Human Health and Disease Set-4

Q1. A contagious disease has basic reproduction number $R_0=5$. A vaccine with efficacy $E=0.8$ (i.e., successfully immunizes $80\%$ of vaccinated individuals) is introduced. Using the critical vaccination coverage formula $v_c=\dfrac{1-1/R_0}{E}$, what minimum percentage of the total population must be vaccinated to achieve herd immunity (round to the nearest whole percent)?

Q2. A newly emerged respiratory bacterium colonizes the nasopharynx and causes disease mainly by releasing a soluble toxin. A vaccine consisting only of the purified toxin subunit is given intramuscularly and elicits high serum IgG but little secretory IgA at the mucosal surface. Which is the most likely epidemiological outcome after mass immunization with this vaccine?

Q3. A patient infected with pathogen X has serial serum antibody titers measured: day 0 — IgM $0$, IgG $0$; day 7 — IgM $1{:}128$, IgG $1{:}16$; day 28 — IgM $1{:}16$, IgG $1{:}2048$; day 35 — IgM $1{:}4$, IgG $1{:}8192$. Which interpretation best explains these kinetics?

Q4. Assertion (A): Widespread, unnecessary prescription of broad‑spectrum antibiotics for viral respiratory infections increases the prevalence of antibiotic‑resistant bacteria in the community.
Reason (R): This occurs because antibiotics induce production of new resistance genes in human viruses, which are then transferred to bacteria.

Q5. A dengue vaccine candidate elicits strong neutralizing antibodies to DENV‑1 but only weak, subneutralizing antibodies to DENV‑2, DENV‑3 and DENV‑4. In a region where all four serotypes co‑circulate, mass vaccination with this candidate is most likely to cause which epidemiological consequence?

Q6. A novel viral disease has basic reproduction number $R_0=5$. A vaccine of efficacy $e=80\%$ (i.e. $e=0.8$) is introduced. Using the herd-immunity condition $p\cdot e \ge 1 - \frac{1}{R_0}$, what minimum fraction $p$ of the population must be vaccinated to stop sustained transmission? Assume homogeneous mixing.

Q7. In a population with disease prevalence $2\%$, a diagnostic test has sensitivity $Se=95\%$ and specificity $Sp=90\%$. Using the positive predictive value formula
$PPV=\dfrac{Se\times Prev}{Se\times Prev + (1-Sp)\times(1-Prev)}$,
approximate the PPV for a positive test result.

Q8. Two vaccines target the same enteric virus: Vaccine L is live attenuated given orally; Vaccine K is inactivated given intramuscularly. A region using high coverage of Vaccine K reports a marked drop in severe cases but ongoing transmission because many vaccinated people asymptomatically carry and shed virus. Which explanation best accounts for this observation?

Q9. Two patients with dengue have similar viral loads. Patient A: high anti-dengue IgM and low IgG (no prior dengue). Patient B: low IgM, high anti-dengue IgG and a documented dengue infection one year ago. Which patient is at higher risk of developing severe dengue (DHF/DSS) and why?

Q10. An ICU experiences recurrent outbreaks of MRSA and VRE despite strict antibiotic restriction policies. Which single measure will most rapidly reduce patient-to-patient transmission of these organisms?

Q11. Using the herd immunity threshold formula $p_c = 1 - \dfrac{1}{R_0}$, what minimum percentage of the population must be immunized to prevent sustained transmission for a disease with $R_0 = 5$?

Q12. In a town of 10,000 people, 200 individuals are living with a chronic infection at steady state. If the average duration of the disease is 10 years, estimate the annual incidence per 1000 population using $P \approx I \times D$.

Q13. In an antibody titration assay serum X shows positive reaction up to dilution $1:64$, while serum Y shows positive up to dilution $1:512$. Assuming antibody concentration is proportional to the reciprocal of the endpoint dilution, by what factor is the antibody concentration in serum Y higher than in serum X?

Q14. A diagnostic assay has sensitivity $Se=90\%$ and specificity $Sp=95\%$. In a population with disease prevalence $P=1\%$, the positive predictive value is given by $PPV=\dfrac{Se\times P}{Se\times P + (1-Sp)\times(1-P)}$. Which value is closest to the PPV for this setting?

Q15. Consider a bacterial population with initial counts $S_0=10^6$ (antibiotic-sensitive) and $R_0=10^3$ (resistant). On antibiotic-free days each day sensitive multiplies by 5 and resistant by 4; on antibiotic-treated days sensitive is reduced to $0.2$-fold per day while resistant multiplies by 6 per day. If antibiotic is administered for 3 consecutive days followed by 4 antibiotic-free days (one-week cycle), which statement is true about the populations after one week? (You may use $S_{final}=S_0\times(0.2)^3\times5^4$ and $R_{final}=R_0\times6^3\times4^4$.)