infection (force of infection) is given as where the parameters and are the probabilities that infection will occur if an adult cow is bitten by an infectious tick or poked by a mechanical device carrying the pathogen. The parameters and denote the tick biting rate and contact rate of the adult cow with a mechanical device, respectively. We assume that a fraction of infected susceptible adult cattle move into the asymptomatic class and the remaining fraction move into the symptomatic infectious adult cattle class. The asymptomatic and symptomatic infectious adult cattle progress to the carrier class at the rates () and (), respectively. It is also assumed that asymptomatic adult cattle do not die due to the infection [11]. We further assume that , meaning that younger cattle have a faster rate of progressing from asymptomatic and symptomatic classes into the carrier class [17]. Also, it is assumed that adult cattle are much likely than juveniles to move between populations, due to their ability to be sold individually. Therefore, the adult symptomatic infectious cattle are the only compartment with disease-induced death due to anaplasmosis at the rate (). Thus, the equation for the symptomatic infectious adult cattle class is given as The population of nymph (juvenile) ticks which are susceptible to anaplasmosis () is generated through the recruit at the rate (). Ticks have been found to vertically transmit anaplasmosis to their new offspring, so is the fraction of nymphs born by healthy ticks, and the remaining fraction () represents the fraction born by infectious ticks (). Susceptible nymph ticks move to the infectious nymph compartment at a rate () given as where the parameter is the probability that infection will occur if a susceptible tick bites any infected or carrier cow. Both the susceptible and infectious nymphs mature into adult ticks at the rate and are removed by natural death at the rate (). This leads to the following system of equations for juvenile ticks:Adult tick susceptible and infectious equations are similarly determined.

The last compartment to be considered is the environmental portion of the model. The environmental compartment is composed of any mechanical device by which anaplasmosis can be spread; these include any unsterilized needles, scissors, knives, or anything else capable of collecting infected erythrocytes and placing them within another cattle host. Pathogen enters into the environment at a rate () and has a decay rate due to pathogen death at the rate (). This sets the equation for the environment as Given the above assumptions we have the following deterministic system of nonlinear differential equations for the transmission dynamics of bovine anaplasmosis:For conceptualization, a flow diagram of the bovine anaplasmosis model with juvenile and adult cattle, juvenile and adult ticks, and mechanical transmission is shown in Figure 1. The corresponding parameters and variables are described in Description of the Parameters and Variables for the Bovine Anaplasmosis Model (12).