OPINION
ANDEWELT, Judge.I.
In this vaccine action, petitioners, Ira and Claudia Gershenson, seek compensation under the National Childhood Vaccine Injury Act of 1986, as amended, 42 U.S.C. §§ 300aa-l to -34 (the Vaccine Act), for injuries their son, Adam David Gershenson (Adam), allegedly suffered as a result of a DT (diphtheria-tetanus) vaccination administered on May 19, 1984. In a February 10, 1997, order, the special master assigned to consider the petition pursuant to Section 12(d) of the Vaccine Act dismissed the petition on the ground that petitioners had failed *299to establish the facts necessary to secure compensation under the Vaccine Act. Petitioners filed a timely motion pursuant to Section 12(e)(1) seeking review by this court of the special master’s decision. For the reasons set forth below, this court affirms the special master’s decision.
II.
The Vaccine Act establishes procedures to compensate individuals for injuries or deaths resulting from the administration of specified vaccines. Section 14 of the Vaccine Act, entitled “Vaccine Injury Table,” identifies certain vaccines and specifies illnesses, disabilities, injuries, and conditions (hereinafter conditions) that have been associated with those vaccines. A petitioner can secure compensation under the Vaccine Act if, inter alia, the petitioner can demonstrate that the administration of a vaccine in fact caused or significantly aggravated a particular condition, whether or not that condition is listed in the Vaccine Injury Table. 42 U.S.C. §§ 300aa-ll(c)(l)(C)(ii) and -13(a)(1). A petitioner also can secure compensation if the petitioner can demonstrate by a preponderance of the evidence that the vaccine recipient suffers from a condition specified in the Vaccine Injury Table (Section 14(a)) and that “the first symptom or manifestation of the onset or of the significant aggravation of [the condition] occurred within the time period after vaccine administration set forth in the Vaccine Injury Table” (Section ll(c)(l)(C)(i)). If a petitioner makes such a showing, then the petitioner is entitled to compensation unless there is a preponderance of the evidence that the condition “is due to factors unrelated to the administration of the vaccine.” 42 U.S.C. § 300aa-13(a)(l)(B).
Herein, Adam suffers from encephalopathy, a condition listed in the Vaccine Injury Table and defined as “any significant acquired abnormality of, or injury to, or impairment of junction of the brain.” 42 U.S.C. § 300aa-14(b)(3)(A). Adam has exhibited speech problems, fine motor difficulties, and learning disabilities. Before the special master, petitioners contended that the administration of the May 19, 1984, DT vaccination caused or, in the alternative, significantly aggravated Adam’s encephalopathy. To support their allegations, petitioners initially submitted, inter alia, medical records, affidavits of Adam’s attending physician, and a report by a medical expert, Dr. Shlomo Shinnar. The special master found that although Dr. Shinnar’s initial report was “well drafted” and “cogent,” the report failed to establish a prima facie case for compensation under the Vaccine Act. The special master, in effect, solicited a second, supplementary report by Dr. Shinnar. After petitioners filed such a report, respondent filed a motion to dismiss. The special master granted respondent’s motion and dismissed the petition.
III.
A.
In his decision dismissing the petition, the special master describes in detail the pertinent facts contained in Adam’s medical records, including the affidavits of Adam’s attending physician and the two reports by Dr. Shinnar. The medical records show that Adam received DPT vaccinations on January 13 and March 17, 1984, and two subsequent DT boosters but that the only vaccination to which Adam had a reaction of a type and within the time period specified in the Vaccine Injury Table was the May 19, 1984, DT vaccination. The special master discusses at length only one theory of liability — that Adam suffered a significant aggravation of a pre-existing encephalopathy as a result of the May 19,1984, vaccination.
This limited focus is warranted. Petitioners did not present any scientific evidence demonstrating a causal link between the May 19 vaccination and Adam’s current condition. Hence, to prevail, petitioners had to demonstrate by a preponderance of the evidence that the first symptom or manifestation of onset or significant aggravation of Adam’s encephalopathy occurred within the time period after vaccine administration specified in the Vaccine Injury Table. For encephalopathy, the qualifying time period for the first symptom or manifestation of onset or significant aggravation is three days. On May 21, 1984, two days after receiving the DT vaccination, Adam was “cranky and irritable” and experienced a seizure. Hence, to establish *300entitlement to compensation, petitioners had to show either that Adam’s May 21, 1984, reactions represented the first symptom or manifestation of the onset of encephalopathy or alternatively that these reactions represented the first symptom or manifestation of a significant aggravation of a pre-existing encephalopathy. The special master found convincing Dr. Shinnar’s conclusion in his supplemental report that it was more likely than not that Adam’s encephalopathy predated the May 19, 1984, vaccination. Hence, this finding left petitioners with only one possible theory for recovery — that the May 19, 1984, DT vaccination significantly aggravated Adam’s pre-existing encephalopathy.
B.
In evaluating petitioners’ proof on the theory of significant aggravation, the special master applied the approach dictated in Whitecotton v. Secretary, HHS, 81 F.3d 1099 (Fed.Cir.1996). Therein, the Court of Appeals for the Federal Circuit concluded that in evaluating whether a petitioner has established a prima facie case for significant aggravation, the special master must complete the following steps:
(1) assess the person’s condition prior to administration of the vaccine, (2) assess the person’s current condition, and (3) determine if the person’s current condition constitutes a “significant aggravation” of the person’s condition prior to the vaccination within the meaning of the statute.
Id. at 1107. If after completing these steps the special master concludes that the vaccine recipient has suffered a significant aggravation, the Federal Circuit lists a fourth step to which the special master must proceed: “(4) determine whether the first symptom or manifestation of the significant aggravation occurred within the time period prescribed by the Table.” Id.
Applying the first step of the Whitecotton analysis, the special master concluded that prior to May 19, 1984, except for his motor encephalopathy, Adam’s development was normal and “Adam’s neurological problems were minor.” Applying the second step, the special master summarized Adam’s current condition, as follows:
Adam currently has learning, speech and behavioral difficulties. However, Dr. Shinnar stated that these problems, more likely than not, are not related to the vaccine. Adam also has difficulties with fine motor movements. Dr. Shinnar referred to these difficulties as “relatively minor” in his first report and as “mild” in his second report. As stated, he could not link Adam’s current motor difficulties to the 19 May 1984 DT vaccination. In an evaluation performed for the Bellmore-Merrick Central High School District, Adam was considered to have “strong reading and comprehension skills” and “excellent computational skills and problem solving skills.” His overall written language skills were considered weak. His fine motor development was listed as “below age level.” The evidence presented leads to the conclusion that Adam currently has mild neurological problems.
Gershenson v. Secretary HHS, No. 90-4005V, 1997 WL 79874, at *6 (Fed.Cl. Feb. 10,1997) (citations omitted).
The third step of the Whitecotton analysis requires a determination of “significant aggravation.” Section 33(4) of the Vaccine Act defines “significant aggravation” as “any change for the worse in a preexisting condition which results in markedly greater disability, pain, or illness accompanied by substantial deterioration of health.” To clarify the statutory phrase “markedly greater disability, pain, or illness,” the special master quoted the following statement from the House Report:
The committee has included significant aggravation in the Table in order not to exclude serious cases of illness because of possible minor events in the person’s past medical history. This provision does not include compensation for conditions which might legitimately be described as preexisting (e.g., a child with monthly seizures who, after vaccination, has seizures every three and a half weeks), but is meant to encompass serious deterioration (e.g., a child with monthly seizures who, after vaccination, has seizures on a daily basis).
H.R. Rep. 99-908, at 15-16 (1986), reprinted in 1986 U.S.C.C.A.N. 6344, 6356-57.
*301In the context of these definitions, the special master explained his conclusion that petitioners had not demonstrated a “significant aggravation” as follows:
While Adam probably had a low grade fever and definitely had a seizure within 72 hours of his 19 May 1984 DT vaccination, it was the only seizure he had, it was minor in degree, and he was alert, smiling and cooing afterwards. Adam’s mother noted very few episodes of tremors after the 21 May 1984 seizure event. As admitted by Dr. Shinnar, Adam had a pre-existing motor encephalopathy and tremors. While Adam may have experienced increased tremor activity for a few days following the 19 May 1984 DT vaccination, such increase clearly subsided within days. Simply stated, Adam had minor neurological problems before the 19 May 1984 DT vaccination, and has had minor neurological difficulties after the shot. Dr. Shinnar opined that Adam suffered a significant aggravation but failed to support his assertion with any substantive analysis. Gratuitous assertions are insufficient for the court to base an opinion upon.1
A thorough review of the records revealed no “markedly greater disability, pain, or illness.” Adam has not exhibited a “substantial deterioration of health” after the DT vaccination. The records do not reveal a “serious deterioration,” post 19 May 1984, as envisioned by the legislative history. Adam’s profile cannot be considered one of significant aggravation within the meaning of the Vaccine Act, and Program precedent.
Gershenson, 1997 WL 79874, at *6 (citations omitted) (footnote added). The special master went on to conclude that even if petitioners had demonstrated a significant aggravation of Adam’s encephalopathy, the petition must be dismissed because petitioners failed to demonstrate that Adam’s current condition is sequela to the Table injury.
IV.
The Vaccine Act grants special masters significant discretion in evaluating petitions filed thereunder and permits this court to set aside a determination by a special master only if the determination is found to be “arbitrary, capricious, an abuse of discretion, or otherwise not in accordance with law.” 42 U.S.C. § 300aa-12(e)(2)(B). “The scope of review under the ‘arbitrary and capricious’ standard is narrow and a court is not to substitute its judgment for that of the [decision maker].” Motor Vehicle Mfr. Ass’n of the United States, Inc. v. State Farm, Mut. Auto. Ins. Co., 463 U.S. 29, 43, 103 S.Ct. 2856, 2866, 77 L.Ed.2d 443 (1983). “The touchstone of [the arbitrary and capricious standard] is rationality.” Hyundai Elecs. Indus. Co. v. ITC, 899 F.2d 1204, 1209 (Fed. Cir.1990). A court must affirm the decision maker’s findings of fact if the decision maker has considered the relevant factors and has not made a clear error of judgment. See id. A court reviews findings of law on a de novo basis. See Munn v. Secretary, HHS, 970 F.2d 863, 870 (Fed.Cir.1992).
Petitioners contend that the special master erroneously applied the third step of the Whitecotton “significant aggravation” analysis when he concluded that petitioners had failed to demonstrate that Adam suffered the first symptom or manifestation of any significant aggravation of his encephalopathy within three days of the May 19, 1984, vaccination. Petitioners characterize Adam’s symptoms prior to the May 19,1984, vaccination as “ephemeral, fleeting, [and] transitory” and his symptoms after the vaccination as far more serious and as representing a significant aggravation of his pre-existing condition. At its essence, however, petitioners’ dispute amounts to a disagreement as to the weight the special master gave to certain evidence concerning Adam’s condition prior to May 19, 1984. But “[d]etermining the weight and credibility of the evidence is the special province of the trier of fact.” Inwood Labs., Inc. v. Ives Labs., Inc., 456 U.S. 844, *302856, 102 S.Ct. 2182, 2189, 72 L.Ed.2d 606 (1982). Herein, the special master considered the relevant evidence, including Dr. Shinnar’s two reports, and based on that evidence reasonably concluded that petitioners had failed to establish a “significant aggravation” of Adam’s encephalopathy after the May 19, 1984, vaccination. The record contains ample evidence to support the special master’s underlying findings, including those to the effect that Adam suffered minor neurological problems both before and after the May 19, 1984, vaccination and that Adam’s physical reactions on May 21, 1984, were not of any lasting significance. Under the standard of review set forth above, this court must affirm the special master’s determination that petitioners failed to establish a “significant aggravation.”
Petitioners argue alternatively that the special master should have granted compensation based on a comparison of Adam’s condition prior to administration of the first DPT vaccination on January 13, 1984, and Adam’s condition after administration of the third vaccination on May 19, 1984. Petitioners contend that prior to the first vaccination, Adam did not exhibit any of the significant symptoms of encephalopathy that he exhibited after May 19, 1984. Hence, petitioners argue, it is sufficient that petitioners demonstrate that Adam’s encephalopathy was significantly aggravated at some point after the first DPT vaccination.
Even if petitioners are correct that there was a significant aggravation of Adam’s condition when comparing his condition prior to the first vaccination with his condition after the third, such a showing would not support an award of compensation. As generally described above, the Vaccine Act addresses each vaccine administration separately. A petitioner can secure compensation by presenting scientific evidence that the particular administration of a covered vaccine in fact caused a particular condition. Alternatively, a petitioner may rely upon the Vaccine Injury Table and demonstrate that the first symptom or manifestation of the onset or of the significant aggravation of a condition listed therein occurred within the specified time period after the particular vaccine administration. Compensation is not available under the Vaccine Injury Table if the vaccine recipient experienced the first symptom or manifestation after vaccine administration but not within the specified time period. Hence, contrary to petitioners’ argument, a showing that Adam suffered a significant aggravation of encephalopathy at some undetermined time between the date of the first vaccination and the last day of the three-day period after the administration of the third vaccine is not sufficient to support compensation. In order to establish liability based on the Vaccine Injury Table, a petitioner must demonstrate that the first symptom or manifestation of the significant aggravation occurred within the specified time period after the administration of a covered vaccine.
V.
The court has considered the arguments presented by the parties in their briefs regarding the special master’s alternative ground for dismissing the petition — that petitioners failed to demonstrate that Adam’s current condition is sequela to the Table injury. The court has certain questions with respect to these arguments, the resolution of which would require oral argument and possibly additional briefing. Given the court’s firm conviction that the special master acted well within his discretion in dismissing the petition for the reasons discussed above, the court will not subject the parties to the time and expense of further addressing the special master’s alternative ground for dismissing the petition.2
Conclusion
For the reasons set forth above, this court affirms the special master’s February 10, *3031997, decision. The Clerk of the Court shall enter judgment accordingly.
IT IS SO ORDERED.
. In his initial report, Dr. Shinnar stated: [I]t is quite probable that Adam had a preexisting encephalopathy affecting his motor system____ According to the records, Adam had jitteriness and signs of not being a completely normal child prior to the vaccine____ He already had jitteriness before the immunization and thus clearly was at risk to have motor and cognitive impairment of the degree that he does.
. Petitioners' argument that the special master applied a standard inconsistent with the Fifth Amendment's equal protection clause appears to be limited to this alternative ground for dismissal. In any event, petitioners have not presented any reasonable argument that the special master's application of the significant aggravation requirement in the Vaccine Act raises any equal protection concerns.